neurons, viscose fluids, freshwater polyp hydra— and … · neurons, viscose fluids, freshwater...

Steffen StaabUniversity of [email protected]

T r e n d s & C o n t r o v e r s i e s

72 1094-7167/03/$17.00 © 2003 IEEE IEEE INTELLIGENT SYSTEMS

The Meaning of Self-Organization inComputingFrancis Heylighen and Carlos Gershenson,Free University of Brussels

The first user-friendly PCs in the 1980s and the Web inthe 1990s unleashed a wave of innovation that seems tohave drowned in complexity and confusion. Softwaredevelopers are scrambling to keep their systems up to datewith all the new standards, plug-ins, and extensions.

Although we constantly hear announcements of spectacu-lar innovations, few seem to reach maturity. The problemis, developers tend to underestimate the task environment’scomplexity: Today’s information systems depend on somany modules, data sources, network connections, andinput and output devices that predicting or controlling theirinteractions has become impossible. The result is softwarefull of bugs, corrupted data, security holes, viruses, andother potentially catastrophic side effects. Moreover, sys-tems have become so complex that the human mind can no

Neurons, Viscose Fluids,Freshwater Polyp Hydra—and Self-Organizing InformationSystems

I first encountered the principle ofself-organization in my last year of highschool, when our teacher had us give aseries of talks on a high-level view of theworks of Ilya Prigogine, Humberto Mat-urana, Hermann Haken, and others. Mytalk happened to be on self-organiza-tion in the neocortex, where an orches-tration of neurons seemed to find theirplaces and functions without any con-ductor (also see Nigel Shadbolt’s article“Beyond Brittleness, IEEE IntelligentSystems, Nov./Dec. 2002,). The principallesson we learned then—that complex,functioning systems might develop bot-tom-up rather than top-down—was veryintriguing. At the end of the 1980s,however, these principles—developedsince the beginning of the 1960s—appeared to be dormant in engineering.With some exciting exceptions (forexample, genetic and ant algorithms orartificial life), they had not really movedinto mainstream computer science.

Now, however, the idea of self-organi-zation is more vivid than ever in com-puter science, becoming apparent indiverse fields relevant for intelligent sys-tems, such as fields that are concernedwith ad hoc assembly when

• The sum of the individual, rather thana centralized authority, determinesthe system shape

• It involves resources that no singleauthority can provide

• Authority can no longer remain cen-tralized in applications such as knowl-edge management

• Centralized orchestration becomestoo unwieldy to enforce—such as inapplications with larger numbers ofautonomous agents

• Mobile environments enforce ad hoccoordination

Correspondingly, our discussion herecontributes to these different observa-tions and needs. Gary Flake, David Pen-nock, and Daniel Fain reflect on how theWeb is shaped from the bottom up.David De Roure discusses how he viewse-science, requiring a grid of intelligentcomponents interacting toward agreater understanding of the science atheart. Karl Aberer applies self-organiza-tion to peer-to-peer systems that lendthemselves to information systems thatdo not work with centralized authority,such as knowledge management forskilled knowledge workers. Wei-Min

Shen elaborates on how self-organiza-tion might be exploited in software orhardware agents. Eventually, currentmobile applications often defy central-ized control, as Olivier Dousse andPatrick Thiran explain. Before we start,Francis Heylighen and Carlos Gershen-son briefly introduces the principles ofself-organization that the other contrib-utors exploit.

Now, are you still wondering aboutviscose fluids and hydra? These weresome topics of our classes then. A sur-prising fact about the former (and incontrast to less viscose fluids such aswater under “normal” circumstances) isthat if you cautiously warm a flat dish ofviscose fluid underneath, you willobserve that the heat does not propa-gate chaotically. Rather, inside the fluid,macroscopical structures (rolling cylin-ders) show up that remain stable (unlessyou overheat) and transport warmth tothe top. You will find out about the lat-ter in the remainder of this department.And you will see by these examples thatthe transfer of self-organization from adescriptive approach in the sciences toan engineering approach in intelligentsystems now appears imminent.

Published by the IEEE Computer Society

longer learn or remember all proceduresneeded to use them. Mix in the constantchange in hardware, software, protocols,data, and user expectations, and you have arecipe for chaos.

This complexity bottleneck not only cre-ates stress and confusion, it also severelylimits the speed of further progress. Thenumber of possible interactions growsexponentially with the number of compo-nents. Because components and theircapacity increase exponentially, overallcomplexity increases superexponentially.Developers’ cognitive capacity obviouslyincreases much more slowly, so it lags fur-ther and further. This means that large pro-jects, such as the Semantic Web, will eitherget endlessly delayed or end up withunworkable products.

We need a radically different approachto overcome this bottleneck. One step for-ward is IBM’s autonomic-computing initia-tive (www.research.ibm.com/autonomic).IBM researchers envision systems thatfunction largely independently from theirhuman supervisors, adapting, correcting,and repairing themselves whenever a prob-lem occurs. IBM uses the metaphor of theautonomic nervous system, which runs ourbody for us without conscious intervention.How they hope to achieve this is less clear.Their suggestions seem to center aroundmodels of feedback, adaptation, and con-trol first proposed in the 1950s. Althoughwe applaud this “cybernetic” approach tocomputing, we believe an even more radi-cal vision is needed: self-organization.

Self-organizing systemsA self-organizing system not only regu-

lates or adapts its behavior, it also createsits own organization. In that respect it dif-fers fundamentally from our present sys-tems, which designers create. We defineorganization as structure with function.Structure means that a system’s compo-nents are arranged in a particular order. Itrequires both connections that integrate theparts into a whole and separations that dif-ferentiate subsystems to avoid interference.Function means that this structure fulfills apurpose.

Designers obviously create systems for aparticular purpose. A watch’s function is totell time, a database’s is to store data, and aspreadsheet’s is to calculate. But naturalsystems have functions, too. Roots exist toextract nutrients from the soil, stomachs to

digest, and eyes to see. In the 18th century,the sophisticated structures and functionsof living organisms led William Paley toargue that they must have an intelligentdesigner—God. We now know that nodesigner is necessary to produce such intel-ligent organization; natural systems appearto have emerged and evolved without out-side intervention or programming. Yet, theyare incredibly robust, flexible, and adap-tive, tackling problems far more complexthan any computer system.1,2

Self-organization then means that afunctional structure appears and maintainsitself spontaneously. The control needed toachieve this must be distributed over allparticipating components. If it were cen-tralized in a subsystem or module, thenyou could in principle remove this module,and the system would lose its organization.Remove the processor chip from a computerand it becomes useless. Take any smallpiece of tissue from a living brain (as com-monly happens during brain surgery), andthe brain will continue to function more orless as it did before.

Self-organizing systems are intrinsicallyrobust—they can withstand various errors,perturbations, or even partial destruction.They will repair or correct most damagethemselves, returning to their initial state.When the damage becomes too great, theirfunction will start to deteriorate, but “grace-fully,” without sudden breakdown. Theywill adapt their organization to environ-mental changes, learning new tricks tocope with unforeseen problems. Out ofchaos, they will generate order. Seeminglyrandom perturbations will help—ratherthan hinder—them in achieving an everbetter organization.

This description might sound too goodto be true. Yet, plenty of systems exist thatexhibit these qualities. We find them tovarying degrees in organisms, brains,ecosystems, societies, markets, swarms,and dissipative chemical systems. Comput-ing also offers a few examples. Scientistsdesigned the TCP/IP protocol that under-lies the Internet to be robust enough tomaintain communication during a nuclearwar. It achieves this by cutting up messagesinto packets that are sent through differentroutes and reassembling them at the desti-nation—resending those that get lost ifnecessary. Neural networks that havelearned to recognize patterns, such as hand-writing, still produce pretty good results

when part of their nodes and links aredeleted. Genetic algorithms solve complexproblems by evolving subsequent genera-tions of candidate solutions.3 They mutate,recombine, and reproduce only the best ones,until they find a good-enough solution.

Mechanisms of self-organization

These computing examples show thepower of self-organization but only in lim-ited contexts, where both the componentsand their desired functions are well defined.How can we apply self-organization to anenvironment as complex and diverse as theWeb, a corporate intranet, or even a desktopcomputer with its ever-changing softwareand data configuration? To achieve self-organization on that scale, we need a muchdeeper insight into how it works.2 Let usreturn to the systems we find in nature andanalyze their mechanisms in terms generalenough to apply to complex informationsystems.

A self-organizing system consists ofmany interacting components, such as mol-ecules, neurons, insects, or people. Thesystem is dynamic; the components areconstantly changing state relative to eachother. But owing to mutual dependency,changes are not arbitrary. Some relativestates are “preferable,” in that they will bereinforced or stabilized, while others areinhibited or eliminated. For example, twomolecules that approach each other in theright geometrical configuration mightreact—forming a chemical bond and thus alarger molecule—or simply drift past eachother. Two people discussing might eitherfind common ground and establish a work-ing relation, or leave in disagreement.

Changes are initially local. Componentsonly interact with their immediate neigh-bors. They are virtually independent ofcomponents farther away. But self-organi-zation is often defined as global orderemerging from local interactions. We canpicture this process as follows. Two inter-acting components pass through variousconfigurations until they find one that ismutually satisfactory—that is, stable. Wemight say that they have adapted to eachother and now fit together. To achieveglobal order, this fit must propagate to theother components. For example, two mole-cules that have bonded might be joined bya third one, and a fourth one, and so on,eventually forming a macroscopic crystal.

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Two people who discover a common interestmight start talking about it to others and endup founding a club, political movement, orcompany. If the components are interchange-able, such as molecules of the same chemicalsubstance, the resulting structure will beregular, like a crystal. If each componentshas its own, individual characteristics, suchas a species in an ecosystem, the structurewill be more complex. Each componentmust fit in its own niche within the environ-ment formed by others.

This propagation of fit is typically self-reinforcing—additional components joinever more quickly. This occurs because alarger assembly exerts a stronger attractionon the remaining independent components,offering more niches in which they can fit.This positive feedback produces an explo-sive growth or reproduction of the assem-bly. Growth only stops when the resourcesare exhausted—that is, when all compo-nents that could be fit into the assemblyhave been fit. This might happen becausethe remaining components are too differentto fit in this type of configuration orbecause they were assimilated into a rivalassembly. For example, a chess club willstop growing when the remaining people intown are either not interested in chess oralready belong to a different chess club.

Once the assembly stabilizes, feedbackbecomes mostly negative. This means thatit will counteract any loss of organization.Self-maintenance has become its implicitpurpose, and each component will performits function toward this goal. For example,the rules and individual relationships in anestablished club make it difficult for mem-bers to switch to a rival club. The assemblyas a whole, however, can still interact withother assemblies but at a different level. Forexample, two chess clubs might engage inan interclub tournament. So, assembliesformed from individual components startacting like higher-level components. Thesecan in turn self-organize into even higher-level components, the way chess clubs canassemble into a federation. This processcontinues recursively, for as long as thereare components to interact with, generatingever higher levels of complexity.

The self-organized system is stable orrobust, but this does not mean static or rigid.When the environment changes, the compo-nents that directly interact with it must adapttheir states until they are fit again. This fitwill propagate inward, until the whole assem-

bly is adapted to the new situation. Thus,the system constantly reorganizes, mutu-ally balancing the different internal andexternal pressures for change, while tryingto maintain its essential organization. Themore perturbations it encounters, the largerthe variety of different configurations itwill explore, and therefore the “better” theeventual solution it settles in. The cyber-neticist Heinz von Foerster called this prin-ciple “order from noise.” The thermody-namicist Ilya Prigogine4 called it “orderthrough fluctuations.”

The future of computing?How can we apply this general vision to

information systems? Imagine variouscomponents—hardware and software mod-ules, files, Web sites, interfaces, and users.They all interact by exchanging informa-tion. Assume that neighboring componentscan mutually adapt. By sending messagesback and forth, they negotiate until theyachieve a common “understanding” inwhich they both can settle. But coordina-tion does not stop there; it propagates backand forth between all components, creatinga globally stable order. Any change, such asa newly introduced component or localbreakdown, will restart the negotiationprocess with its immediate neighbors. Itseffects will ripple further through theneighborhood until this perturbation is alsoabsorbed and the system is back to equilib-rium. Of course, we will need to overcomeimportant hurdles before we can achievethis vision. Most obviously, we must createa universal protocol for interaction thatsupports unrestricted self-organization.

This all sounds very general and abstract.Can we think of more concrete applications?A well-known example of self-organizationis the way ants lay trails of pheromonesbetween various sources of food. Initially,ants explore and leave pheromones ran-domly, but good trails leading to richsources through quick routes are reinforcedthrough positive feedback, while poor trailseventually evaporate. Thus, food sourcesget organized into a dense, efficientnetwork of foraging paths. Marco Dorigo, apioneer in the domain of ant algorithms, hasshown how a similar mechanism can tacklevarious computing problems, including thenotorious traveling salesman problem.5 Animportant application is the routing of mes-sages along the nodes and links of a com-munication network. Efficient routes are

reinforced, less efficient ones abandoned.The resulting organization adapts in realtime. If routes become congested, their pri-ority is immediately downgraded and thealgorithm explores new routes.

One of us has applied a similar idea tothe Web’s hyperlink organization.6,7 Ourlearning Web algorithms reinforce paths oflinks that users travel frequently, eventuallyreplacing them with a single link. Whileusers decide locally which link to explorenext, the effects of their choice propagatethroughout the Web. This should eventuallylead to a global order—Web pages that fittogether, in the sense that one page is veryrelevant for users of the other, are linkeddirectly. Thus, documents that cover thesame subject get clustered. A higher-leveldocument can now represent this cluster orassembly, presenting an index or summaryfor the subject. Higher-level componentsthemselves become linked and clustered incategories and further into supercategories.Eventually, the Web as a whole might self-organize into an efficient, hierarchicallystructured network of associations that adaptscontinuously to newly introduced documents,changes in user demand, and so on.

With some minor variations, we couldapply this scheme to the construction ofshared ontologies, clustering similar con-cepts into categories and linking the cate-gories that are most strongly associated.Object-oriented programming also couldprofit from this approach, with objects mutu-ally negotiating message-passing protocolsand spontaneously assembling into higher-level objects. For example, the Swarm pro-gramming environment (www.swarm.org)supports the latter. The same goes for ubiqui-tous computing or intelligent environments.Various devices—such as refrigerators, ther-mostats, or phones—connected to a networkcan learn to mutually coordinate their activi-ties, thus minimizing the user’s burden.

The possibilities seem endless. Is this thefuture of computing? Only time can tell.

References

1. K. Kelly, Out of Control: The New Biology ofMachines, Addison-Wesley, 1994.

2. F. Heylighen, “The Science of Self-Organi-zation and Adaptivity,” The Encyclopedia ofLife Support Systems, Eolss Publishers, 2003.

3. J.H. Holland, Adaptation in Natural and Arti-ficial Systems, MIT Press, 1992.

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4. I. Prigogine and I. Stengers, Order Out ofChaos, Bantam Books, 1984.

5. E. Bonabeau, M. Dorigo, and G. Theraulaz,Swarm Intelligence, Oxford Univ. Press, 1998.

6. J. Bollen and F. Heylighen, “Algorithms forthe Self-Organization of Distributed, Multi-User Networks,” Proc. Cybernetics and Sys-tems 96, Austrian Soc. for Cybernetics, 1996,pp. 911–916.

7. F. Heylighen and F.J. Bollen, “Hebbian Algo-rithms for a Digital Library RecommendationSystem,” Proc. 2002 Int’l. Conf. Parallel Pro-cessing Workshops, IEEE CS Press, 2002.

The Self-Organized Web: The Yin to the SemanticWeb’s Yang

Gary William Flake, David M. Pennock,and Daniel C. Fain, Overture Services

Assigning superlatives to the Web iseasy: it’s massive, it’s dynamic, it’s decen-tralized—it’s unlike anything else in theworld. But one of the Web’s most amazingattributes is that it is arguably the largestself-organized artifact in existence. Everyday millions of Web publishers add, delete,move, and change their pages and links, yetwhat results is far from random or haphaz-ard. Rather, from these millions of uncoor-dinated decisions emerges a startling num-ber of regularities and patterns. The Webprogrammer’s task—whether working onsearch, collaborative filtering, data mining,e-commerce, or scientific analysis—is toimprove these structures to make the Webmore digestible to users. This goal comple-ments the Semantic Web’s goal: to havehumans help make the Web more digestiblefor computers. Exploiting the self-organized

Web will improve tomorrow’s algorithms;manually adding computer-friendly anno-tations to the Semantic Web will help today’sless-sophisticated algorithms cope.

Self-organization and the Web Although Web authors’ choices world-

wide are largely uncoordinated, they areanything but uncorrelated. Unlike any (non-degenerate) random graph, the Web graph’slarge-scale structure has a “bow tie” organi-zation that contains four distinct regions: astrongly connected core, an originationbow, a termination bow, and disconnectedislands.1 In the Web’s core, hyperlinks arerelatively sparse, yet they collectively pos-sess small-world properties, forming manyredundant and relatively short paths betweenmost pages.2 When sampled across the Web,inbound and outbound hyperlink distribu-tions follow a clear power law distributionthat resembles distributions in biology.3

Viewed on a small scale, simple and smallbipartite subgraphs are a signature of topicalWeb communities’ formation.4

We also see clear structural self-organi-zation at intermediate levels. For example,when aggregating only over a specific typeof pages (for example, movie, newspaper,photography, or university homepages),hyperlink distributions shift from a strictpower law to a unimodal form, not unlike thechange in the biomass distribution whenaggregated over a single species instead ofall species. A generative Web growth modelwith only one free parameter explains thisunusual hyperlink distribution property withremarkable simplicity and accuracy.5 More-over, a simple definitionthat a Web com-munity is a collection in which each memberis predominately hyperlinked to other com-munity membershas yielded an efficient

procedure for identifying self-organized Webcommunities. Empirically, these communi-ties are topically and textually focused, eventhough the identification procedure uses onlyhyperlinks.6 Figure 1 depicts a few of theWeb’s self-organizing properties.

Web data miningGiven the Web’s size and decentralization,

it seems almost a paradox that pure hyper-link data mining algorithms work. Nearly allcurrent hyperlink methods strongly overlapwith methods pioneered in graph clusteringand where the problems are typically NP-hard.7 The Web’s enormous size suggeststhat it would be a more difficult domain, yetthe reality is somewhat different.

Two popular Web data mining algorithms,HITS8 (hypertext induced topic search) andPageRank,9 have shown considerable suc-cess when coupled with text retrieval. Bothmethods attempt to capture Web pages’importance by recursively analyzing howpages hyperlink to each other. The Page-Rank algorithm can be roughly interpretedas simulating how a random walker wouldtraverse the Web graph over forward links ifalso allowed to teleport to other pages withsome small probability. After completion,PageRank assigns to a Web page a scorethat is about equal to the probability that therandom walker will visit that page. Intu-itively, the PageRank score is similar to therecursive definition that a Web page isimportant if other important pages link to it.

PageRank clearly improves text retrieval,as evidenced by the popularity of Google(the inventors’ search engine9), whichlargely attributes its competitive edge toPageRank. What is truly interesting, how-ever, is that PageRank is an existence proofthat:


Figure 1. Self-organized Web structures of various scales: (a) the large-scale bow tie; (b) intermediate-scale Web communities; (c)small-scale bipartite community cores.

(a) (b) (c)

1. The Web is well behaved in that worst-case complexity results are far too pes-simistic.

2. The Web’s self-organization can beused to improve Web search and datamining.

Consider the first point. PageRank istechnically equivalent to a power methodestimation of the maximal eigenvector of asimple transformation of the Web graph’sadjacency matrix. Linear algebra shows thatthe power method converges at a rate relatedto the ratio of the first two eigenvalues of thematrix being used. Simply put, the moresimilar the first two eigenvalues, the slowerthe procedure’s convergence rate.

Many matrices are ill suited for powermethod procedures because of the conver-gence properties. However, in the Web’scase, the power law distribution on inboundhyperlinks nearly guarantees that the Webwill never possess such pathologiesbecause Web pages with many other pageslinking to them are exceedingly rare and insome sense very competitive with eachother. In other words, the Web doesn’tseem to like having two maximal eigenval-ues of nearly equal value.10

As for the second point, think of Page-Rank as something of a collective votingscheme, where pages not only vote for eachother but also vote to determine how manyvotes each should have. The votes arelabeled, in a sense, with anchor text; a stringmatch in a referring page’s anchor text isweighed more heavily than a match in thetarget page itself. The links and labels fromthe Open Directory Project (ODP)—a volun-tary effort to categorize Web sites—are themost important. In such a collective, distrib-uted framework, it isn’t at all obvious that theaggregate vote would add any value to theretrieval task. But, when coupled with textretrieval, PageRank is remarkably adept atproducing the “correct” answer when cor-rectness and popularity are highly correlated.

Top-down, bottom-up, andlessons learned

Recently, many have championed theSemantic Web11 as a means to improveinformation retrieval on the Web. Propo-nents argue that the Web is ill suited in itscurrent form for automated processingbecause the information is unstructured tothe point that semantics are nearly impossi-ble for machines to infer. In the Semantic

Web, authors will use a markup languageto annotate data with semantic labels somachines can identify content meaning anduse rules for manipulating semantic infor-mation appropriately. In a best-case sce-nario, the markup language will be nearlycomplete and agreeable, and used consis-tently by Web authors. Authoring toolsmight generate the markups implicitly, butsuch markups will need to make sensealongside those the authors add manually.Implicit markup is easy to envision forproduct catalogs, but semantically markingup long passages of text—magazine arti-cles, for example—could be daunting.

Realistically, Semantic Web advocatesunderstand that some holes and inconsis-tencies in the markup language areinevitable and that author adoption rates

and proficiencies will be heterogeneous.Witness the failure of Xanadu,12 a hyper-text framework arguably superior toHTML/HTTP. It failed partly because itsrules and guarantees imposed too great aburden on authors. A simple example ofWeb authors’ natural laziness is the preva-lence of rasterized text unmarked by ALTtext tags. Some of Xanadu’s ideas wererevived in less-demanding forms. Forexample, instead of keeping an up-to-dateset of backlinks at the target page, Webbacklinks are retained in search engines.But relaxing enforcement in the SemanticWeb will lead to another form of self-orga-nized entity, even if more structured thantoday’s Web. To add to the confusion, aslong as there is search spam, a contingentsupplying false information through meta-data will exist. This underscores the valueof objective third-party annotation, evenwhen minimal, such as ODP.

A complementary best-case scenarioenvisions Web algorithms intelligentenough to infer semantics from the current,nonannotated, self-organized Web, withoutthe aid of semantic markups. Informationextraction tools are progressing, makinginroads on problems such as parsingresumes and finding contact information,but today’s best algorithms still fall woe-fully short of people’s capability to extractmeaning from the Web. We have onlyscratched the surface of the self-organizedWeb’s potential. Future data mining meth-ods will use efficient algorithms optimizedfor the expected case of Web data (ratherthan the worst case or random case), usepredictable Web properties to reduce prob-lem sizes and input dimensionality, andhave performance bounds consistent withgenerative Web growth models. With thesealgorithms, search engines will be able tocluster and classify the entire Web alongmultiple dimensions (topic, type, and genre,for example). The most advanced searchengines and autonomous Web agents willbe able to use richer forms of metadata ifand when a new markup structure isadopted.

But for the foreseeable future, efforts toleverage the self-organized Web will com-plement efforts to build the Semantic Web.Both open up opportunities for innovativenew algorithms—data mining on one hand,symbolic inference on the other. Wherethese efforts meet, tools will arise for vastlyimproved search, filtering, personalization,economic efficiency, and scientific under-standing of the social forces and trendsreflected in the Web. We believe that theWeb’s properties—structure, content, andexplicit or inferred metadata—will con-tinue to evolve in a decentralized and self-organized way. Users will benefit most ifwork on creating the Semantic Web co-evolves with work on tools for data-drivenanalysis of the self-organized Web.

References

1. A. Broder et al., “Graph Structure in the Web:Experiments and Models,” Proc. 9th WorldWide Web Conf. (WWW9), Elsevier, 2000.

2. D.J. Watts and S.H. Strogatz, “CollectiveDynamics of ‘Small World’Networks,” Nature,vol. 393, no. 6684, June 1998, pp. 440–442.

3. A.L. Barabási and R. Albert, “Emergence ofScaling in Random Networks,” Science, vol.286, no. 5439, Oct. 1999, pp. 509–512.


Users will benefit

most if work on creating the

Semantic Web coevolves with

work on tools for

data-driven analysis of the

self-organized Web.

4. R. Kumar et al., “Trawling the Web forEmerging Cyber-communities,” Proc. 8thWorld Wide Web Conf. (WWW8), Elsevier,1999.

5. D.M. Pennock et al., “Winners Don’t Take All:Characterizing the Competition for Links onthe Web,” Proc. Nat’l Academy of Sciences,vol. 99, no. 8, Apr. 2002, pp. 5207–5211.

6. G.W. Flake et al., “Self-organization of theWeb and Identification of Communities,” Com-puter, vol. 35, no. 3, Mar. 2002, pp. 66–71.

7. M.R. Garey and D.S. Johnson, Computersand Intractability: A Guide to the Theory ofNP-Completeness, W.H. Freeman, 1979.

8. J. Kleinberg, “Authoritative Sources in aHyperlinked Environment,” J. ACM, vol. 46,no. 5, Sept. 1999, pp. 604–632.

9. S. Brin and L. Page, “The Anatomy of aLarge-Scale Hypertextual Web SearchEngine,” Proc. 7th World Wide Web Conf.(WWW7), Elsevier, 1998.

10. F. Chung and L. Lu, “The Average Distancesin Random Graphs with Given ExpectedDegrees,” Proc. Nat’l Academy of Sciences,vol. 99, no. 25, Dec. 2002, pp. 15,879–15,882.

11. T. Berners-Lee, J. Hendler, and O. Lassila,“The Semantic Web,” Scientific American,vol. 284, no. 5, May 2001, pp. 34–43.

12. T.H. Nelson, “Xanalogical Structure, NeededNow More Than Ever: Parallel Documents,Deep Links to Content, Deep Versioning, andDeep Re-use,” ACM Computing Surveys, vol.31, no. 4, Dec. 1999, pp. 194–225.

On Self-Organization and theSemantic GridDavid De Roure, University of Southampton

The term grid computing has previouslysuggested a world of networked supercom-puters, Beowulf clusters, fat pipes, andpetabyte storage. But now the “grid prob-lem” is defined as “resource sharing andcoordinated problem solving in dynamic,multi-institutional virtual organizations.”1

High-performance computing might oncehave focused on accelerating scientificcomputation, but contemporary grid com-puting is also about accelerating the scien-tific process. It is the infrastructure of e-science, and indeed e-engineering, andpotentially e-many-other-things too.

The notion of “the Grid” is an analogy to

the electricity power grid—you can pluginto the common interface to tap its com-putational power. The middleware thatimplements it, de facto the Globus Toolkit,hides the heterogeneity of the diverse com-putational resources. In principle, the mid-dleware makes it easier to cross not onlyoperating system and version boundaries butalso organizational boundaries. This is sig-nificant because the computational powercan come from different power generators.

Grid infrastructure and applications aretypically service oriented, and in the lastyear or so, the middleware effort has fallenin line with the prevailing movement toWeb services to enjoy a degree of industry-standard interoperability. This takes theform of the Open Grid Services Architec-ture,2 an enhanced Web services modelcreated to meet the grid community’s spe-cialist requirements.

A huge number of grid projects exist,fueled by national funding programs suchas the UK’s US$500 million e-Science pro-gram, which reaches across a spectrum ofresearch disciplines. Every time we embarkon a new project, we would like to reuseand repurpose the data, services, softwarecomponents, resources, and indeed knowl-edge from our own scientific communitiesand others’ previous projects. So, where weonce needed the Grid to hide computationalresources’ heterogeneity, the new Gridproblem is hiding the heterogeneity of thebits and pieces needed to quickly and easilyassemble new projects, or even new grids.The vision is a generically usable e-scienceinfrastructure, comprising easily deployedcomponents whose utility transcends theirimmediate application. Our goal is theautomated construction of the desired ser-vices, adapted to the current requirementsand circumstances. This is the self-organi-zation we seek—the assembly and adapta-tion of Grid services.

The Semantic GridUnderlying any form of automated com-

position we need an infrastructure where allresources, including services and workflows,are adequately described in a machineprocessable form; that is, knowledge isexplicit—Semantic Web technologies pro-vide the infrastructure. This has led us tothe Semantic Grid,3 where we apply thosetechnologies in grid-computing develop-ments, from grid infrastructure machinery(such as the Globus Toolkit’s grid services)

to grid applications. “Semantics” permeatesthe full vertical extent of the Grid and is notjust a semantic layer on top; it is semanticsin, on, and for the Grid. Some of theseSemantic Web technologies are ready forimmediate deployment (the ResourceDescription Framework tools, for example),while others are on the research agenda.Realizing the Semantic Grid vision involvesbridging two rather disjoint communities,each with its own standards process. At oneend is the World Wide Web Consortium andthe Semantic Web research community; atthe other is the Global Grid Forum andGrid research community. GGF now has aSemantic Grid Research Group, charteredto help the Grid developers apply estab-lished metadata technologies while track-ing, for example, the evolution of OWL(the Web Ontology Language) and associ-ated tools.

The Semantic Grid is a complex andlarge-scale piece of machinery. Someaspects of the system are beyond central-ized control. Looking inside will let us seethe opportunities for self-organization.

The Semantic Grid’s computational fab-ric comprises interconnected processors—perhaps with some dedicated networkinglocally—that are globally interconnectedthrough the Internet. The Internet is unde-niably a large-scale decentralized system.In fact, the Internet is an adaptive system,comprising simple components with localknowledge that together provide a globalnetwork service that copes with networkcomponent failure. Above this, we mightconsider the Web’s machinery to be a large-scale decentralized system, but I disputethe scale of distributed processing—a typi-cal Web transaction involves just a server, abrowser, and a proxy or two. The evolutionof the Web infrastructure’s deployment,however, is an example of a self-organizingsystem. The large-scale decentralized sys-tem in the Web is actually its content, theglobal linking infrastructure that has gener-ated much analysis in recent years. TheSemantic Web gives us a much richer wayto describe the associations within Webcontent, transcending the limited expres-siveness the simple navigational linkingmodel provides. As the decentralized meta-data grows, it is interlinked by the resourcesit describes. This is a critical basis forSemantic Web content’s self-organization.

The Semantic Web assumes a service-oriented model, such as Web services or


Grid services, or agents, which are produc-ers, consumers, and brokers of services. Weare beginning to see the application ofSemantic Web technologies within that infra-structure, in multiagent systems, and throughSemantic Web services. This emerging,semantically rich service-oriented infrastruc-ture is an important large-scale, decentral-ized system in our Semantic Grid. It’s thelast to emerge, but it fits in the middle—it isthe semantic middleware.

Opportunities for self-organization

These three ingredients—communicationor computation, semantic middleware, andsemantic content—provide opportunitiesfor self-organization that support the visionof the self-organizing Semantic Grid.

The first is at the level of job submissionand control over the computational fabricof large clusters or supercomputers, and theaggregations of these into grids. A singleparallel computation can be predictable,with a known shape and extent, or dynamicand evolving. When you run an entire usercommunity on that fabric, with myriad,diverse computations accessing distributeddata, you have what is essentially a hugeoptimization problem. With job schedulingcurrently managed by individual sched-ulers, we should enjoy self-organization’sbenefits as we scale up. We would surelybenefit from the fault tolerance that self-organization could provide because com-ponent failure is inevitable in systems ofthis scale.

The second opportunity is at the servicelevel because this level has some homo-geneity and scale and is where the manygrids are beginning to meet to form theGrid. The organization task here is discov-ering and binding the services together tomeet the requirements. This might behighly engineered, with prescribed work-flows, for example. It might also be highlydynamic, with opportunistic use of servicesthat have been instantiated and local data.The picture bears some relationship withpeer-to-peer. Again, we have a massivedistributed optimization problem.

The third opportunity relates to theinformation and knowledge that is the“stuff” of e-science—the computations andexperiments’ inputs and outcomes, and thedescriptions of the processes that createdthem. Here we have scale, and we need tojoin the information with the processes that

consume and generate it. Science is a col-laborative process, and we might also viewmatching information to individuals as aprocess of organization.

Reality intrudesBut is the Grid really a large-scale dis-

tributed system? Anticipation of distributedprocessing on a massive scale has moti-vated its development. But currently manydisjoint grids exist, just as many networksonce existed that eventually combined intothe internetwork known as the Internet. Wecan foresee the current grid islands simi-larly aggregating into an “intergrid,” knownas the Grid. Surely this kind of aggregationwas the reason for the Web’s clichéd“exponential growth.” Once the Gridaggregates, we will have a large-scale dis-

tributed system with highly engineered,complex infrastructure machinery. Internetor Web nodes forward packets and docu-ments; the Grid’s nodes will do that andsome computation. We do not yet knowhow much intergrid coupling will occur atthe lower level (Web couples using theHTTP protocol) versus at a higher level (aswith the integration of scientific services).

Of course, the notion of systems that canself-diagnose and self-repair is compelling,and the Grid community has recentlyshown some enthusiasm for autonomiccomputing,4 drawing inspiration from theautonomic nervous system. We are alreadyachieving some degree of fault tolerance byengineering an infrastructure that monitorsand repairs faults. This touches a key point:Do we need a self-organizing system, orcan we engineer the necessary behavior?To put it another way, who needs slimemold when shell scripts will do? While our

computing infrastructure is organized as anaggregation of managed resources, we canachieve a degree of centralization in con-trol and coordination of the function ofthose resources. We are not obliged to bedecentralized. Self-organization is attrac-tive when it offers some optimization with-out risk—as Web caching does—but canwe deploy it in a world where code is hand-crafted for performance?

Of course, this vision assumes we have aSemantic Grid and shares some of theusual Semantic Web obstacles. It requires ametadata-enabled world, but where will themetadata come from? Except where classi-fications and domain-specific ontologiesalready exist, the Grid community mustagree on the schema and ontologies. Whatwill motivate this effort? I would claim thatwith the Semantic Grid, we have a fightingchance. The Grid community is a coherent,organized, enthusiastic community withreal application drivers and couldgenuinely benefit from semantic interoper-ability. It will also stress Semantic Webtechnologies because it demands an extra-ordinary degree of automated interoper-ability, such as ontology mapping, andlarge-scale performance.

The vision also assumes masses of com-putational power, but we can be somewhatconfident in this trend. Apart from morepowerful processors, we will simply havemore processors, emphasizing the issues ofscale. Consider the provocative amorphouscomputing example of embedding proces-sors in materials (for example, “concreteby the megaflop”), which, incidentally,insists on self-organization (see www.swiss.ai.mit.edu/projects/amorphous).Notice also the broad similarity betweenthe service-oriented adaptive SemanticGrid vision and the service-oriented adap-tive ubiquitous-computing vision. Severalservices must come together locally tomeet our needs on a distributed architecturewhere devices come and go.

Back to the futureLet’s push that autonomous processing a

stage further and combine self-organizingservices with self-organizing informationand knowledge. Our self-organizingSemantic Grid is now a constantly evolvingorganism, with ongoing, autonomous pro-cessing rather than on-demand processing.This evolving, organic Grid can generatenew processes and new knowledge. Con-


The Grid community is a coherent,

organized, enthusiastic

community with real application

drivers and could genuinely

benefit from semantic

interoperability.

sider, for example, a genetic approach tocreating new workflows to solve a scien-tific problem. Imagine watching thisautonomous, self-organizing SemanticGrid in action, visualizing the informationflows in the system. It might be very simi-lar to watching a bunch of e-scientists atwork. But surely individual scientists bringproblem-solving insight to the process?Maybe, but on the macro scale is theremuch difference? Remember, this is Gridcomputing, and we have the facility forlarge-scale processing. Additionally, peo-ple are slow. The DNA microarray hascaused a revolution by permitting massesof parallel experimentation, as has combi-natorial chemistry. Experimentation in silico is another such shift. Some Gridapplications can and will absorb as muchcomputational power as is available to pro-duce better or faster results, but we willalso be able to do more parallel exper-iments more quickly, monitoring and steer-ing them dynamically.

I’ve shown that we have some opportuni-ties for self-organization, but the currentinfrastructure might not be ready for it.And I’ve shown a vision of a self-organiz-ing Semantic Grid that serves the scientistby assembling services on the fly and couldeven embark autonomously on scientificdiscovery. The challenge is to determinewhich parts of our self-organization arehighly engineered, perhaps through theproactive behavior of agents, and when tolet go.

References

1. I. Foster, C. Kesselman, and S. Tuecke, “TheAnatomy of the Grid: Enabling Scalable Vir-tual Organizations.” Int’l J. SupercomputerApplications, vol. 15, no. 3, 2001.

2. I. Foster et al., “The Physiology of the Grid:An Open Grid Services Architecture for Dis-tributed Systems Integration,” Open Grid Ser-vice Infrastructure WG, Global Grid Forum,22 June 2002; www.globus.org.

3. D. De Roure, N. Jennings, and N. Shadbolt,“The Semantic Grid: A Future e-ScienceInfrastructure,” Grid Computing: Making TheGlobal Infrastructure a Reality, F. Berman,A.J.G. Hey, and G. Fox eds., John Wiley &Sons, 2003, pp. 437–470; www.semanticgrid.org.

4. IBM, An Architectural Blueprint for Auto-nomic Computing,Apr. 2003, www.ibm.com/autonomic.

Self-Organization and P2PSystemsKarl Aberer, Swiss Federal Institute ofTechnology, Lausanne

The Internet has enabled the provision ofglobal-scale distributed applications. Suchapplications’ providers include some of thebest-known Internet companies, such aseBay, Yahoo, and Google. These applica-tions’ centralized client-server architectureleads to heavy resource consumption at theserver sites; for example, Google is operat-ing a workstation cluster of about 15,000Linux servers. From this observation, youmight conclude that providing a global-scale application necessarily implies amajor development, infrastructure, andadministration investment. However, a newclass of applications—initially developed tohelp users share information, such as musicfiles, recipes, and so on—shows that thisconclusion is inaccurate. These systems arecommonly called peer-to-peer file-sharingsystems. The main service they provide isresource location, which lets users searchfor resources based on a resource identifier.Napster was the first and most famous pro-ponent of this new class of systems, whichessentially exploit the principle of resourcesharing. The Internet makes plenty ofresources available at its “edges”—that is,at end-user computers. By integrating thesecomputers into a larger system, user com-munities can build applications at a globalscale without experiencing the investmentbottleneck mentioned earlier.

In Napster’s case, the coupling ofresources was facilitated through a centraldirectory server, where users registeredtheir music files and could search for otherusers’ files. After locating the files, userscould download them directly from otherpeers—therefore, we consider Napster aP2P system. Through this scheme, Napsterexploited several resources the communityof cooperating peers made available. Themost notable of these was storage andbandwidth for handling large music files;less obviously, users provided knowledgewhen annotating files during registration.Finally, music file ownership was a keyfactor in Napster’s fast adoption, but it alsocaused the music industry to react stronglyto potential copyright infringement. Nap-ster was eventually shut down, which waspossible because the system depended on acentral directory server.

Another music file-sharing system,Gnutella, then entered the stage. AlthoughGnutella provides essentially the samefunctionality as Napster, it uses no centraldirectory server. Search requests are simplyflooded over the network. Thus Gnutellaavoids any distinguished component in itsarchitecture: It is a fully decentralized sys-tem. Because Gnutella avoids any singlepoint of failure, attacks (legal, economic,or malicious) are very difficult.

Self-organization in P2Psystems

Gnutella’s lack of central coordinationmakes you wonder how any useful behavioroccurs. Unsurprisingly, this is where self-organization comes into play. But whatexactly does it mean, in Gnutella’s case, tobe self-organizing? To shed light on thisquestion, we must more closely understandhow Gnutella operates. In fact, the Gnutellaprotocol has two components. The first is anetwork maintenance protocol, which con-structs and maintains a network of Gnutellapeers called the overlay network. The otheris a search protocol, which helps userslocate resources in the overlay network. Byusing the network maintenance protocol, apeer discovers new peers in the network byflooding “ping” messages. Other peersrespond with “pong” messages announcingtheir network participation. From theresponses, the first peer selects certain peersand establishes direct network links withthem. In Gnutella, each peer maintains afixed number of active links. So, using thenetwork maintenance protocol, the networkcontinuously changes its structure.

This process is clearly self-organizing inthe sense of Francis Heylighen’s characteri-zation: “The basic mechanism underlyingself-organization is the noise-driven varia-tion, which explores different regions in asystem’s state space until it enters an attrac-tor.”1 The state space consists of all directedoverlay network graphs with constant out-degree, and the noise results from the ran-dom time of node joins, communicationlatency, and autonomous local decisions onconnectivity. Many recent experimentalinvestigations have attempted to identifythe attractor—that is, the resulting overlaynetwork’s graph structure. Researchershave found two main properties.2

First, the network has a small diameter,which ensures that a message-floodingapproach for searching a resource in a net-


work works with a relatively low time tolife (approximately seven network hops).

Second, the overlay network’s nodedegrees follow a power law distribution. So, a few peers have many incoming links,whereas most peers have only a few suchlinks. Researchers have discovered powerlaw distributions of node degrees for manytypes of networks, such as the World WideWeb, citation networks, or genetic networks.The property is credited to the network con-struction mechanism—the networks contin-uously grow, and new nodes preferentiallyattach to already well-connected nodes.3

Both of these properties affect a Gnutellanetwork’s performance. This is apparent forthe first property. For the second property,we can observe that the highly connectednodes are typically those that provide highbandwidth and have high availability. Thesenodes naturally form a backbone that (pre-sumably) optimizes resource consumption,although we can’t say whether such effectswere expected during the Gnutella proto-col’s design.

Despite the similarity of the networkmaintenance and search protocols inGnutella, the two protocols serve funda-mentally different purposes and are inde-pendent. The network maintenance proto-col implements a self-organization processthat changes the system state—that is, theoverlay network’s structure. The searchprotocol implements a distributed algorithmfor searching the overlay network. OtherGnutella-style networks have more effi-cient search protocols that reduce the highmessage load for search, which limits thetotal system throughput. Examples are therandom-walker model4 and the percolationsearch model.5 These approaches assume aGnutella-style network; that is, they supporta combination of the Gnutella group mem-bership protocol and an improved searchprotocol. These observations illustrate that afully decentralized P2P resource locationsystem comprises two orthogonal compo-nents that must complement each other:

• Network construction is a self-organizingprocess that exhibits adaptive behaviorwith respect to resource consumption.

• Search is a randomized, distributed algo-rithm that exploits the emergent networkstructure.

However, this observation applies so faronly to unstructured P2P systems, such as

Gnutella, which you can characterize bythe fact that peers are unaware of the kindsof resources neighboring peers maintain.So, peers are fairly independent and can act autonomously, which facilitates self-organization. As a drawback, searches areforwarded “blindly.” This results in the typ-ical high message loads because to locate aresource, all peers in the network musteventually be contacted, setting aside possi-ble optimizations using replication.

Unstructured to structured P2P systems

To reduce the message bandwidth duringsearches in P2P systems, researchers havedeveloped several decentralized data accessschemes, commonly called structured P2Psystems. You can characterize them by

peers’ specialization to specific kinds ofresources and the use of routing tables toselectively forward search requests to peersthat are more likely to provide a requestedresource. Frequently, such systems arebased on variations of prefix routing. Prefixrouting is based on an underlying logicaltrie structure from which each peer ran-domly selects a trie node. This selectiondefines the resources the peer holds andserves as the peer’s identifier. Additionally,peers maintain routing tables with links toother peers along the path from the trie rootto their own trie nodes, so the system canforward search requests not pertaining toone peer’s trie node to other peers associ-ated with other trie branches. This organi-zation enables answering search requestswith a logarithmic number of messages inthe number of peers participating in thenetwork. This improvement in search per-formance from linear to logarithmic cost

comes at a price: peers are no longer inde-pendent. When peers update their data orwhen the network changes its structure—as when nodes join the network, for exam-ple—multiple peers are affected. Specifi-cally, updates to the routing tables becomenecessary. So, structured P2P networksrequire distributed algorithms to maintainthe peer network’s consistency duringupdates.

What about self-organization in struc-tured P2P systems? In many originaldesigns, it is not present. The network con-struction is based on distributed algorithmsfor node join that are (mostly) determinis-tic once peers have chosen their identities.Typically, peers perform this choice ran-domly to achieve a uniform coverage in theresource identifier space. When resourceidentifiers carry application meaning (forexample, being verbose filenames), theyare generally nonuniformly distributed inthe identifier space. Consequently, choos-ing peer identifiers uniformly randomlyfrom the identifier space results in nonuni-form workload for peers. So, adapting thepeer-identifier distribution with respect tothe actual distribution of resource identi-fiers is necessary. Because achieving thisadaptation through central control is unde-sirable, a self-organizing process, as forGnutella, becomes the natural solution.

Can we really adapt structured P2P net-works in this way, while maintaining thedependencies among the peers implied bythe routing infrastructure? My colleaguesand I answered this question positivelywhen developing P-Grid.6 Using a decen-tralized self-organizing process, we con-structed a prefix-routing infrastructure thatadapts to a given distribution of resourceidentifiers. The process is based on pair-wise interactions of peers in which theylocally decide (if enough data is present)whether to refine the routing infrastructurein a given resource identifier subspace.Consequently, the shape of the (virtual) trieunderlying the routing tables’ organizationwill adapt to the resource identifier distrib-ution. This leads to an interesting problemwith respect to search. In the worst case,for degenerate resource identifier distribu-tions, the trie shape no longer provides anupper bound for search cost because itmight be up to linear depth in network size.However, we can show that for a(sufficiently) randomized selection of linksto other peers in the routing tables, proba-


Using a decentralized self-

organizing process, we

constructed a prefix-routing

infrastructure that adapts to a

given distribution of resource

identifiers.

bilistically the search cost in terms of mes-sages remains logarithmic; it is indepen-dent of the length of the paths occurring inthe virtual trie.7 This result illustrates thatthe principal observation we derived forunstructured P2P systems also holds instructured P2P systems. A fully decentral-ized and adaptive P2P resource locationsystem builds on two principles: a self-organization process to construct the net-work and suitable randomized, distributedalgorithms that can exploit the specificemergent network structure.

Hierarchies of self-organization

Resource location is not the final pur-pose of P2P systems but rather the mostbasic infrastructure for enabling higher-level services. Nothing prevents us fromassuming that these services in turn buildon self-organization principles. At theSwiss Federal Institute of Technology, wehave started investigating some examplesof such self-organizing services for peer-identity management in the presence ofchanging physical addresses, for reputationand trust management, and for discoveringheterogeneous schema correspondences(see www.p-grid.org for details). An inter-esting problem for future research in suchmultilayer self-organizing systems is thehigher-level self-organization processes’dependencies on lower-level ones. We stilldon’t know to what extent we can constructsuch complex, multilayer systems on thebasis of analytically understanding theircomponents and at what point we will haveto rely more and more on adaptive, self-orga-nizing processes to construct such systems.

References

1. F. Heylighen, “The Science of Self-Organiza-tion and Adaptivity,” Principia Cybernetica Web,http://pespmc1.vub.ac.be/SELFORG.html.

2. M. Ripeanu and I. Foster, “Mapping theGnutella Network: Macroscopic Properties ofLarge-Scale Peer-to-Peer Systems,” 1st Int’lWorkshop Peer-to-Peer Systems (IPTPS2002), LNCS 2429, Springer-Verlag, 2002.

3. A. Barabasi and R. Albert, “Emergence ofScaling in Random Networks,” Science, vol.286, 1999, pp. 509–512.

4. Q. Lv et al., “Search and Replication inUnstructured Peer-to-Peer Networks,” Proc.16th Ann. ACM Int’l Conf. Supercomputing,ACM Press, 2002.

5. N. Sarshar, V. Roychowdury, and P. OscarBoykin, “Percolation-Based Search onUnstructured Peer-to-Peer Networks, Proc.1st Int’l Workshop Peer-to-Peer Systems(IPTPS 2002), LNCS 2429, Springer-Verlag,2002.

6. K. Aberer et al., “Improving Data Access inP2P Systems,” IEEE Internet Computing, vol.6, no. 1, Jan./Feb. 2002, pp. 58–67.

7. K. Aberer, “Scalable Data Access in P2P Sys-tems Using Unbalanced Search Trees,” to bepublished in Proc. Workshop DistributedData and Structures (WDAS 2002), CarletonScientific, 2003.

Self-Organization throughDigital HormonesWei-Min Shen, University of Southern California

Self-organization is ubiquitous in nature,and it appears in almost all branches of sci-ence, including physics, chemistry, materi-als sciences, biology, life sciences, socialorganization, and astronomy. The classicexplanation for such common phenomenais that self-organization is a spontaneousand leaderless behavior emerging frominteractions among massive autonomousentities. Alan Turing’s diffusion-reactionmodel is perhaps the earliest example ofthis explanation.1

Self-reconfiguration is a special type ofself-organization wherein global patternsand activities involve not only changesinside component entities but also modifi-cations in configuration and structureamong the entities. Technically speaking,the requirements for self-reconfigurablesystems include the following steps when atask is given from an external source:

1. Execute the current behavior with thecurrent configuration in the currentenvironment.

2. Detect that the current configurationcannot accomplish the task in the cur-rent environment.

3. Select a better (or the best) configurationfor the current task and environment.

4. Morph into the selected configuration.5. Select an appropriate behavior in the

new configuration for the task.6. If the task is not accomplished, return

to Step 1 or accept a new task.

It is now time to launch a full-scale inves-tigation in self-reconfiguration. Recentprogress in biology, information systems,distributed computing, biomimetic robotics,metamorphic robots, material science, andhardware manufacture have provided a solidfoundation for developing a complete self-reconfiguration solution. (See the sidebarfor possible real-world self-reconfigurationapplications.) Biology, in particular, hasaccumulated considerable evidence andknowledge for self-reconfiguration innature. Software engineers have built dis-tributed real-time controllers for very largecommercial systems, and many roboticsresearchers have built prototype self-recon-figurable robots and demonstrated greatpotential for further investigation.2–4 Someelements of the self-reconfiguration theoryhave already been developed and demon-strated in selected cases.

The Digital Hormone Model5 (DHM) isone such attempt. Biological experimentsand mathematical modeling suggest thatwe can model and control self-reconfigura-tion through a framework similar to thehormone receptor mechanism in biologicalcells. Colleagues and I have developed theDHM to control self-reconfigurable robotsand swarms of robots, but its implicationsgo beyond this.

Self-reconfiguration in biologyMorphallaxis is a typical example of

self-reconfiguration wherein a biologicalorganism can regenerate a part or all ofitself from a fragment by self-reorganizingexisting cells without cell proliferation.You can observe this tissue reorganizationprocess in many lower animals followingsevere injury, such as bisection. The processinvolves reforming cells, moving organs,and redifferentiating tissues. The result isusually a smaller but complete individual,derived entirely from the tissues of part ofthe original animal.

Scientists believe that this reorganizationprocess is the most efficient way for simpleorganisms to self-heal and self-regenerate.A remarkable example of morphallaxis isan invertebrate freshwater animal called ahydra.6 If you cut a hydra in half, the headend reconstitutes a new foot, while thebasal portion regenerates a new hydranthwith a mouth and tentacles. Even if youmince a hydra and scramble the pieces, thefragments grow together and reorganizethemselves into a complete whole. The


hydra might be this indestructible becauseeven the intact animal is constantly regen-erating itself. Just below its mouth is agrowth zone from which cells migrate tothe tentacles and to the foot, where theyeventually die. So, the hydra is in a cease-less state of turnover, with cell loss at thefoot and the tentacle tips balanced by theproduction of new cells in the growth zone.X-raying a hydra, however, inhibits theproliferation of new cells, and it graduallyshrinks and eventually dies owing to theinexorable demise of cells and the inabilityto replace them.6 Although how organismsinitiate and control such a process is still amystery, a recent discovery in developmen-tal biology7 suggests a hypothesis that cellssecrete hormonal chemicals that regulatecell pattern formation. This discovery wasone factor that inspired the DHM.

The DHMThree other factors influenced the cre-

ation of the DHM:

• Existing self-organization models, suchas Turing’s reaction-diffusion model

• Stochastic cellular automata• Distributed control systems for self-

reconfigurable robots

In biological systems, different cells respondto different hormones because they have dif-ferent receptors designed to bind with partic-ular hormones. The different types of hor-mones and target cells in vertebrates are sogreat that virtually every cell either processesor responds to one hormone or another. Hor-mones provide the common mechanism thatlets cells communicate without identifiers

and addresses, and they support a broad spec-trum of seemingly diverse biological effects.

The DHM’s basic idea is that a self-reconfigurable system is a network ofautonomous entities or agents that candynamically change their physical or logi-cal links. Through the network links, enti-ties use hormone-like messages to commu-nicate, collaborate, and accomplish globalbehaviors. The hormone-like messages aresimilar but not identical to content-basedmessages. They do not have addresses butpropagate through the links in the organiza-tion. All organizational entities run thesame decision-making protocol, but theywill react to hormones according to theirlocal topology (where they are in the cur-rent configuration) and state information.So, a single hormone might cause differentrobots or robotic modules in the network toperform different actions. Hormone propa-gation is different from message broadcast-ing. There is no guarantee that all entitiesin the network will receive the same copyof the original message, because a hormonemight be modified during its propagation.Hormones also differ from pheromonesbecause they do not leave residues in theexternal environment.

Mathematically speaking, the DHM hasthree components: a dynamic networkspecification, a probabilistic function forindividual robot behavior, and a set ofequations for hormone reaction, diffusion,and dissipation. We specified the first com-ponent as a network of autonomous nodes.A unique property of such networks is thateach node has a set of reconfigurable con-nectors that can dynamically change theconnections with other nodes. The connec-

tors can be physical, as in a reconfigurablerobot, or logical, as in an agent-humanorganization. The interaction between thesystem, the task, and the current environ-ment triggers the self-reconfigurationprocess, which produces a new configura-tion along with a better solution for thetask. This is a dynamic and distributedlearning process that must continuouslypropose and execute new configurationsand solutions for new tasks and new envi-ronments. Unlike classical models, nodesdo not have unique IDs. The number ofnodes and links in the network is unknown,and there is no global broadcast. A nodecan communicate only with its currentneighbors through its current links.Through local communication, nodes caneither generate or propagate hormones. Bydefault, a node will propagate a generatedhormone to all its current neighbors. Whenreceiving a hormone, a node will propagatethe hormone to all its neighbors except theone that sent the hormone The secondcomponent is a specification of individualnode behavior, which is similar to recep-tors in biological cells. A network node canselect its actions on the basis of a probabil-ity function conditioned on four local fac-tors: the local topological information (howit connects to the neighbors), the local sen-sor information, the local state variables,and the received hormones. This function is local and homogenous for all nodes butcan greatly influence the network’s globalbehaviors and predict and analyze the globalnetwork performance. This function differ-entiates the DHM from standard diffusion-reaction models for self-organization, and itcan determine whether the system can form


In engineering, self-reconfiguration provides a new andcritical capability for many real-world applications. Self-recon-figuration will let smart materials self-assemble into differentstructures for best performance. In homeland security, self-reconfiguration will let unmanned ground or air vehiclesrestructure and repair their organization in unexpected situa-tions. In information systems, software agents could adjusttheir relationships to gather and deliver critical information ina timely fashion. In search-and-rescue or inspect-repair applica-tions, self-reconfigurable robots could maneuver in tightspaces that are hard to reach for humans or conventionalrobots.

A self-reconfigurable robot could become a ball to roll down

a slope, slither between stones as a “snake” to locate a personor artifact, morph smoothly into a “crab” and climb over rub-ble, and then transform a leg into a gripper to grasp and carryobjects. Underwater, a self-reconfigurable robot might becomean “eel” to swim in open water, change into an “octopus” tograsp objects, and then spread itself into many small but agileunits to monitor large areas.

Self-reconfiguration could help teach engineering studentsnew principles for designing novel fault-tolerant, distributed,and multifunctional systems. In science, principles of self-reconfiguration might help us deepen our understanding ofhow self-organizing natural systems evolve and adapt to theirenvironments.

Self-Reconfiguration and Real-Life Applications

any global patterns. You can program thesefunctions at the outset, or the nodes candynamically change them through a learningtechnique just as hormones might influencea cell’s behaviors by activating or inhibitingdifferent receptors.

The third component is the specificationfor hormone reaction, diffusion, and dissi-pation, similar to but different from thosespecified by Turing1 and, later, AndrewWitkin and Michael Kass.8 Each hormone’sconcentration is a function of position andtime that we specify as a set of differentialequations. These equations’ parameterscontrol the diffusion rate and the manner ofreaction among hormones. The differencesbetween the DHM and early diffusion-reaction models are that hormone propaga-tion can be realized through wireless com-munications, thus achieving “remote”influences that are not limited by geographicdistances.

The DHM’s execution is simple. Allnodes in a self-reconfigurable system asyn-chronously execute the basic control loopas follows:

1. Select actions based on behaviorfunctions.

2. Execute the selected actions.3. Perform hormone generations and

propagations.4. Simulate hormone diffusion, reaction,

and dissipation.5. Return to Step 1.

We have successfully applied the DHMto several types of self-reconfiguration sys-tems, including the simulation of embryoskin cells in forming feather buds,9 the dis-tributed control of robot swarms,10 and theadaptive communication and control ofself-reconfigurable robots.5

Under the control of the DHM, theCONRO robot5 has demonstrated severalunique features for self-reconfigurable sys-tems, including online bifurcation, unifica-tion, and behavior shifting. No fixed“brain” module exists in CONRO, andevery module behaves properly accordingto its relative position in the current config-uration. For example, we can bifurcate amoving CONRO snake robot into pieces,yet each individual piece will “elect” a newhead and continue to behave as an indepen-dent snake. Multiple snakes can be con-catenated (for unification) while runningand become a single, coherent snake. For

online behavior shifting, we can disconnecta snake’s tail-spine module and reconnectit to the side of the body while the systemis running, and its behavior will automati-cally change to that of a leg (the reverseprocess is also true). For fault tolerance, ifa multilegged robot loses some legs, it canstill walk on its remaining legs withoutchanging the control program.

In addition, CONRO also demonstratedself-reconfiguration from a snake to a two-legged creature that has a locomotion gaitsimilar to the two-arm butterfly stroke inswimming. This is probably the first timeany robot has performed such a metamor-phic action in a physical system using atotally distributed control method. In thisreconfiguration sequence, the tail modulefirst docks to a body module’s left connec-tor to form a loop. Then the middle twomodules in the loop disconnect so that theentire configuration becomes a two-leggedcreature with a body. After that, the newconfiguration automatically switches onthe butterfly behavior for locomotion. Youcan find video that demonstrates what self-reconfigurable systems can accomplish atwww.isi.edu/robots.

Future research in self-reconfigurablesystem must solve the six challengingproblems listed at the beginning of the arti-cle in a coherent and integrated way. Thesolutions might call for new approaches fordistributed control, sensor fusion, agentcoordination, and understanding the inter-action between configurations, tasks, andenvironments.

AcknowledgmentsI thank Cheng-Ming Chuong and Peter Will

for their valuable input and discussions duringthe DHM’s development. This work is partiallysupported by research grants from the AirforceOffice of Scientific Research.

References

1. A.M. Turing, “The Chemical Basis of Mor-phogenesis,” Philosophical Trans. of theRoyal Socienty of London, Series B, Biolog-ical Sciences, vol. 237, no. 641, 14 Aug. 1952,pp. 37–72.

2. M. Yim, Y. Zhang, and D. Duff, “ModularRobots,” IEEE Spectrum, vol. 39, no. 2, Feb.2002, pp.30–34.

3. D. Rus et al., “Self-Reconfiguring Robots,”

Comm. ACM., vol. 45, no. 3, Mar. 2002, pp.39–45.

4. W.-M. Shen and M. Yim, eds., Special Issueon self-reconfigurable modular robots, IEEE/ASME Trans. Mechatronics, vol. 7, no. 4, Dec.2002.

5. W.-M. Shen, B. Salemi, and P. Will, “Hor-mone-Inspired Adaptive Communication andDistributed Control for CONRO Self-Recon-figurable Robots,” IEEE Trans. Robotics andAutomation, vol. 18, no. 5, Oct. 2002, pp.700–712.

6. “Regeneration,” Encyclopædia BritannicaOnline, http://search.eb.com/eb/article?eu=119855.

7. M. Yu et al., “The Morphogenesis of Feath-ers,” Nature, vol. 420, no. 21, Nov. 2002, pp.308–312.

8. A. Witkin and M. Kass, “Reaction-DiffusionTextures,” Computer Graphics, vol. 25, no. 3,1991.

9. W.-M. Shen, C.-M. Chuong, and P. Will,“Digital Hormone Models for Self-Organi-zation,” Proc. 8th Int’l Conf. Simulation andSynthesis of Living Systems (ALIFE VIII),MIT Press, 2002.

10. W.-M. Shen, P. Will, and C.-M. Chuong,“Hormone-Inspired Self-Organization andDistributed Control for Massive RobotSwarms,” submitted to Autonomous Robots,2002; www.isi.edu/robots.

Physical Connectivity of Self-Organized Ad Hoc WirelessNetworksOlivier Dousse and Patrick Thiran, SwissFederal Institute of Technology, Lausanne

In wireless cellular networks (such asGroup Spéciale Mobile or UniversalMobile Telecommunications System),nodes can connect to each other through adense network of antennas (base stations)linked by a wired network. In wireless adhoc networks (such as Bluetooth), nodesconnect to each other without using fixedbase stations. If nodes lie in a limited geo-graphical area, destinations can be reach-able within a single hop from the source.The problem becomes much more complexwhen the ad hoc network comprises severalnodes scattered over a wide area, becausecommunications then require multihopconnections.


A cellular network’s infrastructure isowned by an operator who can allocateresources and control network perfor-mance. In contrast, self-organizing ad hocnetworks have no infrastructure and relyentirely on distributed, local decisions forevery operational aspect: self-configureddeployment, topology discovery, routing,scheduling, medium access control, andcooperation mechanisms for relaying otherusers’ connections. Even the most basicnetwork property, its connectivity, becomesa nontrivial issue in multihop ad hoc net-works, as you will see.

Network connectivitySuppose that all nodes randomly placed

on a plane transmit at maximum power.(Forget, temporarily, interferences betweensimultaneous communications.) In this case,a simple criterion for deciding whether twonodes can connect in a single hop is thattheir distance be less than some prescribedmaximal range R. What is the resultingnetwork’s connectivity?

One approach is to assume that the num-ber of nodes N is very large (theoreticallyinfinite), but that they all lie within a finitegeographical area; in other words, the geo-graphical density of nodes per surface areaλ tends toward infinity. Piyush Gupta andPanganamala Kumar have proven that, if Rdecreases at a rate slower than ,the network is then almost fully connected.1

A second approach is to allow a finitegeographical density of nodes per surface

area λ but assume that nodes are dispersed inthe entire plane. Assume, moreover, that thisprocess is Poisson. Because the number ofnodes is unbounded, some of them will bedisconnected. The question is then, are long-distance communications still possible, orare they all limited to some local range? Thisquestion is related to the continuum percola-tion theory for the Poisson Boolean Model.2

The percolation probability is the probabilitythat an arbitrary node will belong to a clusterof infinite size (and thus that an arbitrarynode can be connected to another node arbi-trarily far away by a multihop path).

The percolation theory’s main result isthat a finite, positive value λc of λ (or equiv-alently, a finite, positive value Rc of R)exists under which the percolation probabil-ity is zero (the subcritical phase) and abovewhich it is nonzero (the supercritical phase).In the subcritical phase, all clusters arealmost surely finite, and their size is a ran-dom variable whose distribution has anexponentially decreasing tail. In the super-critical phase, the percolation probabilityusually increases rapidly with λ. Figure 2illustrates this phase transition phenome-non. By comparing the two graphs, you willnotice that a slight increase of the radius Rhas created only a few edges (black lines inFigure 2b), but that these few edges connectmost of the colored clusters into one largecluster (theoretically infinite). This proba-bility’s exact value is still an open question.Ronald Meester and Rahul Roy, and EdgarGilbert obtained some bounds on the criti-

cal intensity λc, below which the percola-tion probability is zero.2,3

Why is knowing that the network is asupercritical phase so interesting? After all,this property “only” means that a nodecluster of infinite size with positive proba-bility exists, which is not a satisfactoryguarantee for users of large-scale ad hocnetworks. If the percolation probabilitywere a smoothly increasing function of λand R, this property would probably indeednot have much impact. Its importance is thesudden phase transition phenomenon thatoccurs in the Boolean model and alsooccurs in other models of random graphs.4

To illustrate this claim, consider a hybrid(or multihop cellular) network, which is anintermediate solution between fully cellu-lar networks and pure ad hoc networks. Insuch a network, base stations are linkedtogether by a wired network, but only a fewexist, so that most nodes need many hopsto connect to a base station. What is thebenefit, in terms of connectivity, of havingsuch a sparse network of base stations reg-ularly placed in the network? If nodes arescattered in two dimensions, and if thenode density (or radius) is above the perco-lation threshold, there is virtually no bene-fit. Indeed, there is an infinite cluster,which will almost surely connect to at leastone base station. So, the only nodes thatwill connect to the infinite cluster exclu-sively owing to the presence of base sta-tions are the few isolated nodes that liewithin a distance R from a base station.

log /N N( )

84 computer.org/intelligent IEEE INTELLIGENT SYSTEMS84 computer.org/intelligent IEEE INTELLIGENT SYSTEMS

Figure 2. The Poisson Boolean model: (a) the subcritical phase (R is slightly less than Rc); (b) the supercritical phase (R is slightlylarger than Rc).

(a) (b)

Because few such nodes and few base sta-tions exist, the benefit remains marginal.

On the other hand, if the node density isless than the percolation threshold but stilllarge enough, the presence of a few basestations does help, although many nodes still

remain unconnected. The benefit is muchmore dramatic when the nodes’ spatial dis-tribution is one-dimensional. In this case,the network is in the subcritical phase for allfinite values of λ and is thus made of finiteclusters whose size distribution has an expo-

nential tail. If λR is large, then base stationscan be far away from each other yet makelong-distance communications possible.These features hold for node distributionsbesides Poisson.5 However, these resultsapply only to connectivity properties and not

JULY/AUGUST 2003 computer.org/intelligent 85JULY/AUGUST 2003 computer.org/intelligent 85

Francis Heylighen is a research professor andcodirector of the interdisciplinary center LeoApostel at the Free University of Brussels(VUB). His research focuses on the self-organi-zation and evolution of complex systems, whichhe addresses from a cybernetic perspective. Hereceived his PhD in mathematical physics fromVUB. He is editor of the Principia CyberneticaProject, chairman of the Global Brain Group,and member of the editorial boards of the Jour-

nal of Memetics, Journal of Collective Intelligence, Informatica, andEntropy. Contact him at the Center Leo Apostel, Vrije Universiteit Brus-sel, Krijgskundestraat 33, B-1160 Brussels, Belgium;[email protected].

Carlos Gershenson is a PhD student at theCenter Leo Apostel at the Free University ofBrussels and a contributing editor for the weeklyelectronic distribution Complexity Digest. Hisinterests include self-organizing and complexsystems, distributed cognition, theories of evolu-tion, and philosophy of science. He received hisMSc in evolutionary and adaptive systems at theUniversity of Sussex. Contact him at the CenterLeo Apostel, Vrije Universiteit Brussel, Kri-

jgskundestraat 33, B-1160 Brussels, Belgium; [email protected].

Gary William Flake is the chief science officerof Overture Services. His research interestsinclude machine learning, Web data mining,efficient algorithms, and complex systems. Hereceived his PhD in computer science from theUniversity of Maryland. He is a member of theACM, the IEEE, and DIMACS. Contact him [email protected].

David M. Pennock is a senior research scientistat Overture Services. His research interestsinclude electronic commerce, Web modeling, andartificial intelligence. He received his PhD incomputer science from the University of Michi-gan. He is a member of the ACM, the IEEE, theAAAI, DIMACS, INFORMS, and AAAS. Con-tact him at [email protected].

Daniel C. Fain is a the director of R&D Algo-rithms at Overture Services. His research inter-ests include information extraction and retrieval,in particular, topic identification, relevance eval-uation, and applications of machine learning. Hereceived his PhD in computation and neuralsystems from the California Institute of Technol-ogy. Contact him at [email protected].

David De Roure is a professor of computer sci-ence at the University of Southampton, where heis head of Grid and Pervasive Computing in theDepartment of Electronics and Computer Scienceand codirector of the Southampton e-ScienceCenter. His interests include large-scale distrib-uted systems and the relationship between seman-tic, pervasive, and grid computing. He receivedhis PhD in distributed systems from the Univer-sity of Southampton. Contact him at the Dept.

Electronics and Computer Science, Univ. of Southampton, Southampton,SO17 1BJ, UK; [email protected].

Karl Aberer is a professor for distributed infor-mation systems at the Swiss Federal Institute ofTechnology, Lausanne. His research interestsfocus on self-organization principles in informa-tion management, addressing issues of P2P datamanagement, semantic interoperability, trustmanagement, and Web services. Contact him atLSIR-Distributed Information Systems Labora-tory, EPFL-I&C, 1015 Lausanne, Switzerland;[email protected]; lsirwww.epfl.ch.

Wei-Min Shen is the director of the Polymor-phic Robotics Laboratory at the InformationSciences Institute and a research assistant pro-fessor in computer science at the University ofSouthern California. His research interestsinclude artificial intelligence, robotics, and lifescience. He received his PhD from CarnegieMellon University under Herbert A. Simon onthe subject of autonomous learning from theenvironment based on actions and percepts. He

is a member of the IEEE, the ACM, and AAAI. Contact him at the Infor-mation Sciences Institute, Univ. Southern California, 4676 AdmiraltyWay, Marina del Rey, CA 90292; [email protected]; www.isi.edu/~shen.

Olivier Dousse is a PhD student from the Institutefor Communication Systems at the Swiss FederalInstitute of Technology, Lausanne (EPFL). Hisresearch interests include connectivity and capac-ity of multihop ad hoc and cellular networks. Hereceived his MS in physics from EPFL. He is amember of the research group IP1 of the NationalCompetence Center in Research on Mobile Infor-mation and Communication Systems (NCCR-MICS). Contact him at LCA-ISC-I&C, Ecole Poly-

technique Federale de Lausanne, CH-1015 Lausanne, Switzerland; [email protected].

Patrick Thiran is a professor of communicationsystems at the Swiss Federal Institute of Technol-ogy, Lausanne (EPFL). His research interestsinclude communication networks (in particular adhoc networks), performance analysis, dynamicalsystems, and stochastic models. He received hisPhD in electrical engineering from EPFL. Contacthim at LCA-ISC-I&C, Ecole Polytechnique Fed-erale de Lausanne, CH-1015 Lausanne, Switzer-land; [email protected].

to capacity, which can increase owing to thepresence of wired base stations.

Percolation might, however, impactcapacity too. Figure 2b shows that—with abarely supercritical network—the blacklinks connect many colored clusters ofnodes but still form bottlenecks. Thisaffects capacity and routing in the network.Only for very large spatial densities canthese network “hot spots” disappear.

Accounting for interferencesWireless channels’ physical features will

require more sophisticated models than theBoolean model just described.

One feature is the anisotropy of radiationin real networks, which replaces the Booleanmodel’s circle of radius R with an irregular,rotationally nonsymmetric contact surface.Although many links will disappear in com-parison to the Boolean model, the resultinggraph will have a few long edges essentialfor its long-range connectivity, such as insmall-world graphs.6 The irregularity istherefore a positive factor, letting the per-colation occur at a lower density than in aBoolean model.7

A second feature is the interferencesbetween simultaneous channels. One modelassumes that a link exists between two nodesif and only if the signal-to-noise ratio at thereceiver (noise being the sum of the back-ground noise and the interference contribu-tions from neighboring nodes) is larger thansome prescribed value.8 The problem is morecomplex because now direct connectionsbetween two particular nodes depend onother nodes’positions. The node degree isbounded, contrary to the Boolean model.Moreover, two parameters (the orthogonalitycoefficient of the CDMA [code division mul-tiple access] system coping with interfer-ences and emitting power) now exist, insteadof one (power). The conditions for a super-critical phase are more stringent than in theBoolean model, but percolation still occursdespite the interferences for a nonzero valueof the code’s coefficient of orthogonality,provided it is small enough. As such, aCDMA code might be difficult to use in self-organized ad hoc networks. An alternative isto adopt a simple TDMA (time division mul-tiple access) system, where each node ran-domly picks one time slot every n time slotsto transmit, while all nodes listen at all times.We found that such a system led to similarconnectivity as the original CDMA schemewith an orthogonality factor n times smaller.

The qualitative explanation is that the in-creased irregularity in the resulting graphsobtained in the TDMA case, with manyshort edges and a few long ones, compen-sates for a large orthogonality factor.8

The idea of applying percolation theoryto ad hoc networks dates back to Gilbert’spioneering work3 and transcends the basicproperty of potential long-distance com-munications in a purely ad hoc network. Aswe outline in this article, percolation theoryis a key to understanding many differentperformance aspects of large-scale ad hocand sensor networks. Interest is growing inpercolation analysis based on extensions ofthe Boolean model that capture additionalfeatures of ad hoc networks’ physical lay-ers. Some results can be initially surprising(for example, irregularity is good for con-nectivity). Percolation will also be instru-mental in analyzing the higher layers ofself-organized networks. For instance, youmight view setting a time-out value in aflooding algorithm for P2P networks as apercolation problem because the searchalgorithm must reach nodes arbitrarily faraway from the request source. Percolationhas been applied to devise probabilisticbroadcast algorithms in mobile ad hoc networks.9

AcknowledgmentsThis work was supported (in part) by the

National Competence Center in Research onMobile Information and Communication Sys-tems, which the Swiss National Science Founda-tion supports under grant number 5005-67322.

References1. P. Gupta and P.R. Kumar, “Critical Power for

Asymptotic Connectivity in Wireless Net-works,” Stochastic Analysis, Control, Opti-mization and Applications: A Volume in Honorof W.H. Fleming, W.M. McEneany, G. Yin, andQ. Zhang, eds., Birkhäuser, 1998, pp. 547–566.

2. R. Meester and R. Roy, Continuum Percola-tion, Cambridge Univ. Press, 1996.

3. E.N. Gilbert, “Random Plane Networks,”SIAM J., vol. 9, Dec. 1961, pp. 533–543.

4. B. Bollobas, Random Graphs, AcademicPress, 1985.

5. O. Dousse, P. Thiran, and M. Hasler, “Con-

nectivity in Ad Hoc and Hybrid Networks,”Proc. INFOCOM 2002, vol. 2, IEEE Press,2002, pp. 1079–1088.

6. D. Watts and S. Strogatz, “Collective Dynam-ics of Small World Networks,” Nature, vol.363, June 1998, pp. 202–204.

7. L. Booth et al., “Ad Hoc Networks with NoisyLinks,” to be published in Proc. IEEE Infor-mation Theory Symposium (ISIT 03), 2003.

8. O. Dousse, F. Baccelli, and P. Thiran, “Impactof Interferences on Connectivity in Ad HocNetworks,” Proc. INFOCOM 2003, IEEEPress, 2003.

9. Y. Sasson, D. Cavin, and A. Schiper, “Proba-bilistic Broadcast for Flooding in WirelessMobile Ad Hoc Networks,” Proc. 2003 IEEEWireless Comm. and Networking Conf.(WCNC), IEEE Press, 2003.


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