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Localized Algorithms and Their Applications in Ad Hoc Networks

Jie WuDept. of Computer Science &

EngineeringFlorida Atlantic University

Boca Raton, FL 33431

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Outline Ad Hoc Wireless Networks Localized Algorithms Three Sample Applications Other Applications Conclusions Future Directions

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(I) Ad Hoc Wireless Networks Wired Networks

LAN, MAN, WAN, and Internet Wireless Networks

Infrastructured networks (cellular networks) Infrastructureless networks (ad hoc wireless networks)

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Wired/Wireless Networks

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Wireless Networks 200 million wireless telephone

handsets (purchased annually) A billion wireless communication

devices in use The first decade of 21st Century:

mobile computing "anytime, anywhere"

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Ad Hoc Wireless Networks (Infrastructureless networks)

MANETs (mobile ad hoc networks) No base station and rapidly

deployable Neighborhood awareness Multiple-hop communication Unit disk graph: host connection based

on geographical distance

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Unit Disk Graph

A simple ad hoc wireless network of six mobile hosts.

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Characteristics Self-organizing: without centralized control Scarce resources: bandwidth and batteries Dynamic network topology

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Mobility management Addressing and routing

Location tracking Absolute vs. Relative, GPS

Network management Merge and split

Resource management Network resource allocation and energy efficiency

QoS management Dynamic advance reservation and adaptive error control

techniques

Major Issues

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MAC protocols Contention-base, controlled

Applications and middleware Measurement and experimentation

Security Authentication, encryption, anonymity, and intrusion

detection Error control and failure

Error correction and retransmission, deployment of back-up systems

Major Issues (Cont’d.)

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(II) Localized Algorithms (Estrin, 1999) Processors (hosts) only interact with

others in a restricted vicinity. Each processor performs exceedingly

simple tasks (such as maintaining and propagating information markers).

Collectively these processors achieve a desired global objective.

There is no (or limited) sequential propagation of information.

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Local information k-hop information

Discovered via k rounds of Hello exchanges

Topology and other information

Usually k=1, 2, or 3 Information gathering

vs. information fusion1-hop information2-hop information3-hop information

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Application I: Safety Level(Wu, 1992) Safety level (fault-tolerant comm. in

hypercubes) Approximation of routing capability of a

node in faulty hypercubes Safety level as a function of neighbors’

safety levels3

3 1

3 1

3

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Application II: Virtual Backbone Formation

Applications include topology management, coverage & routing

Requirements include connectivity, size, formation overhead, routing distance, etc

Using a connected dominating set (CDS) as a virtual backbone Each node has at least one neighbor in VB Each pair of nodes can communicate via

VB

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Marking Process (Wu and Li, 1999) A node is marked true if it has two

unconnected neighbors. Marked node sets (gateway nodes)

form a connected dominating set (CDS).

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Marking Process (Cont’d)

A sample ad hoc wireless network

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Marking Process (Cont’d)

CDS as a virtual backbone0 1 2 3 4 5 6 7 8 9 10

0

1

2

3

4

5

6

7

8

9

10

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(III) Applications in Broadcasting Promiscuous receive mode Coverage & efficiency Flooding: each node forwards the

message once

s

u

v

w

(a)

s

u

v

w

(b)

s

u

v

w

(c)

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Motivation & Objectives Objective: determine a small set of forward

nodes to ensure coverage in a localized way Existing works: different assumptions and

models A generic framework to capture a large

body of protocols One proof for the correctness of all protocols Address various assumptions/techniques Combine techniques to achieve higher efficiency

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Classification Probabilistic vs. Deterministic*

Deterministic algorithms: forward nodes (including the source) form a CDS

Non-localized vs. Localized* Self-pruning* vs. Neighbor-

designating*

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Preliminaries: View Unit disk graph: ad hoc network

G= (V, E) View: a snapshot of network topology

and broadcast state View(t) = (G, Pr(V, t))

Priority: (forwarding status, id) Pr(v, t) = (S(v,t), id(v)), v є V

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Preliminaries: Forwarding status Forwarding status: time-sensitive

forward node vs. non-forward node Local view: View’, partial view within vicinity visible node vs. invisible node (level: 0) G’ is a subgraph of G and Pr’(V) < Pr(V)

timepast view current view

broadcast period

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Pr(v) > Pr(u) based on lexicographical order: visited (2) > unvisited (1) > invisible (0)

Global view: {(2, s), (1, u), (2, v), (1, w)} Local 1-hop view of w: {(0, s), (1, u), (2, v), (1, w)}

Preliminaries: Priority order

s

u

v

wlocal view of w

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A Generic Coverage Condition Node v has a non-forwarding status if

For any two neighbors u and w, a replacement path consisting of nodes with higher priorities than that of v exists

u

v

w…

replacement path

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A Generic Coverage Condition

Proof:

Theorem 1 (Wu&Dai, Infocom’03): Forward node set V’ derived based on the coverage condition forms a CDS

Each pair of nodes u and v are connected via forward nodes

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A Generic Coverage Condition

Proof: Forward status fi(vi)i is computed from G(vi) and Pri(V) Assume fsuper (vi) is computed from a global view

Gsuper = (V(v1) V(v2) ... V(vn), E(v1) E(v2) ... E(vn)) Prsuper (vi) = max{Pr1(vi), Pr2(vi), ..., Prn(vi)}

We have fi(vi)fsuper (vi) and {vi|fsuper (vi)=1} is a CDS Therefore, {vi|fi(vi)=1} is a CDS

Theorem 2 (Wu&Dai, ICDCS’03): Theorem 1 still holds when different nodes have different local views

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Timing Issues Static: decision before the broadcast process Dynamic: decision during the broadcast process

First-receipt First-receipt-with-backoff

s>u>v>x>w

v u

sw(b)

xsource

v u

sw(a)

x

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Selection Issues Self-pruning: v’s status determined by itself Neighbor-designating: v’s status

determined by its neighbors Hybrid: The status of v is determined by v

and its neighbors

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Space Issues Network topology information (long lived)

Periodic “hello” message K-hop neighborhood information (k=2 or 3)

Broadcast state information (short lived) Snooped: snoop the activities of its neighbors Piggybacked: attach h most-recently visited

node information (including designated forward neighbors)

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Priority Issues Pr(v): (forward status, id) 0-hop priority: id(v) 1-hop priority: deg(v) 2-hop priority: ncr(v)

ncr (neighborhood connectivity ratio): the ratio of pairs of neighbors that are not directly connected to pairs of any neighbors.

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A Generic Broadcast Scheme Dynamic approach: dependent on the location

of the source and the process of the broadcast process Generic distributed broadcast protocol

1) Periodically v exchanges “hello” messages with neighbors to update local network topology Gk(v).

2) v updates priority information Pr based on snooped/piggybacked messages.

3) v applies the coverage condition to determine its status.

4) If v is a non-forward node then stop.5) v designates some neighbors as forward nodes if

needed and updates its priority information Pr.6) v forwards the packet together with Pr.

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Existing Protocols as Special Cases Special cases

Skipping some steps A strong coverage condition (step 3) Designated forward node selections (step 5)

Strong coverage condition v is non-forwarding if it has a coverage set The coverage set belongs to a connected component

of nodes with higher priorities than that of v Complexity: O(D2) compared with O(D3), where D is

density

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Static Algorithms (steps 1 and 3) Special cases:

Marking process with Rules 1 &2 (Wu&Li, DiaLM’99)

Marking process with Rule k (Dai&Wu,ICC’03) Span (Chen et al, MobiCom’01)

1 2 6

5

7 4

3

1 2 6

5

7 4

3

1 2

5

7

3

1 2

5

7

3

2-hop neighborhoodforward nodecurrent node

47>6>5>4>3>2>1

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Dynamic and Self-Pruning (steps 1, 2, 3, and 6) Special cases:

SBA (Peng&Lu,2000) LENWB (Sucec&Marsic,2000)

1 2 6

5

74

3source

2-hop routing historysourceforward nodecurrent node

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Dynamic and Neighbor Designating (steps 1,2,4,5,and 6) Special cases:

Multipoint relay (MPR) (Qayyum et al, 2002) Dominant pruning (Lim&Kim, 2001) Total/partial dominant pruning (Lou&Wu, 2003)

u v

N(v)

N2(u)

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Dynamic and Hybrid (new) Designate one neighbor before applying

the coverage condition

u v

N(v)

N2(u)

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A Sample Broadcasting(n=100, d=6, r=16, k=2)

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(IV) Other Applications Energy-efficient design and power-

aware routing/broadcasting Reducing computation complexity Maximizing the traffic capacity Reducing power consumption Prolonging the life span of each node Reducing MAC-layer power consumption

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Other Applications (Con’t)

Topology Control Localized solutions Location-aware solutions

Localized Delaunay triangulation, Gabriel, Yao, RNG graphs …

MAC Layer Protocols Variable transmission ranges Directional antenna

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Other Applications (Con’t)

Sensor Networks Coverage problem Exposure problem Data dissemination and gathering Dynamic sensor deployment

Peer-to-peer Networks Localized and scalable solutions for the

look-up problem

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Some New Results• Safety Level: Efficient solutions to handle

link faults (IEEE TR 2004)• CDS: Computation complexity reduction in

dense mode (ICDCS 2004) • Broadcast: Mobility management and

consistent view (INFOCOM 2004)

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Open Issues• Complexity and Efficiency Tradeoffs• Mobility Management• Extensibility to other Models

• Directional antenna• Hitchhiking model• …

• Other Applications• Localized security• Localized incentive mechanisms• …

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(V) Conclusions Localized Algorithms

Approximation for optimization problems Simple and scalable design Self-organizing, self-stabilizing, and self-

healing Applications in dynamic systems

Ad hoc wireless networks Sensor networks Peer-to-peer networks

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(VI) Future Directions• Cross Disciplinary Efforts

• NSF Sensor Network Program (March, 2003): Sponsored by multiple divisions/programs

• Encouraging multi-disciplinary team effort• Hitch-hiking Model Energy-efficient design in

sensor networks (UMass- FAU, INFORCOM 2004) • Multiple disciplines

• physical layer• MAC layer• network layer

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Vision of the Field Convergence of Multiple Disciplines

Parallel processing Distributed systems Network computing

Wireless network and mobile computing as an important component in Cyberinfrastructure and Cybertrust

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Vision of the Field (Con’t)

Ultimate Cyberinfrastructure Petascale computing, exabyte storage, and terabit

networksNetwork-Centric Supernetworks: networks are faster than the

computers attached to them Endpoints scale to bandwidth-match the network

with multiple-10Gbps lambdas

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Major Conferences in the Fields General: IEEE INFOCOM Mobile Computing: ACM MobiCom Ad Hoc Networks: ACM MobiHoc Distributed Systems: IEEE ICDCS Sensor Networks: IEEE MASS (Mobile

Ad-hoc and Sensor Networks)

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Any Questions ?