The Neighborhoods Method and Routing in SensorNetworks

A.M. SukhovSamara State Aerospace University

Moskovskoe sh. 34,Samara, 443086, Russia

e-mail: amskh@yandex.ru

D.Yu. ChemodanovSamara State Aerospace University

Moskovskoe sh. 34,Samara, 443086, Russia

e-mail: duman190@gmail.com

Abstract—The paper proposes and tests a new technique forrouting sensor networks. The method is based on the decom-position of a simply connected configuration of sensors on theset of disjoint neighborhoods with respect to the route start.The number of neighborhood which gets the destination nodeis equal to the number of hops. Backward pass neighborhoodswill determine the route as a sequence of nodes. The routingtechnique is generalized to the case of dynamic configuration ofsensors.

Index Terms—neighborhoods method, double pass, new rout-ing technique, dynamic configuration of sensors

I. INTRODUCTION

Sensor networks are distributed, self-organizing networksof nodes that communicate using wireless technology. Thisis a fast-growing communication system whose number ofservice users is increasing. Protection of the environment,transport, industry, utilities, security systems are just a fewof its possible fields of application [1], [2]. The developmentof microelectronics has provided many cheap element baseswhich are currently being rapidly improved.

In this paper, sensor networks will be considered as apossible testing ground for developing routing principles [3],[4]. Sensor network architecture allows the use of all existingrouting methods, including dynamic protocols. An analogybetween the sensor nodes and autonomous systems to theglobal Internet can be carried out to examine the principles ofinter-domain routing. Border Gateway Protocol (BGP) [5] alsoprovides some of the principles of self-organizing networks.

In this paper, we propose a neighborhoods method forrouting [6], which divides the whole set of nodes into disjointsets. These sets are called neighborhoods and they consist ofall the nodes that are located at a distance of N hops. Suchdecomposition is very useful, since we can immediately findthe number of hops on the route.

The potential network congestion resulting from collectinginformation about the neighbors, carried by broadcast [7], isnot investigated in this work. These techniques have beendeveloped and a review of these methods and the calculationof the time between successive updates of the data about theneighboring nodes should be discussed in a separate article.

This article is organized as follows: Section II of thepaper provides a brief overview of previous work, Section III

describes the method of neighborhoods, the fourth sectiondeals with the special simulator, designed to test the proposedmethod and the results of testing different methods are inSection V. The method of upgrading neighborhoods for thedynamic configuration of sensors is discussed in Section VI.

II. RELATED WORKS

The simplest and most common method of routing in self-organizing networks is that of geographic routing. In thiscase, the geographic position of the node is selected as thelocation [8], [9], [10]; greedy forwarding technology is mostcommonly used, through which a data packet is directed to aneighboring node that is closer to the destination than the nodeholding the packet [11], [12]. Greedy forwarding technologyallows the transmission of packets over the shortest route, butits use may give rise to a situation called the problem of localminimum [11]. The problem of local minimum is the absenceof a neighboring node that is closer to the destination than thecurrent node holding a packet for transmission.

In this case, an alternative mode of geographic routing wasintroduced, the so-called strategy of bypassing the void [13].A number of ways to bypass eventually were developed and agood review of these can be found in the papers [4], [14]. Thebasic technology of bypass holes is the technique of the planargraphs, the Greedy Perimeter Stateless Routing (GPSR) [11],[14]. Numerous versions of this refinement technique has beendeveloped, but all of them are based on the technique ofgraphs. The most common method for overcoming obstacles isbypassing the perimeter of the void on the right-hand rule [15].The GPRS method was chosen by us as the basic method oftraditional routing and all comparisons will be carried out withthis protocol. Other technologies that bypass voids are planargraph, geometric, flooding, cost and heuristics.

The concepts of neighbor nodes and neighborhoods arewidely used when developing strategies to circumvent voids.However, existing policies are almost always limited to asmall number of neighborhoods; usually the first two or threeneighborhoods are considered.

This paper deals with the improvement of greedy routingtechnology in order to solve the problem of local mini-mum [16]. The basis of our approach is the concept of aneighborhood [17], [18], [19], including all the neighboring

Fig. 1. Neighborhoods illustration

nodes. The simplest information in the form of a list of nodesand their immediate neighbors allows the calculation of theshortest route. Decomposition of the set of sensors for theneighborhood is not limited to two or three levels, therefore itis necessary to divide the entire one connected graph. Theneighborhoods method for route searching is described indetail in Section III of this paper.

III. DESCRIPTION OF THE METHOD

By N neighborhood of node we mean the set of allneighboring sensors located at a distance of N hops. Thus,the nearest neighbors form a neighborhood at first level, andthe neighbors that are located at a distance of 5 hops, form aneighborhood at level 5.

Unlike the greedy forwarding we do not need built-in GPSreceivers that allow the acquisition of the coordinates of nodes.The initial data for routing is a list of all possible nodes,indicating the nearest neighbors. These data can be easilycollected through broadcast requests and acquiring them doesnot require any special equipment, which greatly simplifies thearrangement of sensors.

One of the two nodes X and Y of a route is chosen as thestart of the route (X). At this point it is necessary to build a setof neighborhoods. In the neighborhood of the first level Xi1

1

next-door neighbors will be included. The neighborhood of thesecond and subsequent levels Xin

n will include the neighborsof nodes from the previous level, except for those that metearlier (see Figure 2)).

In the Nth step the endpoint of the route Y falls in thecorresponding neighborhood XiN

N , at this first stage the routesearch can be considered complete. Its outcome is a set ofnodes that make up the N neighborhoods and the number oftransitions from X to Y .

For a node Y we can construct the intersection of its firstneighborhood Y i1

1 to N − 1 neighborhood XiN−1

N−1 . This set is

Fig. 2. Illustration of the neighborhoods method

not empty; it includes at least one node. Let us denote this nodeas Y X

1 = Y i1i

⋂X

iN−1

N−1 , for this node(s) the intersection ofits first neighborhood with the previous neighborhood XiN−2

N−2of node X is again constructed. By repeating this iteration Ntimes, we obtain a complete set of the shortest paths from X toY with the number of transitions N . The efficiency of deliveryroutes by matching the corresponding metric functions ofdynamic routing remains to be compared [20].

There are three key algorithms that describe the partition ofthe set of nodes into disjoint neighborhood. The algorithm 1successively builds neighborhoods and analyzes their contentas long as the neighborhood containing a destination nodeis found. The other two algorithms are complementary. Thealgorithm 2 builds the first neighborhood relative to thebeginning of the route. Algorithm 3 describes the constructionof the second and subsequent neighborhoods.

Algorithm 1: BuildRings(x,y,RINGS)

1 /*the function returns rings (neighbours) from source todestination nodes if destination node was reached in lastring*/

2 /*x - source node*/3 /*y - destination node*/4 /*RINGS - set of rings */5 begin6 if RINGS ∈ ∅ then7 AddRootRing(x,RINGS);8 else9 AddNextRing(RINGS);

10 end11 if y ∈ RINGS[size] then12 return RINGS ;13 else14 return BuildRings(x,y,RINGS);15 end16 end

The neighborhoods method is always able to find a solutionto the simply connected configuration of sensors. Conversely,it is easy to show that the route obtained by the neighborhoodsmethod is the shortest of the entire set of possible routes.

Algorithm 2: AddRootRing(x,RINGS)

1 /*the function add root ring (first neighbourhood) toempty set of rings*/

2 /*x - source node*/3 /*RINGS - set of rings */4 begin5 RINGS[0]←− getNodeNeighbours(x)6 end

Algorithm 3: AddNextRing(x,RINGS)

1 /*the function add next ring (next neighbourhood) to setof rings*/

2 /*RINGS - set of rings */3 begin4 ring ←− ∅ ;5 for each i ∈ RINGS[size] do6 for each j ∈ getNodeNeighbours(i) do7 /*check that last ring and new ring don’t

already contain new node*/8 if j /∈ RINGS[size] ∧ j /∈ ring then9 ring ←− ring ∪ j ;

10 end11 end12 end13 RINGS ←− RINGS ∪ ring ;14 end

We found the optimal solution that is easy to prove bycontradiction. Suppose that the found route is not optimaland there is a shorter path containing N − 1 hopes. Thendestination node should appear in the N − 1 neighborhood,which contradicts the original statement.

IV. SIMULATION TECHNIQUE

In order to test our routing method a special simulatorwritten in Java was developed. It allows to specify of anarbitrary configuration of M sensors on a rectangular field ofsize K ∗L. Upper subtitle menu Creation Area is responsiblefor this function, the menu item Max X sets K, Max Y setsL, and the number of sensors M is prescribed in the SensorsCount. Each sensor is marked on the map with a range of twolimiting circles; all the sensors are numbered and that numberis shown inside the circles (see Figure 3)). We define a nodedensity θ as

θ =M

KL(1)

The simulator allows the creation of any number of rect-angular holes with a length Zi and width Wi; for this thecoordinates of the opposite vertices of a rectangle must beentered in the fields (Min X, Min Y) and (Max X, Max Y)of the Creation Hole section. Performing the tests describedin Section V, the size and location of holes are generated

randomly. Besides in real tests the node density θ is replacedby a coverage ratio η

η =πCR2

4KL(2)

where R is the radius of communication. That is, the connec-tion can be established with all the sensors inside the circle ofradius R centered at a given point, and the nodes within thatcircle are the first neighborhood. The number of remainingnodes C is obtained by subtracting from M the number ofsensors which fall in the area of voids

∑ni=1WiZi.

Then the simulator can build a set of neighborhoods fromthe beginning of the route and find the number N of theneighborhood which appears at the end node of the route.The backward pass will display a list of routes; each route isa sequence of nodes. The Find Route section is responsiblefor this process. A more detailed description of the simulatorcan be found in [21].

The simulator also enables finding of routes by the standardmethod of greedy forwarding (GF) and the hybrid method.In the standard method GF the coordinates of the nodesare additionally used to determine the nearest node to thedestination point. In the absence of the nearest point in thedirection of the target (the problem of local minimum), theright-hand rule takes effect, according to which obstacles arebypassed. This method GPRS is also implemented in thesimulator (Find Route By GPRS button).

The third method is a hybrid method, which involves, in theevent of a local minimum, application of the neighborhoodsmethod and its use to reach the final destination (Find RouteBy Hybrid button).

V. TEST RESULTS

For a comparison of the three routing protocols: greedyforwarding, hybrid protocol and the neighborhoods methodwe used the simulator described in the previous section. Withthis simulator arbitrary configurations of sensors and voidswere assigned. After fixing the sensors configuration we havegradually increased the number and size of voids, therebyreducing the coverage ratio η.

On the map of nodes multiple routes have been preselected,i.e. corresponding source and destination points are fixed. Forthese nodes the simulator finds routes for all three methods,including the number N of hops between the intermediatenodes of the route. Taking the result of an absolute oneprovided by the neighborhoods method, we can comparethe performance of the greedy forwarding and of the hybridprotocols. Figures 4-6 show the dependence of the route lengthN from the coverage ratio η for all three routing protocols.Since several routes were initially selected, the average lengthof the route appears on the final graphs. In addition we haverepeated the process of generation of voids several times, soeach point on the Figures 4-6 is obtained by averaging at least8 values.

In Figures 4-6 the average length of the route plotted on they-axis and the coverage ratio in decreasing order is delayed on

Fig. 3. PrintScreen of control interface of simulator

Fig. 4. Compare the route lengths for different protocols (initial coverageratio η = 4524%)

the horizontal axis. All three graphs clearly show an advantageof the neighborhoods method for routing in sensor networks.This advantage increases with a decrease in the coverage ratioη.

Fig. 5. Compare the route lengths for different protocols (initial coverageratio η = 3519%)

At the conclusion of this section we note that the neighbor-hoods method can also be used in the problems of inter-domain(global) routing in the Internet. This problem differs only innetwork scale and low dynamics.

Fig. 6. Compare the route lengths for different protocols (initial coverageratio η = 2513%)

VI. MODERNIZATION OF THE PROTOCOL FOR DYNAMICCONFIGURATION

Any type of routing in sensor networks has to be adapted todynamically changing the configuration of the sensors, sincemost of the tasks that can be applied to sensor networks requirethe movement of sensors.

In order to adapt any sensor network routing methods todynamic configuration, we suggest two approaches.

The first approach involves the introduction of the metricfunction, which allows to compare the performance of differentroutes [20]. The path metric is selected as the lowest signallevel Pj of the j route hop (j = 1, N ). I.e. the signal strengthof transmitting sensor Pj is compared to all j route hops andthe lowest level is selected as a metric P = minj=1,N Pj . Ofthe many possible i routes (i = 1,K) the one with the highestmetric will be selected.

Popt = maxi=1,K

minj=1,N

P ij , (3)

where P ij is the signal level at the j hop of the i possible

route.The second method uses the reduction of the communication

radius R from Egn. (2) for a single sensor, i.e. limiting thenumber of nearest neighbors. The reduction ∆R of commu-nication radius should be proportional to the time betweenupdates of the network ∆t configuration data and some speedv, which characterizes the relative change in the location ofsensors.

In order to estimate this reduction ∆R two sequential nodeconfiguration recorded through a time interval ∆t should beanalyzed. For arbitrary node Y it is easy to fix its neighborsYi, that is, those nodes with which a node Y can establisha connection. It should be noted that a node Y is selectedrandomly. The new value for signal strength P or the radiusof communication R can be easily found by comparing twosuccessive configurations of neighbors (Y1, Y2, ...Yk, ...Yn) and(Y ′1 , Y

′2 , ...Y

′k, ...Y

′m). If k nodes are the same for the two con-

Fig. 7. Communication radius for dynamical configuration

figurations, we can find the standard deviation of the receivedsignal R between the old and the updated configuration:

∆P =

√√√√1

k

k∑i=1

(P ′i − Pi)2 (4)

This value ∆P can be used to describe the change in thenodes configuration.

We denote Rmin the lower limit of the communicationradius at which the connection between the sensors is stillpossible (see Figure 7). Then, for successful communicationin the case of dynamic configuration of sensors, it is necessaryto increase the communication radius for the nearest neighborsthat belongs to the first neighborhood to the value:

R′ = Rmin − α∆R (5)

Here, α is a constant that may vary according to the motiontype. In tests conducted on our simulator α = 1. In order totest the modified protocol we add the ability to move nodesin our simulator:• at the same speed relative to the central node of the

neighborhood;• at variable speed (uniformly accelerated motion);• with variable acceleration.During the test series three configurations were built ac-

cording to the above moving laws. The third configurationwas based on the first two neighboring sets according to theselection rule (see Eqn. (5)). Further artificially constructedconfiguration is compared with the real neighboring nodes andthe percentage of matches is calculated.

Twenty tests were conducted, during which a new rangeof communication was designated and an attempt was madeto predict the new composition of the neighborhood nodes.

The average prediction accuracy is 0.90 for nodes moving atthe same speed, 0.89 for nodes moving at a variable rate and0.915 for sites with variable acceleration. That is, the methodis somewhat universal and does not depend on the type ofdisplacement.

VII. CONCLUSIONS

In this paper we designed and implemented testing methodfor the route length that shows the advantage of the neighbor-hoods method, which gives the shortest route. The advantageof this routing method increases in complex topology withdecreasing coverage ratio.

In addition, the undoubted advantage of the neighborhoodsmethod is the minimum set of data used to find the route. Weneed to know only the nearest neighbors of each node. Greedyforwarding method requires knowledge of the geographicalcoordinates of the node, which complicates the device becauseof the need to have a GPS module which increases the costof the sensor as well as power consumption.

In this paper a first attempt to summarize the proposedneighborhoods method for the dynamic configuration of sen-sors is studied and different ways to compensate for themotion sensors are discussed. In the future we are planning toimplement the proposed protocol on real sensor networks andwe have already started developing of the appropriate software.

VIII. ACKNOWLEDGEMENTS

This work was supported by grant of the Russian Foundationfor Basic Research (RFBR) 13-07-00381a.

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