Collision Aware Coloring Algorithm for wirelesssensor networks

Imen Jemili∗, Dhouha Ghrab∗, Abdelfettah Belghith∗, Bilel Derbel, Amine Dhraief∗University of Manouba, Tunisia

Email: imen.jemili@hanalab.org, dhouha.ghrab@hanalab.org, abdelfattah.belghith@ensi.rnu.tn

bilel.derbel@lifl.fr, amine.dhraief@hanalab.org

Abstract—Wireless sensor networks (WSN) have receivedsignificant attention over the last few years as they afforda growing number of applications in various fields. At thesame time, these networks provide numerous challenges dueto their constraints, primarily related to energy scarcity. Toovercome energy waste caused by collisions and contention basedalgorithm, the channel assignment mechanisms, like TDMA 1,seem to be an effective way for scheduling node transmissions.To solve channel assignment problems, graph coloring theoryhas been exploited in many research works, primarily in orderto assure collision-free communications. In this paper, we presenta novel distributed coloring algorithm for WSNs taking intoaccount the constraints of a real WSN environment. Our collisionaware coloring algorithm assures a 2 hop nodes coloring, in adeterministic time execution, without requiring a neighborhooddiscovering phase. Performance evaluation results have shownthe effectivness of our algorithm in terms of exchanged controlpackets per node as well as the chromatic number.

Keywords—Wireless Sensor Networks, Graph coloring, TDMAscheduling, collisions, interferences.

I. INTRODUCTION

Sensor networks are eliciting more and more interest fromthe research and the industry communities. They have beenenvisioned in a versatile number of application areas, likemedical, military and environmental fields [13], [17]. Wirelesssensor networks are composed of a large number of tinysensing self-powered nodes which gather information abouttheir environment and cooperate to communicate the collecteddata in a wireless fashion to a base station, called the sink.Such networks provide endless opportunities in many fields,however great challenges are imposed by the intrinsic char-acteristics of sensor nodes expressed in terms of the limitedtransmission power, the storage capacity and especially thelimited energy power. In fact, nodes are running on limited andgenerally non renewable power resources. Hence, protocolsoperating in such networks should be energy efficient tomaximize the network lifetime.Radio communication is one of the main sources of energydissipation. As nodes share the same medium, collisions andinterferences become very frequent, particularly in dense net-works. In such situation, packet retransmissions, due to packetloss, contribute also to deplete rapidly nodes energy. MediumAccess Control (MAC) protocols, managing the access tothe channel, have a direct impact on energy consumption. In

1TDMA : Time Division Multiple Access

this context, contention based mechanisms suffer from theirineffectiveness especially for dense WSNs, such as CSMA/CA2 [2], [3], [7]–[9]. In addition to the large amount of collisionsthat can be produced, the active sensing of the medium, therecourse to the backoff algorithm and packet retransmissions,typically performed by this access mechanism, are inefficientin term of energy consumption.In addition to energy consumption, minimizing transmissiondelay and assuring fairness when sharing the medium are otherimportant objectives to be considered. However, it is hard toassure these properties due to the nature of the contentionbased access to the channel. As an alternative solution, channelassignment mechanisms [14] can be deployed in order toorganize the access to the channel, like TDMA. Thanks to thismechanism, the packet sending time of each node is limitedand assigned to a specific time slot in a periodic time frame.Hence, assuring a collision free communication will be ableby meeting certain requirements when attributing time slots tonodes. Based on neighbor schedulings, nodes can turn off theirtransmitters or receivers, unless they are expecting to receiveor transmit a packet, reducing consequently the in vain energywaste [4].Recently, several researches have been interested into applyinggraph coloring theory to the channel assignment in wirelessnetworks. The aim is to assign to interfering nodes distin-guiched colors in order to assure a conflict-free communica-tion. Colors can represent in these cases slot times, frequenciesor codes [14]. Most of coloring algorithms, proposed in thiscontext, have been designed to work in an ideal environmentwhich assumes that all links are bidirectional and supposesthe absence of collisions. In this paper, we present a newdistributed coloring algorithm for wireless sensor networksoperating without any prerequisite neighborhood knowledge,a Collision Aware Distributed Coloring Algorithm (CADCA).Our main motivation is to take into account the intrinsiccharacteristics of a real WSN environment and to reducethe complexity of the coloring process in terms of timeconvergence and the number of control messages required toobtain a correct coloring.The remainder of this paper is organized as follow. Section2 reviews recent coloring algorithms in WSNs. We exposeour proposed algorithm CADCA in section 3. An analyti-cal study is proposed in section 4 to compute some usefulparameters for the performance evaluation. Then, in section5, we present conducted simulations in order to evaluate ouralgorithm. Finally, section 6 summarizes our important results,and discusses future works.

2CSMA/CA:Carrier Sense Multiple Access/Collision Avoidance

978-1-4673-2480-9/13/$31.00 ©2013 IEEE 1546

II. STATE OF THE ART

Graph coloring concerns the assignment of different colorsto all nodes in a graph while satisfying the constraints relatedto a certain problem. In wireless networks, coloring has beenexploited mainly to resolve interference and collision problemsby managing access to the channel [4], [5], [10]. The scarcityof spectrum requires efficient channel assignment techniqueswhich can be based on time, frequency or code divisionmedium access. Therefore, most of coloring algorithms aim toreduce the number of used colors needed to color the wholegraph, called the chromatic number. Recently, there has been alarge amount of works related to coloring in wireless networks.In [14], the authors proposed a 2-hop centralized coloringalgorithm, called Unified Algorithm. It consists on a labelingphase followed by a coloring phase. In order to organize thecoloring phase, the labeling phase allows assigning to eachnode a unique label between 1 and n, n is the number of nodesin the network. During the coloring phase, colors are chosenin a greedy fashion. They attribute to each node the leastcolor that can be assigned without violating any constraint.The algorithm initiates with coloring the node labeled nand progresses until the node labeled 1 is colored. Threeordering label heuristics have been studied : Random (RAND),Minimum Neighbors First (MNF) and Progressive MinimumNeighbors First (PMNF). DRAND, described in [15], is thedistributed version of RAND coloring algorithm. It assumesthat all nodes know their one and two hop neighbors. It isexecuted in rounds. In each round i, the algorithm performs thefollowing steps: With a probability Pi, each node A broadcastsa request message to its one-hop neighbors if it has not decidedyet on its time slot. The probability Pi is set to the inverse ofthe number of contending nodes (including itself) that have notdecided yet their slots in earlier rounds. These neighbors haveto reply by a grant message if they didn’t receive already otherrequests from other nodes than A. Otherwise, they will denythe request sent by A. If A receives grant messages from allits one-hop neighbors, it selects the least color available takinginto account its two-hop neighbors colors. Then, it broadcastsa release message to inform its one-hop neighbors. Theseneighbors will rebroadcast the received message to their one-hop neighbors. The basic idea describes the algorithm in adistributed synchronous message-passing model where everyoperation runs in a synchronous round and communicationis reliable. In an asynchronous environment, a new messagecalled re ject was required.

Finocchi et al proposed in [6] a simple 1-hop distributedcoloring algorithm, called the basic algorithm, organized alsoin several rounds. Initially, all nodes are asleep. Simultane-ously, a node v may wake up with a probability p. In eachround, currently uncolored nodes are assigned a tentative colorfrom their palette. In a conflict resolution step, nodes, with nonconflict colors, confirm their colors as final. The remainder ofnodes are uncolored, they return to the initial step to repeatthe execution of the algorithm. Coloring Unstructured RadioNetworks algorithm, depicted in [12], is a 1-hop coloringalgorithm for newly deployed sensor networks. The basic ideais to elect first a set of mutually independent leaders and toassociate each slave to a leader within its neighborhood. Thetask of the leader is to assign a unique color range to everynode in its cluster. Upon receiving the color-range, each nodeverifies the eventual conflict with neighbors belonging to adja-

cent clusters. In such situation, conflict nodes will choose thenext color in the color-range and verify with each other again.SERENA, presented in [11], is another distributed algorithmproposing a 3-hop coloring algorithm used to schedule nodeactivity. The basic idea is presented in an ideal environmentwith bidirectional links and no packet loss. The functionalbehavior of SERENA requires that each node already knowsits neighborhood up to 3-hops. Each node calculates its priorityequals to the cardinality of its 3-hop neighborhood. In case ofparity, node address will be considered as a second criterionto define the priority. A node colors itself, if and only if ithas the higher priority than its uncolored 3-hop neighbors, bychoosing the smallest available color. Then, it has to informits one up to 3 hop neighbors about the selected color. Thediffused packet contains the information about the address, thecolor, the node priority and the information about its one andup to 3 hop neighbors. The authors have also identified thedifferent types of color conflict caused by unidirectional linksand have studied different variants of SERENA to cope to copewith them. Since the size of the packet used by SERENA isvery large, the authors in [1] propose an optimized versionof SERENA, OSERENA (Optimized SERENA). The maincontribution of this version consists on optimizing the sizeof the exchanged packets.

III. CADCA ALGORITHM

In wireless network, the network connectivity is modeledby a unit disk graph (UDG) G(V,E), where V represents theset of vertices and E represents the set of edges. Nodes in Vare embedded in the plane. Each node is characterized by atransmission range r. An edge (u,v) in E exists between nodesu and v if and only if u and v are within the transmissionrange of each other.

Graph coloring problem concerns the assignment of differ-ent colors to all the nodes in a graph using a limited numberof colors while meeting the constraints. In context of wirelesssensor network, the coloring process is exploited especiallyfor optimizing resources allocation problems, like channelscheduling by adopting TDMA. In such problems, colors willrepresent time slots during which nodes can transmit theirmessages without collision risks. Nodes can experience acollision in two cases. First, a direct collision occurs if anytwo neighbors are transmitting in the same time. Second, ahidden collision can occur because of the hidden terminalproblem. In such situations, collided messages must be retrans-mitted, source of energy dissipation. To make a collision freescheduling TDMA, coloring must take into account these twotypes of collision. Previous proposed centralized approachesrequire the knowledge of the global network topology to beable to color the whole network, while most of the distributedapproaches rely on a reliable communication model that thatabstracts away problems such as interference, collisions or thehidden-terminal problem and necessitate the knowledge of khop neighborhood.In this context, we propose a novel distributed two hopscoloring algorithm CADCA. Our main objective is to presenta simple coloring algorithm with a deterministic executiontime. Taking into account the constraints of a real multihopwireless sensor environment constitutes the main characteristicof our algorithm, particularly collision occurrence responsibleof control packet loss and color conflicts. In real applications,

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without considering this issue, the functional behavior of thecoloring process will be negatively affected, due to lackinginformation required for node decision.

CADCA operates without requiring a neighborhood dis-covering phase to collect information about the k neighbor-hood. Each sensor node has no a-priori information aboutthe network, including its neighbors, the network topologyand the network size. However, we assume that every sensornode knows its position towards the sink and the informationabout the expected deployment density λ, a pre-estimate roughbound. Based on the estimated density, we can estimate themaximal degree δ of the network and calculate the maximalnumber of required colors. Based on the distance towards thesink, the network is divided into parallel and equidistant layerscentered on the sink node and having as the diameter thetransmission range. Each node is able to determine the distancein term of hop count towards the sink, and consequently todefine its layer.The basic idea of our algorithm is to reduce the number ofnodes executing the coloring process in a fixed time T in orderto reduce the eventual collisions between the control messagesexchanged during the coloring phase. To this end, we organizethe coloring process into layered phases. We assume that allthe nodes are synchronized thanks to an external agent.

Fig. 1: Layered process of CADCA

The coloring process will progress layer by layer. In orderto avoid interferences between nodes belonging to adjacentlayers, these nodes are not allowed to participate in the coloringprocess during the same phase. Indeed, since each node in layeri can have one and two hop neighbors that belong to layersi+ 1, i+ 2 and i− 1, i− 2, their simultaneous participation inthe coloring process can cause eventual collisions and interfer-ences. We impose the termination of the coloring process in aspecific layer before allowing nodes in the subsequent layer tostart the coloring process. Thus, to color the whole network,three phases are required respectively for nodes belongingto layers i+ 3 ∗ k, i+ 3 ∗ k + 1 and i + 3 ∗ k + 2, 0¡k¡n. Forexample, assuming that the network is divided into 9 layers,nodes belonging to layers 1, 4 and 7 will execute the algorithmin the first phase. Then, nodes belonging to layers 2, 5 and 8will be able to execute the algorithm in the second phase. Andfinally, in th third phase, the algorithm is executed by nodesin layers 3, 6 and 9. The layer concept allows us to reduce theamount of gathered information from neighbors to be recorded

by a given node to be able to verify the validity of the selectedcolor.Initially, we attribute a distinct palette to color a given layer.So, three disjoint palettes having the same size P1, P2 andP3 are required to color nodes belonging to layers i, i+1 andi+2. At a given layer, each coloring phase includes five stages.Initially, nodes are marked uncolored and unaffected. In thefirst stage, all nodes choose a tentative color and will competeto access to the medium to broadcast their color. Nodes,receiving less than two declaration messages, are authorizedto diffuse their declaration message. To be able to distinguishbetween participating nodes during the different stages, thesenodes are labeled as CH. The remaining nodes are affectedthe GW label and have to retry during the second stage.The distinction between nodes into CH and GW allows usto discern the different types of color conflicts.

With the lack of neighborhood information and the colli-sion occurrence, color conflicts can occur. Three other stagesare required to resolve these eventual conflicts. In the follow-ing, we present a detailed description of each stage. Then, weexplain possible conflicts and we define adopted rules to copewith them.

A. Stage1: Cluster-heads declaration

In this stage, each node selects a color from its paletteand has to inform its immediate neighbors. To broadcast itsdeclaration message, a node competes for channel access bychoosing a random delay. The choice of the backoff valuedepends on the node position in the layer. In fact, in orderto reduce collision probability in the same layer, we adopt asecond division of the same layer based on the distance towardsthe sink. Nodes, belonging to the first sublayer, are allowed toselect an even backoff value, while the nodes of the secondsublayer are allowed to choose an odd backoff value. Besides,in order to minimize color conflict risks, nodes belonging tothe first sublayer can select their color form [c1,cn/2] and theother nodes pick their color form [cn/2+1,cn], where c1 and cn

are respectively the first and the last colors in the palette.

The random delay timer is decremented according to thedefined CSMA/CA backoff algorithm. A node will be affectedthe GW label, if two or more correct declaration packets arrivebefore the random delay timer has expired. Such node cancelsthe remaining random delay and the pending declaration trans-mission. Otherwise, the node will be marked CH and sends itsdeclaration.

A declaration message indicates the sender identifier (ID),the selected color, a list of the known one hop neighbors andtheir colors, a list of backoff values of intercepted collisionsand a list of conflict nodes containing the IDs of involved nodesand the conflict color. Upon receiving neighbor declarations,a node has to update the list of its one hop neighbors andthe list of its two hop neighbors. It updates, also, its paletteof colors by omitting chosen colors by its one and two hopneighbors in order to avoid color conflicts. Based on exchangeddeclarations, a GW node can detect eventual color conflictsbetween its CH neighbors. In such situation, it keeps the IDsof conflict nodes and their color. And, it waits for the nextstage to claim the node having the biggest ID to change itscolor, in order to avoid that the two nodes change their colorin the same time.

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B. Stage2: Gateway declaration

The main objective of this second stage is the declarationof nodes GW and the verification of colors chosen by CHnodes. Mainly, only GW nodes are allowed to send declarationmessages. Since nodes are synchronized, time is divided intodiscrete time slots with the same size. This stage requiresx time slots, where x is equal to the size of the palette ofcolors (maximal number of one and two hop neighbors inthe same layer). At the beginning of this stage, each GWnode chooses a color from its palette and waits for the slotassociated to its color to be able to send its declaration. Themessage declaration contains the ID and the color of thesender, the list of its known one hop neighbors and theircolors, a list containing the ID and the color of neighborsin conflict and finally the list of slots during which a nodehas intercepted a collision in the current stage. Each node,receiving a declaration message, updates its lists of one andtwo hop neighbors and its palette by removing the set ofselected colors. We consider the example illustrated in figure2. The node 3 gains the GW status since it has received thedeclaration messages of nodes 0 and 8 during the first stage.So, it has to include these two neighbors in its conflict list,since they have selected the same color.

Fig. 2: Example of the coloring process

Based on GW declarations, a CH node verifies if it isconcerned by a color conflict through checking the list of nodesin conflicts. In case of color conflict, it changes its color andcontinues its attempt to validate its color in the future stage.Otherwise, it validates its color. A CH node is allowed to senda notification during its associated slot to alert its CH neighborsabout the color conflict detected during the previous stage.

C. Stage3: CHs color correction and verification of GWscolors

During the second stage, CH and GW nodes inform theCH nodes in conflict. The list of nodes in conflict includes CHnodes which have selected the same color and send correctlytheir declaration. In case of collision occurrence, the backoffvalue will be indicated in the declaration message. In thisway, CH nodes, which have selected previously this backoffbefore transmitting their declaration, will be aware that theyare involved in a collision. They will be concerned by thisstage in order to choose a new color from the up-to-datepalette and diffuse it. This stage is divided in x slots likethe previous stage. Only CH nodes participate in this step bysending declaration messages in their associated slots.

It is important to update information about neighbor colorsin case of color changes. This stage contributes to exchangemissed information about neighborhood and to verify colorsof GW nodes. The CH nodes will be able to notify GW nodes

about detected color conflicts. Referring to the example offigure 2, the GW nodes 4 and 6 select the same color 8,consequently they will send their declaration during the sametime slot. The CH node 5 will notify them by indicating theconflict color in its declaration.

D. Stage4: GWs color correction and verification of CHscolors

Similar to the previous stage, this stage aims to correctcolors of GW nodes in conflict and to verify colors of CHnodes after updates. Each GW node, concerned by a colorconflict, selects another available color. It is necessary for nodeto complete missed information about their two hops neighborsand their colors based on exchanged messages, in order toavoid new conflicts. Only GW nodes are authorized to senddeclaration messages in their associated slots. Based on GWdeclarations, a CH node verifies if it is concerned by a colorconflict through checking the list of nodes in conflicts andproceeds in the same manner as in stage 2.

E. Stage5: Conflict resolution

During the two first stages, we allow CH and GW nodesto choose their color and to inform their immediate neighborsthanks to declaration messages. The two other stages aimto verify the correctness of attributed colors and to resolvepossible conflicts. However, some conflicts can persist and wetry to resolve them in this stage. In fact, conflict nodes, notifiedduring the 4 stage, have changed their colors and they don’thave the opportunity to inform their neighbors. Such nodes areable to send their declaration in their associated slot.

Furthermore, nodes belonging to previous layer can partic-ipate to resolve persistent conflicts. Such situation can occurswhen conflict nodes do not share neighbors in the same layer,Conflict resolution will be more detailed in the next paragraph.

F. Possible conflicts and rules

A color conflict appears when two nodes in the 2 hopneighborhood choose the same color. We can distinguish be-tween color conflicts between two CHs, two GWs or betweena CH and a GW. Conflicts between CHs occur during the firststage. In such case, nodes could have chosen different or thesame backoff value. In the first situation, this conflict can besolved easily by a common neighbor. This node will receivecorrectly the declaration of these CHs and will be able to detectthe conflict when comparing their colors. During the secondstage, it can notify them forcing the node with the highestID to change its color. In the second situation, the collisiondue the simultaneous node declarations will prevent neighborsfrom identifying the involved senders and to be sure ofcolor conflict. These neighboring nodes intercept this collisionand can indicate the backoff value leading to collision sincewe decrement this delay timer according to the CSMA/CAmethod. Besides, during the third stage, when these conflictnodes will retransmit their declaration in the slot associatedto their color, their transmissions will collide. Based on thetime slot position, neighbors will be able to determine theconflict color and to warm them. Since the identities of conflictnodes are anonymous, both of them will try to change theircolor. Conflicts between two GWs can be detected in the same

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manner as the last case of conflict. Finally, conflicts between aCH and a GW are easy to detect by neighboring nodes, sincethey don’t transmit their declarations in the same stage andtheir messages don’t collide. If some cases of conflicts arenot resolved in the four first stages, in the fifth stage nodesbelonging to adjacent layers can step in and help in resolution.We can resume the rules adopted to solve conflicts in thesefollowing points:

• If a node has detected a conflict between two neigh-bors (without collision), it includes their IDs and theconflict color in its declaration message. The conflictnode with the greater ID has to change its color, whenthe color conflict is between two CH or two GW.In case of a conflict between CH and GW, if thenotification is sent by a GW, the CH node must changeits color. Otherwise, the GW node should change itscolor.

• If a node has intercepted a collision, it is unableto identify the senders. Its declaration message willinclude a notification about the slot during which hehas intercepted the collision.

• If a node has detected a conflict after sending hismessage in the current stage, it will be authorizedto send the notification in the next stage during itsassociated slot.

• If there are conflict cases not resolved during thefour phases, neighboring nodes in adjacent layers canintervene to notify nodes in conflict to change theircolors in the conflict phase 5. Color conflict resolu-tion in this stage must be validated by receiving anacknowledgment from the sender of the notification.The time slot should be large enough so that the nodereceives this acknowledgment during the same slot.

IV. ANALYTICAL ANALYSIS

In this section, we calculate some useful parameters for theperformance evaluation of CADCA.

a) Maximal size of the palette: CADCA is a two hopscoloring algorithm that consists on attributing different colorsto one and two hops neighbors. Hence, to compute the sizeof the palette, we must first find the maximal number of oneand two hops neighbors, including the node itself, that we noteDegree’. Considering r as the transmission radius, the one andtwo hops neighbors are situated in the circle of radius 2∗r andcentered on the node itself. Hence, assuming that the densityis equal to d nodes per squared meters, the Degree’ can becomputed by the following expression:

Degre′ = 4d×π× r2 (1)

In general, the maximum size of the palette is equal to thetotal number of the one and the two hops neighbors. Thus, wecan express it by the following expression:

|Palette|total = 4d×π× r2 (2)

Since the coloring mechanism processes in layer, it isnecessary to calculate the maximal size of a palette withina layer. But, first, we must determine the maximal number of

one and two hops neighbors within one layer. It is equal tothe number of nodes situated in the intersection of the circlecentered on the node itself with a radius equals to 2 ∗ r withthe two arcs of the layers defined by the distance towards thesink. To determine this maximal degree, we consider the worstcase. To have the maximum number of neighbors within alayer, the node must be situated in the middle of the layer. Weapproximate this intersection by the surface of the rectangledefined by width equals to r and length equals to 4 ∗ r asillustrated in the figure 3. The width is equal to r since thenode is situated in the middle of the layer and distant of r/2from the two arcs of the layer. The length is equal to 4 ∗ r

Fig. 3: Intersection between a circle with radius 2r and arcsof the adjacent layers with diameter r

since the diameter of the circle covering the one and two hopneighbors is equal to the double of the transmission range.Hence, the maximal size of a palette is equal to the numberof nodes that we can find in the surface of the rectangle.

|palette|max = Sur f ace(rectangle)∗ d = 4d× r2 (3)

Subsequent layers i, i+1 and i+2 are affected distinguishedpalettes with the same size. The total size of a palette is equalto 3 times the size of a palette within a layer. Its expressionis given by the following:

|palettetotal|max = 3×|palette|max

= 12d× r2

b) The time execution of the algorithm: The executiontime of the algorithm is the time required for a node to beable to return to operating normally. It represents the timespent to color all nodes in the network. To finalize coloringall the layers, CADCA needs 3 times the termination time ofcoloring one layer as layers i and i+ 3 ∗ k, 1 < k < n executethe algorithm in parallel. The figure 4 schematizes the 5 stagesfor coloring process within a layer.

Talgo = 3× (CWmax× slot + 2 ∗ declarationtime

+ 4×|palette|max× slot)(4)

V. PERFORMANCE EVALUATION

In order to evaluate the performances of our coloringalgorithm, we conduct exhaustive simulations over severaltopologies. Simulations were performed using OMNET++ [16]

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Fig. 4: Time needed for coloring a layer

simulator and results are averaged over several simulation runs.The specific metrics that we focused on over the differentperformed tests are:

- The chromatic number : The number of used colors tocolor the whole graph;

- The startup time : The time required to color the wholenetwork;

- The average number of exchanged packets per node :The average number of exchanged packets per node duringthe coloring process and the conflicts evolution.

The first scenario aims to show the scalability of ouralgorithm. To this end, we test CADCA in various networktopologies with different network sizes and different densitiesfor each size. Hence, we generate several topologies in gridwith 100, 200, 300, and 400 nodes and densities of 0.015/m2,0.027/m2 and 0.04/m2. These configurations are generateduniformly by increasing the number of nodes as well as thearea of the sensor field in order to keep the average density ofnodes constant. Results relative to the chromatic number aredepicted in figure 5.

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We remark that the chromatic number depends stronglyon network density and it is almost independent of the nodenumber. These results are expected since when the densityincreases, the number of one and two hop neighbors increases.Consequently, to assign different colors to the one and twohop neighbors we need more colors. Figure 5 shows also thatour algorithm improves network performance (if we exploitit as TDMA scheduling) and that this improvement is moreremarkable when the network size increases. In fact, thedistance between curves points within the first bisectrices givesthe gain obtained by CADCA with regard to classical TDMA

where each node have a different slot time from other nodesin the network.

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Fig. 6: Average number of exchanged controls packets pernode

Figure 6 shows the average number of packets transmittedper node during the coloring process. We observe that themaximal number of messages sent by each node is 4 and it isslightly more remarkable for the high density. Based on thisnegligible difference, we can conclude that the average numberof sent packets does not depend neither on the network densitynor on the network size. According to the algorithm process,each node can be either a CH or a GW. Each CH node isallowed to send a message in the first and the third steps ofthe algorithm, and each GW node is allowed to transmit amessage during the second and the fourth steps. In the last step,all nodes can send a message. We don’t forget the exceptionsfor nodes CH or GW in order to be able in some cases to sendurgent packets out of their steps. Thanks to these notificationsconcerning eventual conflicts, we aim to resolve these conflictsmore quickly.

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Fig. 7: The running time of the algorithm with network sizevariation

Figure 7 exhibits the scalability of CADCA in term ofrunning time. As it is clear, the running time depends onlyon the network density. Indeed, when the density increases,the chromatic number increases. And, as each of the last

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Fig. 8: Impact of the variation of the network density on the conflicts number,(a) density=0.04; (b) density=0.027; (c)density=0.015

four stages are composed of x slots, where x is equal tothe chromatic number, the number of slots will rises up ineach stage and consequently the time execution becomes moreimportant.The first color choice by anu node during the first steps ofthe coloring process (stages 1 and 2) can’t ensure the absenceof conflicts. We distinguish between three types of conflicts :between two CH nodes, between two GW nodes and betweena CH and a GW. In figure 8, we expose results related tothe number of conflicts of each type for different densityvalues during the different stages of the algorithm. We observethat the number of conflicts for the different types increaseswith density. This augmentation is more prominent in the firststage. This is explained by the increase of the probability ofcollision occurrence when the number of contending nodesincreases.However, the conflict number converges to zero atthe end of the algorithm thanks to the rules used for conflictresolution.In fact, in case of a collision occurrence, it will bedifficult to identify the conflict-nodes, initially. Based on theexchanged notifications during the subsequent stages, we areable to resolve most of the conflicts. The recourse to the helpof nodes belonging to the previous layer is also possible incase of a persistent conflict.

VI. CONCLUSION

In this paper, we presented a new distributed two-hopscoloring algorithm for wireless sensor networks. Our simpledistributed coloring mechanism does not rely on a prelim-nary neighborhood discovery phase in order to alleviate thenetwork from excessive conrol packets. Our algorithm takesinto account the constraints of the wireless environment,especially collision and interfernece issues. By adopting alayered coloring process, we aim to reduce the probability ofcollision occurrence and the eventual color conflicts and welimit the number of exchanged messages and the amount ofrecorded information at every node. Simulations results pointout the scalability of our algorithm in terms of the chromaticnumber, the average exchanged control packets per node andthe terminaison time. For future works, further exploitationsof our coloring algorithm are currently being investigated toameliorate multi-hop and multi-path routing in WSNs whiletaking into account energy constraints.

REFERENCES

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