Single-Node Cluster Reduction in WSN andEnergy-Efficiency during Cluster Formation

Chérif Diallo, Michel Marot, Monique Becker

SAMOVAR CNRS Research Lab – UMR 5157; Dept Réseaux et Services de Télécommunications (RST)Institut TELECOM; TELECOM SudParis; 9, Rue Charles Fourier – 91011 Evry CEDEX, France

Email:{cherif.diallo, michel.marot, monique.becker}@telecom-sudparis.eu

Abstract—A large Ad Hoc network can be represented asseveral sets of clusters. Each cluster contains one or more nodesand has its clusterhead (or caryomme) chosen following anelection based on an appropriate criterion. The clustering inwireless networking adds scalability, reduces the computationcomplexity of routing protocols, allows data aggregation andthen enhances the network performance. Several studies havefocused on clustering algorithms, providing some mechanismswell suited to wireless sensor networks (WSN). The MaxMinclustering algorithm proposed by [1] was generalized, correctedand validated in [2],[3] which added the use of criteria functionsto choose appropriate clusterheads. We take part in this workby examining comparative results of different criteria that revealsingle-node cluster phenomena. A single-node cluster is a clusterof which the only member is its clusterhead itself. In WSNclustering, the density of single-node clusters is a performancecriterion. We use MaxMin in a cold chain monitoring applicationwhich shows that single-node clusters have negative impactson the energy consumption. In this paper we compare severalcriteria including the "remaining energy" and the "link qualityindicator (LQI)". We propose an effective manner of usingthe LQI which is among the best performant criteria. Wealso propose a simple mechanism to reduce single-node clusterphenomena which highly enhances the energy efficiency.Index Terms—Wireless Sensors Networks (WSN); Clustering;

MaxMin; Single-node Cluster; Link Quality Indicator (LQI).

I. INTRODUCTIONIn a cold chain monitoring application, due to the size of a

warehouse which hosts large numbers of pallets, provided eachwith a temperature sensor, the WSN can reach several hun-dreds of nodes which collaborate for sending alarms towardsthe base station (BS). This application specifically collectsrare events (alarms) to ensure the proper monitoring of thesystem. If the temperature is over a threshold, an alarm will begenerated; this "interesting event" is then sent towards the BS.In such a context, network clustering techniques add scalabilityfeature and then reduce the computation complexity of datagathering and routing protocols. MaxMin [1] is a popularclustering algorithm which has been subjected to numerouspublications. Originally, it used the node address (node ID)as the criterion for selecting caryommes (clusterheads). Thisalgorithm was generalized, corrected and validated in [2],[3]which proposed a theoretical study of the multihop clusteringin WSN; [2],[3] added the use of criteria functions to selectcaryommes. In this paper, we take part in this work bystudying more general caryomme selection criteria, such as:

the Remaining energy level, the Degree of connectivity, theProximity with respect to the base station, the Link QualityIndicator (LQI), and a hybrid criterion composed of any pairsof these above criteria. The use of the LQI as defined in theZigBee standard [4],[5] is less efficient. So we propose aneffective manner of the LQI use which reduces the energyconsumption. In network clustering, a single-node cluster is acluster of which the only member is the clusterhead itself. Byrunning the MaxMin algorithm for a simple WSN example,we notice a significant density of single-node clusters. It isinteresting to study this phenomenon since a less effectivecriterion leads to a higher density of single-node clustersand vice versa. Obviously, a non-clustered network can beconsidered as a clustered one having as many single-nodeclusters as the network size, hence the importance of hav-ing a low density of single-node clusters. Two main stepscompose clustering schemes: the caryomme selection followedby the cluster construction. After the caryomme selection,the canonical method allows a step by step construction ofthe clusters in which the non-clustered nodes select theircaryomme upon the reception of its announcement in the d-neighborhood. The canonical method is used by Delye in [2].In this paper, we optimize the canonical method by proposinga simple mechanism which reduces the density of single-node clusters. Applying the MaxMin algorithm to a coldchain monitoring application, we show how high densitiesof single-node clusters could have negative impacts on thenetwork performance especially on the energy efficiency. Inthis application MaxMin is used to select the caryommeswhich manage their respective clusters upon a TDMA basedorganization. Regular sensors send alarms to their respectivecaryommes which aggregate them and then forward datatowards the BS using the "Link Reliability based RoutingProtocol" (L2RP) we have proposed in [6]. L2RP is run withthe weighted round robin load balancing mechanism usingthe "MinLQI" metric. The rest of this paper is organized asfollows. After an overview of the related works in the next part,the next one gives a brief summary of the generalized MaxMinalgorithm proposed by [2] and [3]. In the fourth part, a simpleWSN example allows us to better understand the concretesingle-node cluster phenomenon produced by MaxMin. Then,we present the LQI-based and composite clusterhead selectioncriteria (in the fifth section) before presenting the proposed

978-1-4244-8435-5/10/$26.00 ©2010 IEEE

single-node cluster reduction mechanism in the sixth section.The last section presents simulation results pertaining to acold chain monitoring application (presented in the seventhsection).

II. STATE OF THE ARTIn some clustering protocols nodes become caryommes after

a randomized timer (CLUBS in [7] and RCC in [8]). However,the criterion which commonly determines the choice of thecaryomme is the node address ( [9], ACE-C and ACE-Lin [10]), the remaining energy level (LMSSC in [11]) orthe degree of connectivity (such as MECH in [12]). It canalso be based upon a weight basis of several of these abovecriteria (HEED in [13] ). In LEACH [14], clusterheads areselected under a criterion built on a probability function. In[15], Klaoudatou and al. were interested in a WSN applicationdesigned for medical surveillance, in which they selected theclosest node to the BS as caryomme. Multihop clusteringalgorithms address two main challenges: first, the questionarises how to optimally choose caryommes and, secondly,how to construct the parental relationship between regularnodes and their caryommes in such a way that any commonsensor can reach its clusterhead within k hops, that is to say,how to construct an optimally independent k-dominating set.Unfortunately, finding such a set is an NP-complete problem[1], so some heuristics have been proposed. In [16], Daiand Wu proposed three algorithms to build k-dominating setswhich are also k-connected. One method is to compare sensorvalues (criteria) such as node ID, "remaining energy level",weight, etc. (cf. KHOPCA in [17], CABCF in [18], MaxMin in[1]). It is possible that two nodes have the same criterion value.Then, in [19] and [2], the authors propose to consider thepair composed by the degree of connectivity of the node andits address. Some works ([13], [20],[21],[22]) introduced thenotion of single-node clusters as a performance criterion forevaluating clustering protocols, whithout showing why single-node clusters are not a desirable feature in WSN. HEED[13] estimates the percentage of non single-node clusters toprove the protocol effectiveness. Furthermore, in the state ofthe art, it lacks for a comparative study of different criteriathat can be used by the MaxMin algorithm. Also, the relatedworks do not take into account a possible use of the linkquality indicator (LQI) as a criterion for selecting caryommes.[2] and [3] offer a valuable theoretical generalization ofMaxMin by presenting results on the degree of connectivity,without addressing the issue of single-node clusters producedby MaxMin. In this paper, we study the single-node clusterphenomenon produced by MaxMin and compare the impact ofthe following clusterhead selection criteria: "remaining energylevel", "degree of connectivity", "proximity with respect to thebase station", "link quality indicator (LQI)". We propose aneffective manner of using the LQI which is among the bestperformant criteria. We also propose a simple mechanism forreducing single-node clusters. An application designed for acold chain monitoring system shows the negative impacts ofsingle-node clusters on the network performance.

III. THE GENERALIZED FORM OF MAXMIN ALGORITHMThis algorithm is proposed by [2],[3] as a generalization

of the earlier MaxMin algorithm proposed by [1]. It takesplace in 2d+1 rounds. The first round consists of informationexchanges to initialize the algorithm. The following d-roundsare the floodmax phase, which is followed by the floodminphase composed of last d rounds.The WSN can be modeled as a graph G = (V,E), wheretwo nodes are connected by an edge if they can communicatewith each other. Let x ∈ V be a node in the WSN. N1(x)is the neighbourhood of the node x. Let ν be a bijectivefunction defined in V which is a totally ordered set.Initial phase: k = 0,

∀ x ∈ V, W0 = ν(x), S0(x) = x (1)

Floodmax phase: k ∈ [|1, d|],Assuming that ∀x ∈ V ,Wk−1(x) and Sk−1(x) are known in aprevious step. Let yk(x) be the unique node in N1(x) definedby:

∀ y ∈ N1(x) \ {yk(x)} , Wk−1(yk(x)) > Wk−1(y) (2)

Wk and Sk are calculated as follows:

∀ x ∈ V, Wk(x) = Wk−1(yk(x)), Sk(x) = yk(x) (3)

Floodmin phase: k ∈ [|d+ 1, 2d|],Assuming that ∀x ∈ V ,Wk−1(x) and Sk−1(x) are known in aprevious step. Let yk(x) be the unique node in N1(x) definedby:

∀ y ∈ N1(x) \ {yk(x)} , Wk−1(yk(x)) < Wk−1(y) (4)

Wk and Sk are calculated as follows:

∀ x ∈ V, Wk(x) = Wk−1(yk(x)), Sk(x) = yk(x) (5)

The set S of clusterheads is defined by :

S = { x ∈ V, W2d(x) = ν(x)} (6)

IV. SINGLE-NODE CLUSTER PHENOMENONWe run the MaxMin algorithm on a WSN example, where

the remaining energy of sensors is used as the criterion forselecting caryommes. So in this example the ν function isdefined as follows:

∀ x ∈ V, ν(x) = (f(x), id(x)) (7)

Where id(x) returns the address of the node x. The totalordering in V is defined as follows:

∀x ∈ V, ν(x) > ν(y) ⇐⇒ (f(x) > f(y))or (f(x) = f(y) and id(x) > id(y)) (8)

In this example, we consider the WSN in Fig. 1 where theneighbourhood relationships between the 8 sensors are definedby the hedges of the graph.

TABLE IRUNNING MAXMIN ALGORITHM (D=1) FOR THE WSN IN FIG. 1

node id 1 2 3 4 5 6 7 8

W0 100 90 95 70 100 85 85 1051 2 3 4 5 6 7 8

S0 1 2 3 4 5 6 7 8

W1 100 95 100 100 105 100 100 1051 3 1 5 8 5 5 8

S1 1 3 1 5 8 5 5 8

W2 100 95 95 100 100 100 100 1051 3 3 1 5 1 5 8

S2 1 2 2 3 4 3 7 5

Fig. 1. Clusters Produced by the MaxMin Algorithm (d = 1)

TABLE IIRUNNING MAXMIN ALGORITHM (D=2) FOR THE WSN IN FIG. ??

node id 1 2 3 4 5 6 7 8

W0 100 90 95 70 100 85 85 1051 2 3 4 5 6 7 8

S0 1 2 3 4 5 6 7 8

W1 100 95 100 100 105 100 100 1051 3 1 5 8 5 5 8

S1 1 3 1 5 8 5 5 8W2 100 100 100 105 105 105 105 105

1 1 5 8 8 8 8 8S2 3 3 6 5 8 5 5 8

W3 100 100 100 100 105 100 105 1051 1 1 5 8 5 8 8

S3 1 2 1 3 4 3 5 5W4 100 100 100 100 100 100 105 105

1 1 1 1 5 1 8 8S4 1 2 1 3 4 3 5 5

Fig. 2. Clusters Produced by the MaxMin Algorithm (d = 2)

This MaxMin example, ran for d = 1, produces 4 caryommes

Fig. 3. Example of a WSN with LQI values of the links

(1,3,5,8). The clusters represented by caryommes 1 and 8 aresingle-node clusters (Fig. 1).The same WSN computed in MaxMin algorithm, run for d

= 2, produces 3 caryommes (1,5,8). The cluster representedby the clusterhead 8 is a single-node cluster (Fig. 2). Aswe can see on the example above, the single-node clusterphenomenon is a real fact. This phenomenon is especiallyimportant, because the density of single-node clusters (50%and 33%) produced by MaxMin is not negligible. We arenow interested in studying this phenomenon by comparing thecriteria presented in the following section

V. LQI-BASED AND COMPOSITE CLUSTERHEADSELECTION CRITERIA

A. Link Quality Indicator (LQI)

In the Zigbee standard [4],[5], the LQI measurement isdefined as a characterization of the strength and/or qualityreception of a packet. The use of the LQI result by the networkor the application layers is not specified in [4],[5]. The LQImeasurement is performed for each received packet, and theresult is reported to the MAC sublayer as an integer rangingfrom 0 to 255. The minimum and maximum LQI values (0 and255) are associated with the lowest and the highest qualityIEEE 802.15.4 reception detectable by the receiver, and theLQI values in between are distributed between these two limits[4], [5].For moteiv′s Tmote Sky [23] sensors equipped with

chipcon′s CC2420 [24], the LQI values range from 50 to 110.Even so, we stick with the ZigBee standard [4],[5] becausesome manufacturers, such as Sun-SPOT [25] and WiEye [26],are still using the standard LQI values. Then, we use thestandard values (i.e. 0, 255), instead of those of CC2420.In this paper, we define three LQI based clusterhead selectioncriteria: AvgLQI, MaxLQI and MinLQI. The AvgLQI is theaverage calculated from the LQI values of all the links betweenthe node and its neighbors. AvgLQI values give a characteri-zation of sensors throughout their respective coverage quality.This criterion might be useful in the context of the WSNdeployed in a warehouse which hosts a large number of pallets,one upon the other. Such an environment is proned to highunreliability of wireless links. The MaxLQI criterion is themaximum LQI value which matches to the standard definitionof the LQI [4],[5] used in the MultiHopLQI routing algorithm[27],[28]. As for the MinLQI, it is the minimum value beyond

TABLE IIILQI CRITERIA VALUES RELATED TO THE WSN IN FIG. 3

Sensor ID 1 2 3 4 5 6 7 8AvgLQI 150 120 115 120 130 135 80 120MaxLQI 150 120 150 140 180 180 80 120MinLQI 150 120 100 100 120 180 80 120

the given LQI threshold. For example (Fig. 3), assuming thatthe LQI threshold for an acceptable link quality is 100, theMinLQI for node 5 is 120 (LQI of link 5-8) instead of 80(LQI of link 5-7). Thus, Table III gives LQI values for theWSN in Fig. 3.

B. Composite criteria (Hybrid)In this paper, we define the composite criteria (hybrid) as

follows:

Hybrid(LQI,Ci) = α ∗ LQI + (1− α) ∗ Sc(Ci) (9)

Hybrid(Ci, Cj) = α ∗ Sc(Ci) + (1 − α) ∗ Sc(Cj) (10)

where Sc(Ci) is a scale function which returns remainingenergy values comparable to LQI values. It helps avoidingthe composite criteria to be strongly influenced by the Ci

component in equation (9):

Sc(Ci) = β +Ψ ∗ log(1 + (Ci − Ci,min))

log(1 + Ci,max)(11)

Where Ci is a criterion, Ci,min (resp. Ci,max) is the minimum(resp. maximum) value of Ci. If Ci is the remaining energy ofthe node, Ci,min represents the value under which, the sensoris considered dead (battery depletion); while Ci,max is theinitial amount of energy provided with each sensor. β = 50,ψ = 255.Like the LQI criteria definitions, we can also define AvgHy-brid, MaxHybrid and MinHybrid criteria depending onwhether, we are respectively considering AvgLQI, MaxLQIand MinLQI as defined in Table III.

VI. SINGLE-NODE CLUSTER REDUCTION (SNCR)After the selection of caryommes using the generalized form

of the MaxMin algorithm, clusters are then built, according tothe following mechanism. This mechanism is compared, laterin simulations, with the canonical method presented in [2],[3].• At the end of the MaxMin floodmin phase, each cary-omme initializes a timer WT inversely proportional to itsdegree of connectivity.

• At the expiration of the timer WT , the first caryommewhich has the highest degree of connectivity, informs itsneighbourhood that it is a selected clusterhead by sendinga "CH-INFORM-MSG" packet.

• The "CH-INFORM-MSG" message contains the cary-omme ID id(CHi) and has a time-to-live equal to d (thesame d as in the MaxMin algorithm). It is retransmitted toall nodes within d-hops from the originating clusterhead.

• Upon reception of a "CH-INFORM-MSG" message, eachneighbor which has not yet chosen a clusterhead, chooses

the sender as caryomme, decrements the TTL and thenforwards the "CH-INFORM-MSG" message to its neigh-bors.

• Upon reception of a "CH-INFORM-MSG" message, byanother clusterhead, it creates a list "SRC-INFORM-MSG" of senders which contains node IDs id(Si) ofsensors from which the message is received. This node IDis not necessarily the one of the originating caryomme.

• The caryommes send their "CH-INFORM-MSG" mes-sages in descending order of their respective degree ofconnectivity, until all caryommes have announced theirstate.

• A clusterhead of single-node cluster recognizes itself bythe fact that its "CH-INFORM-MSG" message is notretransmitted by any of its neighbors. Such a clusterheadinspects its "SRC-INFORM-MSG" list. If its list is notempty, it chooses the first node of its list as caryomme. Ifits "SRC-INFORM-MSG" list is empty, then the cluster-head has no neighbor. This denotes a single-node clusterarising from the topology deployment of the WSN.

The waiting time WT is calculated according to the followingformula:

WT (CHi) = τ +ζ

1 + log(1 + δi +id(CHi)

Γ ∗ δi)(12)

Where τ and ζ are small nonzero positive constants, δi is thedegree of connectivity of the clusterhead CHi and id(CHi)returns its address. Γ is a constant which is larger than thenetwork size (Γ = 106, for example). This timer functionavoids collisions between caryommes having the same degreeof connectivity. If δi = 0, then the clusterhead CHi has noneighbor. This also denotes a single-node cluster arising fromthe topology deployment of the WSN.

VII. COLD CHAIN MONITORING APPLICATIONA. Network organization and deploymentThe application is designed for a cold chain monitoring

purpose. Its goal is to monitor a warehouse by logging alarmsoriginating from sensors. Alarms are generated when thesensed temperature exceeds a given threshold. After a firstphase consisting of hello exchanges, the MaxMin clusteriza-tion algorithm is run. Then, each caryomme manages a TDMAorganization (Fig. 4) by assigning one slot time (TSlot(Si))to each one of its cluster members. To save energy, sensorsswitch in "sensing mode" and turn off their respective radioswhile leaving sensor modules in the active mode in orderto continue collecting events. Then, in the data collectionphase (TData = 1s) sensors wake up in turn upon theirrespective time slots in which each sensor sends its alarms(kalarm = 64bytes) to its respective caryomme. Since, thecaryommes do not necessary form a connected backbone,all sensors wake up during the routing phase (Fig. 4) inwhich each caryomme aggregates (kdata = 512bytes) thereceived alarms and then sends towards the BS. In the routingphase, only caryommes are sources of data packets. Otherregular sensors are only participating in the routing effort

Fig. 4. Active/Sleep mode organization of the WSN

by retransmitting received data towards the BS. The routingprotocol used is the "Link Reliability based Routing Protocol"(L2RP) we have proposed in [6]. It is run with the weightedround robin load balancing mechanism using the "MinLQI"metric. The routing phase (TRouting = 1min) is followedby a long sensing one (TSleep = 8min59s). With these timevalues, the total duration of a complete cycle (Sensing, Datacollection, Routing) is TCycle = 10min. The assigned timeslots to each regular clustered sensor are computed as follows:

TSlot(Si) =TData

ηi(13)

Where ηi is the number of regular sensors which are in thesame cluster as Si.In the simulation model N sensors are randomly deployed

over an area of length L=100m, and width l=100m. The basestation is located at the (0,0) location. Each node generatesalarms, which are sensed data over than the temperaturethreshold Tempmin, following the Poisson process of parame-ter λ = 1. The transmission range of each sensor (including theBS) is R = 20m. Each node knows the value of its remainingenergy level, its location and that of the BS. At the beginningof the network deployment, the BS broadcasts a messagecontaining its location. This information is then retransmitto all sensors in the network. In this phase, the degree ofconnectivity and the initial LQI values are calculated.

B. Energy consumption modelAs in [29] and [30], let ETx(k, d) the energy consumed to

transmit a k bits message over a distance d [14]:

ETx(k, d) = Eelec ∗ k + εamp ∗ k ∗ d2 (14)

Let ERx the energy consumed to receive a k bits message:

ERx(k, d) = ERx−elec(k) = Eelec ∗ k (15)

Eelec = 50nJ/bit and ε = 100pJ/bit/m2 (16)

The energy consumed by a sensor Si in Active/Sleep modesis calculated following the model proposed by [31]:

ERadio(Si) = PActive ∗ TActive + PSleep ∗ TSleep (17)

As in [31], PActive = 1040mW and PSleep = 200mW .

C. LQI Model for Simulation PurposeAfter the WSN deployment in the warehouse, the BS

initially broadcasts a message containing its location. This in-formation is then retransmitted to all sensors in the network. Inthis phase, each node knows its degree of connectivity. Then,initial LQI values are calculated by using the LQI(Si, Sj)function defined below (similarly to the scale function Scdefined in the composite criterion in equation (11)):

LQI(Si, Sj) = β +Ψ ∗ log(1 + (γi

j − γimin))

log(1 + γimax)

(18)

γij =

1

d(i, j)(19)

γimin = min

Sj∈N 1(Si)γ(i, j) (20)

γimax = max

Sj∈N 1(Si)γ(i, j) (21)

where β = 50, ψ = 255 and d(i, j) is the distance seperatingSj from Si. β = 50 ensures that the LQI value is not zerowhen the sensor Sj is located in the transmission range of thenode Si. The choice of this model is guided by experimentalresults shown in [32] and [33] which stated that the LQI de-creases when the distance between nodes increases in Zigbee-based WSN. As we can see, LQI(Si, Sj) �= LQI(Sj, Si).Hence, the model allows to take into account asymetricalaspects of wireless links. This LQI model is only used forsimulation purpose, so sensor nodes do not compute theseformulas.

VIII. SIMULATION RESULTSSimulations, using Matlab, are run for a network size rang-

ing from 100 to 500 nodes. The performance results presentedhere are obtained by averaging the results for 100 differentsimulations for each scenario, except for the scenario of thecaryomme location (Fig. 16, 17 and 18) for which 80 differentsimulations were run. For each simulation, a new randomnode layout is used. In all simulation results presented below,α = 0.5 for the composite criteria as defined in equations (9)and (10). Then, the MinHybrid criterion (resp. MaxHybrid) iscomposed of 50% of the "Remaining energy" criterion and of50% of the "MinLQI" (resp. MaxLQI) criterion.

A. Single-Node Cluster Reduction (SNCR)The Fig. 5 shows the average density of clusterheads pro-

duced by the MaxMin algorithm combined with the canonicalmethod of cluster construction. The "Proximity with respectto the BS" criterion has an average density (around 45%)relatively high compared to other criteria. It is followed bythe "Remaining Energy Level" criterion (between 25% and30%), and then by the "Degree of Connectivity" criterion.The AvgLQI, MinLQI and MaxLQI criteria produce lowerdensities of clusterheads which decrease when the networkdensity increases.

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Proximity with respect to the BSRemaining Energy LevelDegree of ConnectivityAvgLQIMinLQIMaxLQI

Fig. 5. Average density of clusterheads (canonical method)

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Fig. 6. Average cluster sizes divided by network size (canonical)

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Remaining Energy LevelDegree of ConnectivityProximity with respect to BSMaxLQIMinLQIMaxHybridMinHybrid

Fig. 7. Average density of single-node clusters (canonical method)

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Fig. 8. Average density of single-node clusters (canonical method)

The Fig. 6 shows the ratio of the average cluster size dividedby the number of sensors in the network. The clusters areformed by the canonical method. This result confirms theprevious one, because the criteria that produced the mostof caryommes (Fig. 5) are those which have the smallestaverage ratio of cluster size. So it is consistent to have in thedecreasing order of the average ratio of cluster size: MaxLQI,MinLQI, AvgLQI, degree of connectivity, and "RemainingEnergy Level", "Proximity with respect to the BS".The Fig. 7 shows the average density of single-node clusters

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Fig. 9. Average density of single-node clusters (canonical method)

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Fig. 10. Average density of single-node clusters (canonical method)

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MaxHybridMinHybridMinLQIMaxLQIProximity with respect to the BSDegree of ConnectivityRemaining Energy Level

Fig. 11. Average ratio of single-node cluster reduction (SNCR)

produced by MaxMin combined with the canonical methodof cluster formings. The "Proximity with respect to the BS"(from 62% to 75%)and "Remaining Energy Level" (between30% and 60%) criteria produces high densities of single-nodeclusters which increase when the network density increases.This explains the previous result (Fig. 5) in which these twocriteria produced more clusters than other criteria. The densi-ties for the Hybrid and LQI criteria remain low at around 20%.The "degree of connectivity" criterion has the lowest density ofsingle-node clusters (under 10%). The Fig. 8 for "RemainingEnergy Level" (resp. Fig. 10 and Fig. 9 for MinLQI andthe "degree of connectivity") shows that the average densityof single-node clusters is decreasing when the MaxMin dparameter increases. For the "degree of connectivity" criterion,there is no single-node clusters as soon as d = 4 (Fig. 9).The Fig. 11 shows the single-node cluster reduction den-

sity produced by the proposed single-node cluster reduction(SNCR) mechanism. For all studied criteria, the reductionpercentage is 100%. This means that all the single-nodeclusters, produced by MaxMin run with the canonical method,have been eliminated by this reduction mechanism, whatever

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Fig. 14. Average ratio of clusterheads (Degree of connectivity, d=1)

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Fig. 15. The average ratio of clusterheads (MinLQI, d=1)

the criterion under consideration. Accordingly, in a wirelesssensor network where there is zero non-connected node (i.eeach sensor has at least one neighbor), this mechanism totallyeliminates the single-node cluster phenomenon.The figures (Fig. 12,13,14 and 15) shows the average ratio

of clusterheads for each criterion by comparing the results ob-tained with the canonical method of cluster constructions andwith the single-node cluster reduction mechanism (SNCR).SNCR produces less number of clusterheads than the canonicalmethod. The gap, due to single-node clusters, is the largest

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Fig. 16. Positions of caryommes (SNCR, Proximity-BS, d=1)

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Fig. 17. Positions of caryommes (SNCR, Degree of Connectivity, d=1)

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Fig. 18. Positions of caryommes (SNCR, MinLQI, d=1)

for the "Proximity with respect to the BS" criterion (20% to45%, Fig. 13). The difference is also relatively substantial forthe "Remaining Energy Level" criterion (from 10 to 20%).The results for other criteria are: degree of connectivity (6%,constant gap), MinLQI (decreasing differences from 6 to 2%when the network size increases)

B. Positions of caryommesThe Figures 16, 17 and 18 display the clusterheads selected

with MaxMin combined with the single-node cluster reduction(SNCR) mechanism. These results show that the locations ofcaryommes are not optimal when the "Proximity with respectto the BS" (Fig. 16) and the "degree of connectivity" (Fig. 17)are used as criterion. As for MinLQI (Fig. 18), clusterheadsare sufficiently outspread which denotes better locations forclusterheads. The locations of caryommes generated by thedegree of connectivity criterion are not optimal because ifa node has a high degree of connectivity, then its closestneighbors also have a high degree of connectivity. So thiscriterion promotes the creation of neighboring nodes as clus-terheads. Likely, for the "Proximity with respect to the BS",if a node is close to the BS, its nearest neighbors are also

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MinLQIMaxLQIRemaining Energy LevelDegree of ConnectivityProximity−BS

Fig. 19. Average rate of remaining energy (SNCR, d=1)

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MaxMin d = 1MaxMin d = 2MaxMin d = 3MaxMin d = 4

Fig. 20. Average rate of remaining energy (Proximity-BS)

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MaxMin d = 1MaxMin d = 2MaxMin d = 3MaxMin d = 4

Fig. 21. Average rate of remaining energy (Degree of Connectivity)

close to the BS. Conversely, choosing the MinLQI criterionpromotes the election of sensors enough apart from each other.This leads to a better geographical distribution of caryommes.If caryommes are not sufficiently separated from each other,this affects the energy efficiency of the network. Indeed, whena "regular node" communicates with its own caryomme, theother neighboring caryommes hear the communication whichis not intended to them. Therefore the energy consumptionincreases. Furthermore the risk of collision also increases be-cause two neighboring nodes which have distinct clusterheadscould try to communicate simultaneously with their respectiveclusterheads which are also in the same radio range.

C. Energy consumptionThe application consists of three main phases: the MaxMin

phase, the data collection phase and the routing phase (Fig.4). The MaxMin phase is composed of clustering ones (initial,floodmax and floodmin phases), followed by the step of clusterformation (canonical vs. SNCR).The Figures 19, 20 and 21 show the average rate of

the remaining energy after running the MaxMin algorithm:floodmax, floodmin and cluster formation using SNCR. The

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Fig. 22. Average rate of energy consumed by phase (Energy, d=1)

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Fig. 23. Average rate of the consumed energy by phase (SNCR, d=1)

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Fig. 24. Average rate of the consumed energy by phase (Proximity-BS, d=1)

MaxMin energy consumption depends on the criterion usedto select caryommes. MaxMin consumes less energy withMinLQI. The "Proximity with respect to the BS" and the"degree of connectivity" criteria consume much more energy.The Fig. 20 denotes that increasing the value of d (d=1,2,3),has the effects to increase the MaxMin energy consumptionfor the "Proximity with respect to the BS" criterion for whichthe energy consumption begins to decrease since d = 4.Conversely, for other criteria (Fig. 21 shows the "degree ofconnectivity" criterion), increasing the value of d has theeffects to decrease the energy consumption (since d = 1) ofthe MaxMin algorithm. Increasing the d parameter increasesthe number of rounds for floodmax and floodmin. Thus, theenergy consumption also increases in these phases when thedepletion of the caryomme density is not significant (Fig.20). However, when the d parameter increases, the number ofcaryommes (sometimes considerably) decreases and thereforethe number of "CH-INFORM-MSG" messages. The overallenergy consumption decreases when the depletion of thenumber of caryommes is important (Fig. 21).The Figures 22 and 23 show the average energy consumed

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Data Collection phase : Canonical MethodRouting phase : Canonical MethodMaxMin phase : Canonical Method

Fig. 25. Average rate of the consumed energy by phase (Proximity-BS, d=1)

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MinLQI : SNCRMinLQI : Canonical MethodRemaining Energy : SNCRRemaining Energy : Canonical MethodMaxLQI : SNCRMaxLQI : Canonical Method

Fig. 26. Average rate of the remaining energy (d=1)

in each phase, considering the "Remaining energy level" andMinLQI criteria. The Figures 24 and 25 are related to theenergy consumption of the "Proximity with respect to the BS"criterion. We compare the case where clusters are formed bythe canonical method with the single-node cluster reductionmechanism (SNCR). These results show that the MaxMinphase is the one that consumes less energy. Moreover, itsrate of energy consumption is relatively low (from 2 to 7%)compared with energy expenditure in the data collection phasewhere each sensor sends alarms towards its caryomme (from38 to 45%). The routing phase, in which alarms are aggregatedand sent from each caryomme to the base station, consumesmore energy (approximately from 60 to 48%).The Fig. 26 shows the average rate of the remaining energy

in the network after a complete cycle (node deployments,MaxMin clustering, data collection, routing and sensing phaseFig. 4). The MaxLQI, MinLQI and remaining energy criteriaare compared in the two mechanisms of cluster formations(canonical and SNCR). The SNCR mechanism is more energyefficient than the canonical method. This is explained byprevious results in which SNCR totally eliminates single-node clusters and then produces less number of clusterheadsthan canonical method. Due to the high density of single-node clusters, the large amount of energy spent in the routingphase causes a less energy efficient clustering scheme whencanonical method is used. This result denotes that a highdensity of single-node clusters has negative effects on energyconsumption. Moreover, MinLQI is more energy-efficient thanMaxLQI which matches the Zigbee standard definition.The Fig. 27 displays the average rate of the remaining

energy in the network after a complete cycle for the followingcriteria: "proximity with respect to the BS", "degree of con-nectivity" and "MinLQI". These criteria are compared in both

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MinLQI : SNCRMinLQI : Canonical MethodProximity−BS : SNCRProximity−BS : Canonical MethodConnectivity : SNCRConnectivity : Canonical Method

Fig. 27. Average rate of the remaining energy (d=1)

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Data Collection phaseRouting phaseMaxMin phase

Fig. 28. Average rate of the consumed energy by phase (SNCR, d=1)

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Degree of ConnectivityProximity with respect to the BSRemaining Energy LevelMinLQI

Fig. 29. Average ratio of the energy consumed by the Routing phase

canonical and SNCR mechanisms. MinLQI is more energyefficient than other criteria. The "degree of connectivity"criterion has the worse energy efficiency, its average rate of theremaining energy significantly decreases. The Fig. 27 showsthat this criterion is also less energy efficient with clustersproduced by the canonical method. The figures 28 and 29(for SNCR) denote that the "degree of connectivity" criterionconsumes much more energy in the routing phase comparedwith other critera (compare also Fig. 23 with Fig. 28). Thisexplain why this criterion is less energy efficient than others:the relative locations of selected caryommes are not optimal. Insuch a situation this criterion leads to high energy consumptioneven if it produces low number of single-node clusters (Fig.7).

IX. CONCLUSIONIn this report, we studied the single-node cluster phe-

nomenon pertaining to the MaxMin clustering algorithm. Wecompared several clusterhead selection criteria and then pro-posed a simple single-node cluster reduction (SNCR) mecha-nism. We also proposed a performant manner of using LQI-based criteria (MaxLQI, MinLQI). The density of single-node

clusters is relatively high for the "Proximity with respect tothe BS" criterion and for the "Remaining energy level". The"degree of connectivity" criterion has the lowest average den-sity of single-node clusters. However, even if the phenomenonexists it is less important for LQI and Hybrid criteria. The"Proximity with respect to the BS" criterion is less performingthan the "Remaining energy" which provides intermediate per-formance. The "degree of connectivity" is the worse energy-efficient criterion because the locations of selected caryommesare not optimal. By setting a given LQI threshold, i.e avalue of acceptable LQI, and considering the lowest LQIvalue beyond this threshold, we obtain the optimal MinLQIcriterion which highly enhances the energy-efficiency. ThusMinLQI is better than MaxLQI which matches the Zigbeestandard definition. Single-node clusters have the drawbackof increasing the energy consumption. The proposed single-node cluster reduction mechanism eliminates all connectedsingle-node clusters in the WSN, and then improve the energyefficiency of the network. This work shows that, although it isimportant to be performant in selecting clusterheads, the stepof forming clusters is also crucial. In this step, reducing thedensity of single-node clusters should be the primary objectivein order to achieve energy efficiency.

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