*Node Clustering in Wireless Sensor Networks by Considering Structural Characteristics of the Network GraphNikos Dimokas1Dimitrios Katsaros1,2Yannis Manolopoulos14th ITNG Conference, Las Vegas, NV, 2-4/April/20071Informatics Dept., Aristotle University, Thessaloniki, Greece2Computer & Comm. Engineering Dept., University of Thessaly, Volos, Greece

* Wireless Sensor Network (WSN)Wireless Sensor Networks featuresHomogeneous devicesStationary nodesDispersed NetworkLarge Network sizeSelf-organizedAll nodes acts as routersNo wired infrastructurePotential multihop routes

* Communication in WSNCommunication between two unconnected nodes is achieved through intermediate nodes.Every node that falls inside the communication range r of a node u, is considered reachable.

* WSN - ApplicationsApplicationsHabitat monitoringDisaster reliefTarget trackingMany of these applications require simple and/or aggregate function to be reported.

Clustering allows aggregation and limits data transmissions.

* What is ClusteringNodes divided in virtual group according to some rulesNodes belonging in a group can execute different functions from other nodes.

Cluster memberClusterheadGateway nodeIntra-Cluster linkCross-cluster link

* Clustering in WSNInvolves grouping nodes into clusters and electing a CHMembers of a cluster can communicate with their CH directlyCH can forward the aggregated data to the central base station through other CHsClustering ObjectivesAllows aggregationLimits data transmissionFacilitate the reusability of the resourcesCHs and gateway nodes can form a virtual backbone for intercluster routingCluster structure gives the impression of a smaller and more stable networkImprove network lifetimeReduce network traffic and the contention for the channelData aggregation and updates take place in CHs

* Relevant work ClusteringBased on the construction of Dominating SetNodes belonging to the DS are carrying out all communicationRunning out of energy very soonBased on the residual energy of each nodeProposed ways to rotate the role of CH among nodes of clustersCan be easily combined with the algorithms of the first family

Our proposal : the GESC protocol supportsdynamically estimation of CHs depending on the requester node, and thus improvement of network lifetimea novel metric for characterizing node importancelocalizationminimum number of messages exchanged among the nodes

* Relevant work Topology ControlRelative Neighborhood Graph (RNG): An edge uv is included in RNG iff it is not the longest edge in any triangle uvw.Grabriel Graph (GG): An edge uv is included in GG iff the disk with diameter uv contains no other node inside it.Minimum Spanning Tree (MST) and Localized Minimum Spanning Tree (LMST): Calculated with Dijkstras algorithm and Li, Hou & Sha, respectively.sample graphMSTLMSTDelaunay Triangulation (DT), Partial Delaunay Triangulation (PDT), Yao graph (YG), etc: A lot of other (variants of) geometric structuresTopology Control: Choosing a set of links from the possible ones. Not exactly our problem. So graph-theoretic concepts, than geometric ones.

* Minimal Dominating SetA vertex set is DS (Dominating Set)Any other vertex connected to one DS vertexIt is CDS, if it is connectedIt is MCDS if its size is minimum among CDSDiscovery of the MCDS of a graph is in NP-completeDSCDS

* Motivation for new clustering protocolThe protocol should:be localized, and thus distributedfully exploit the locally available information in making the best decisionsbe computationally efficientminimize the number of message exchange among the nodesbe energy efficient and thus extend network lifetime. This could be achieved with the use of different nodes for relaying messagesnot make use of variants, e.g., node IDs, because a (locally) best decision might not be reached (even if it does exist)

* Well-known CDS algorithmEach node exchanges its neighborhood information with all of its one-hop neighborsAny node with two unconnected neighbors becomes a dominator (red)The set of all the red nodes form a CDSWu and Lis algorithm

* Well-known CDS algorithmA node v can be taken out from the CDS if there exists a node u such that N[v] is a subset of N[u] and the ID of v is smaller than the ID of u A node u can be taken out from the CDS if u has two neighbors v and w such that N(u) is covered by N(v)UN(w) and its ID is the smallest of the other two nodes IDs Open neighbor set N(v) = {u | u is a neighbor of v}Closed neighbor set N[v] = N(v)U{v} Wu and Lis algorithm (Pruning Rules 1 & 2)

* Heed protocol (1/2)Every sensor node has multiple power levels.Periodically selects CHs according to a hybrid of the node residual energy and node degree.TCP is the clustering process duration and TNO is the network operation interval.Clustering is activated every TCP + TNO seconds.Initial number of CHs is Cprob.The probability of a node to become a CH is CHprob.

The probability of a node to become a CH is CHprob.

* Heed protocol (2/2)Intracluster Intercluster communicationIntracluster communication is proportional to:Node degree (load distribution)1 / node degree (dense clusters)If variable power levels ara allowed for intracluster communication then select CHs using average minimum reachability power.

* Leach protocol (1/2)All nodes can transmit with enough power to reach the BS and the nodes use power control.Cluster formation during set-up phase and data transfer during steady-state phase.Each node elects itself as CH at the beginning of round r+1 with probability Pi(t). k is the number of clusters.

All nodes are CHs the same number of times.All nodes have the same energy after N/k rounds.

* Leach protocol (2/2)Every node elects as CH the node that requires the least energy consumption for communication.Every CH set-up a TDMA schedule and transmitted to the nodes. Every node could transmit data in the corresponding time-slot.

WeaknessLimited scalabilityCould be complementary to clustering techniques based on the construction of a DS

* Weakness of current approachesSome approaches can not detect all possible eliminations because ordering based on node ID prevents this. As a consequence they incur significantly excessive retransmissionsOthers rely on a lot of local information, for instance knowledge of k-hop neighborhood (k > 2), e.g., [WD04,WL04] Other methods are computationally expensive, incurring a cost of O(f2) or O(f3), where f is the maximum degree of a node of the ad hoc network, e.g., the methods reported in [WL01, WD03, DW04] and [SSZ02]some methods (e.g., [QVLl00,SSZ02]) do not fully exploit the compiled information; for instance, the use of the degree of a node as its priority when deciding its possible inclusion in the dominating set might not result in the best local decision

* Terminology and assumptionsWSN is abstracted as a graph G(V,E)An edge e=(u,v) exists if and only if u is in the transmission range of v and vice versa. All links in the graph are bidirectional.The network is assumed to be connectedN1(v) : the set of one hop neighbours of vN2(v) : the set of two hop neighbours of vN12(v) : combined set of N1(v) and N2(v) LNv : is the induced subgraph of G associated with vertices in N12(v)dG(v,u) : distance between v and u

* A new measure of node importanceLet uw=wu denote the number of shortest paths from u V to w V (by definition, uu=0). Let uw(v) denote the number of shortest paths from u to w that some vertex v V lies on. We define the node importance index NI(v) of a vertex v as:

Large values for the NI index of a node v indicate that this node can reach others on relatively short paths, or that v lies on considerable fractions of shortest paths connecting others. In the former case, it captures the fact of a possibly large degree of node v, and in the latter case, it captures the fact that v might have one (some) isolated neighbors

* The NI index in sample graphsIn parenthesis, the NI index of the respective node; i.e., 7(156): node with ID 7 has NI equal to 156.Nodes with large NI:Articulation nodes (in bridges), e.g., 3, 4, 7, 16, 18With large fanout, e.g., 14, 8, UTherefore: geodesic nodes

* The NI index in a localized algorithmFor any node v, the NI indexes of the nodes in N12(v) calculated only for the subgraph of the 2-hop (in general, k-hop) neighborhood reveal the relative importance of the nodes in covering N12 For a node u (of the 2-hop neighbourhood of a node v), the NI index of u will be denoted as NIv(u)

* NI computationAt a first glance, NI computation seems expensive, i.e., O(m*n2) operations in total for a 2-hop neighbourhood, which consists of n nodes and m links: calculating the shortest path between a particular pair of vertices (assume for the moment that there exists only one) can be done using bfs in O(m) time, and there exist O(n2) vertex pairsFortunately, we can do better than this by making some smart observations. The improved algorithm (CalculateNodeImportanceIndex) is quite complicated and beyond the scope of this presentationTHEOREM. The complexity of the algorithm CalculateNodeImportanceIndex is O(n*m) for a graph with n vertices and m edges

* Pseudocode for CalculateNodeImportanceIndex (1/2)

* Pseudocode for CalculateNodeImportanceIndex (2/2)

* Evaluation setting (1/2)We compare GESC to:WL 1+2, improved scheme incorporating the rules indicated MPR, the MultiPoint Relaying method described in [QVL00]SSZ, reported in [SSZ02], which was selected as a Fast Breaking Paper for October 2003Implementation of protocols using J-Sim simulation librarySensor network topologies with 100, 300, 500 nodes.Each topology consists of square grid unitsEach sensor node is uniformly distributed between the point (0,0) and (100,100)Two sensor nodes are neighbors if they are placed in the same or adjacent grid units.

* Evaluation setting (2/2)Varying levels of node degree from 4 to 10Run each protocol at least 100 times for each different node degree. Each time a different node is selected to start broadcastingPerformance metricEnergy dissipationBroadcast messagesLatency

* Impact of the #nodes (1/2)

* Impact of the #nodes (2/2)

* Impact of the average node degree

* Impact of energy consumption

* Conclusions and Future WorkDefined and investigated a novel distributed clustering protocol for WSN based on a novel localized metricThe calculation of this metric is very efficient, linear in the number of nodes and linear in the number of linksProved that it is very efficient in terms of communication cost and in terms of prolonging network lifetimeThe protocol is able to reap significant performance gains, reducing the number of rebroadcasting nodesSimulated an environment to evaluate the performance of the protocol and competitive protocols using J-Sim simulatorComparison with protocols based on residual energy (LEACH,HEED)

GESC GEodegic Sensor Clustering has been proven to prevail

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