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Node Clustering in Wireless Sensor Networks by Considering Structural Characteristics of the Network Graph

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### Node Clustering in Wireless Sensor Networks by Considering Structural Characteristics of the Network Graph

Nikos Dimokas1

Dimitrios Katsaros1,2

Yannis Manolopoulos1

1Informatics Dept., Aristotle University, Thessaloniki, Greece

2Computer & Comm. Engineering Dept., University of Thessaly, Volos, Greece

4th ITNG Conference, Las Vegas, NV, 2-4/April/2007

Wireless Sensor Network (WSN)

Wireless Sensor Networks features

- Homogeneous devices
- Stationary nodes
- Dispersed Network
- Large Network size
- Self-organized
- All nodes acts as routers
- No wired infrastructure
- Potential multihop routes

Communication in WSN

- Communication 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 - Applications

- Applications
- Habitat monitoring
- Disaster relief
- Target tracking
- Many of these applications require simple and/or aggregate function to be reported.
- Clustering allows aggregation and limits data transmissions.

What is Clustering

Cluster member

Clusterhead

Gateway node

Intra-Cluster link

Cross-cluster link

- Nodes divided in virtual group according to some rules
- Nodes belonging in a group can execute different functions from other nodes.

Clustering in WSN

- Involves grouping nodes into clusters and electing a CH
- Members of a cluster can communicate with their CH directly
- CH can forward the aggregated data to the central base station through other CHs
- Clustering Objectives
- Allows aggregation
- Limits data transmission
- Facilitate the reusability of the resources
- CHs and gateway nodes can form a virtual backbone for intercluster routing
- Cluster structure gives the impression of a smaller and more stable network
- Improve network lifetime
- Reduce network traffic and the contention for the channel
- Data aggregation and updates take place in CHs

Relevant work – Clustering

- Based on the construction of Dominating Set
- Nodes belonging to the DS are carrying out all communication
- Running out of energy very soon
- Based on the residual energy of each node
- Proposed ways to rotate the role of CH among nodes of clusters
- Can be easily combined with the algorithms of the first family
- Our proposal : the GESC protocol supports
- dynamically estimation of CHs depending on the requester node, and thus improvement of network lifetime
- a novel metric for characterizing node importance
- localization
- minimum number of messages exchanged among the nodes

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Relevant work – Topology ControlMinimum Spanning Tree (MST) and Localized Minimum Spanning Tree (LMST): Calculated with Dijkstra’s algorithm and Li, Hou & Sha, respectively.

MST

LMST

sample graph

Relative 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.

Delaunay Triangulation (DT), Partial Delaunay Triangulation (PDT),Yao graph (YG), etc: A lot of other (variants of) geometric structures

- Topology Control: Choosing a set of links from the possible ones. Not exactly our problem. So graph-theoretic concepts, than geometric ones.

Minimal Dominating Set

- A vertex set is DS (Dominating Set)
- Any other vertex connected to one DS vertex
- It is CDS, if it is connected
- It is MCDS if its size is minimum among CDS
- Discovery of the MCDS of a graph is in NP-complete

DS

CDS

Motivation for new clustering protocol

- The protocol should:
- be localized, and thus distributed
- fully exploit the locally available information in making the best decisions
- be computationally efficient
- minimize the number of message exchange among the nodes
- be energy efficient and thus extend network lifetime. This could be achieved with the use of different nodes for relaying messages
- not make use of “variants”, e.g., node IDs, because a (locally) bestdecision might not be reached (even if it does exist)

Well-known CDS algorithm

Wu and Li’s algorithm

- Each node exchanges its neighborhood information with all of its one-hop neighbors
- Any node with two unconnected neighbors becomes a dominator (red)
- The set of all the red nodes form a CDS

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Well-known CDS algorithmWu and Li’s algorithm (Pruning Rules 1 & 2)

A 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

Open neighbor set N(v) = {u | u is a neighbor of v}

Closed neighbor set N[v] = N(v)U{v}

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

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 communication
- Intracluster 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.
- Weakness
- Limited scalability
- Could be complementary to clustering techniques based on the construction of a DS

Weakness of current approaches

- Some approaches can not detect all possible eliminationsbecause ordering based on node ID prevents this. As a consequence they incursignificantlyexcessive retransmissions
- Others rely on a lot of “local” information, forinstance knowledge of k-hop neighborhood (k > 2), e.g., [WD04,WL04]
- Other methodsare computationally expensive, incurring a cost of O(f2) or O(f3), where f is themaximum degree of a node of the ad hoc network, e.g., the methodsreported in [WL01, WD03, DW04] and [SSZ02]
- some methods(e.g., [QVLl00,SSZ02]) do not fully exploit the compiled information; forinstance, the use of the degree of a node as its priority when deciding itspossibleinclusion in the dominating set might not result in the best local decision

Terminology and assumptions

- WSN is abstracted as a graph G(V,E)
- An edge e=(u,v) exists if and onlyif u is in the transmission range ofv and vice versa. All links in the graph arebidirectional.
- The network is assumed to be connected
- N1(v) : the set of one hop neighbours of v
- N2(v) : the set of two hop neighbours of v
- N12(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 importance

- Let σuw=σwu denote the number of shortest paths from uV towV (by definition, σuu=0).
- Let σuw(v) denote the number ofshortest paths from u to w that some vertex vV lies on.
- We define thenode importance indexNI(v) of a vertex v as:
- Large values for the NI index of a node v indicate that this node can reach otherson relatively short paths, or that v lies on considerable fractions of shortestpaths connecting others. In the former case, it captures the fact of a possibly large degreeof node v, and in the latter case, it captures the fact that v might have one (some) “isolated” neighbors

The NI index in sample graphs

In 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, 18
- With large fanout, e.g., 14, 8, U
- Therefore: geodesic nodes

The NI index in a localized algorithm

- For any nodev, the NI indexes of the nodes in N12(v) calculatedonly for the subgraph of the 2-hop (in general, k-hop) neighborhood reveal the relative importance of the nodes in coveringN12
- For a node u (of the 2-hop neighbourhood of anode v), the NI index of u will bedenoted as NIv(u)

NI computation

- At 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 momentthat there exists only one) can be done using bfs in O(m) time, andthere exist O(n2) vertex pairs
- Fortunately, we can do better than this by making somesmart observations. The improved algorithm (CalculateNodeImportanceIndex) is quite complicated and beyond the scope of this presentation
- THEOREM. The complexity of the algorithm CalculateNodeImportanceIndex is O(n*m) for agraph with n vertices and m edges

Evaluation setting (1/2)

- We compare GESC to:
- WL1+2, improved scheme incorporating therules indicated
- MPR, the MultiPoint Relaying method described in [QVL00]
- SSZ, reported in [SSZ02], which was selected as a Fast Breaking Paper for October 2003
- Implementation of protocols using J-Sim simulation library
- Sensor network topologies with 100, 300, 500 nodes.
- Each topology consists of square grid units
- Each 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 10
- Run each protocol at least 100 times for each different node degree. Each time a different node is selected to start broadcasting
- Performance metric
- Energy dissipation
- Broadcast messages
- Latency

Conclusions and Future Work

- Defined and investigated a novel distributed clustering protocol for WSN based on a novel localized metric
- The calculation of this metric is very efficient, linear in the number of nodesand linear in the number of links
- Proved that it is very efficient in terms of communication cost and in terms of prolonging network lifetime
- The protocol is able to reap significant performance gains, reducing the number of rebroadcasting nodes
- Simulated an environment to evaluate the performance of the protocol and competitive protocols using J-Sim simulator
- Comparison with protocols based on residual energy (LEACH,HEED)
- GESC – GEodegic Sensor Clustering has been proven to prevail

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