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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

Relevant work Topology Control

Minimum Spanning Tree (MST) and Localized Minimum

Spanning Tree (LMST) Calculated with Dijkstras

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) best decision might not be

reached (even if it does exist)

Well-known CDS algorithm

Wu and Lis 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

Well-known CDS algorithm

Wu and Lis algorithm (Pruning Rules 1 2)

Open neighbor set N(v) u u is a

neighbor of v Closed neighbor set Nv

N(v)Uv

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

- A node v can be taken out from the CDS if there

exists a node u such that Nv is a subset of

Nu and the ID of v is smaller than the ID of u

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 r1 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

eliminations because ordering based on node ID

prevents this. As a consequence they incur

significantly excessive retransmissions - Others rely on a lot of local information, for

instance knowledge of k-hop neighborhood (k gt 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 assumptions

- WSN 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 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 suwswu denote the number of shortest paths

from u ? V to w ? V (by definition, suu0). - Let suw(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 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 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 computation

- At a first glance, NI computation seems

expensive, i.e., O(mn2) 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 pairs - Fortunately, we can do better than this by making

some smart observations. The improved algorithm

(CalculateNodeImportanceIndex) is quite

complicated and beyond the scope of this

presentation - THEOREM. The complexity of the algorithm

CalculateNodeImportanceIndex is O(nm) 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 12, 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 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

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 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 nodes and 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