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

1
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
2
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

3
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.

4
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.

5
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.

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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

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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 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.

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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
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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)

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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

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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

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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.

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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.

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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.

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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

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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

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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

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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

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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

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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)

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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

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Pseudocode for CalculateNodeImportanceIndex (1/2)
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Pseudocode for CalculateNodeImportanceIndex (2/2)
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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.

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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

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Impact of the nodes (1/2)
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Impact of the nodes (2/2)
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Impact of the average node degree
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Impact of energy consumption
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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