CLUSTERING SCHEMES FOR MOBILE AD HOC NETWORK

Speaker： Fu-Yuan ChuangAdvisor： Ho-Ting WuDate： 2006.04.25

Outline

Introduction Clustering Scheme Overview Classifying Clustering Schemes DS-based clustering

Wu’s CDS AlgorithmChen’s WCDS Algorithm

Summary of DS-based Clustering

Introduction

Dynamic routing is the most important issue in MANETs

A flat structure encounters scalability problem Proactive routing protocols is O(n^2) Reactive routing sheme:

RREQ flooding over the whole network Route setup delay

A hierarchical architecture

Clustering Scheme Overview

Virtual group Clusterhead

a local coordinator, performing intra-cluster transmission arrangement, data forwarding

Clustergateway non-clusterhead node with inter-cluster links access neigh

boring clusters, forward information between clusters

Clustermember ordinary node, non-clusterhead node without any inter-clus

ter links

Three Benefits

spatial reuse of resources to increase the system capacity the same frequency or code set

routing The generation and spreading of routing information can be

restricted in the set of clusterheads and clustergateways an ad hoc network appear smaller and more stable in

the view of each mobile terminal when a mobile node changes its attaching cluster, only nod

es residing in the corresponding clusters need to update the information

The cost of clustering (1/3)

Explicit control message for clustering Clustering requires explicit clustering-related informati

on exchanged between node pairs

Ripple effect of re-clustering The re-election of a single clusterhead may affect the

cluster structure of many other clusters and completely alter the cluster topology over the whole network

The cost of clustering (2/3)

Stationary assumption for cluster formation Assume that mobile nodes keep static when cluster

formation is in progress

Constant Computation round Computation round is the number of rounds that a

cluster formation procedure

The cost of clustering (3/3)

Communication complexity The total amount of clustering-related message

exchanged for the cluster formation

Classifying Clustering Schemes(1/3)

DS-based clusteringFinding a (weakly) connected dominating set to

reduce the number of nodes participating in route search or routing table maintenance

Low-maintenance clusteringProviding a cluster infrastructure for upper layer

applications with minimized clustering-related maintenance cost

Classifying Clustering Schemes(2/3)

Mobility-aware clustering Utilizing mobile nodes’ mobility behavior for cluster

construction and maintenance and assigning mobile nodes with low relative speed to the same cluster to tighten the connection in such a cluster

Energy-efficient clustering Avoiding unnecessary energy consumption or balancing

energy consumption for mobile nodes in order to prolong the lifetime of mobile terminals and a network

Classifying Clustering Schemes(3/3)

Load-balancing clustering Distributing the workload of a network more evenly into

clusters by limiting the number of mobile nodes in each cluster in a defined range

Combined-metrics-based clustering Considering multiple metrics in cluster configuration,

including node degree, mobility, battery energy, cluster size

DS-based clustering

A dominating set of a graph G= (V, E) is a vertex subset S V⊆ , such that every vertex v V is either ∈in S or adjacent to a vertex of S

A connected dominating set (CDS) of a graph G is a dominating set whose induced graph is connected

DS-based clustering(cont.)

Table-driven routing Only codes in the CDS are required to construct and

maintain the routing tables

On-demand routing The route search space is limited to the CDS

To keep a DS connected and with approximately minimum size is not a trivial task

DS-based clustering AlgorithmWu’s CDS Algorithm Marking Process

To find CDS Prune redundant nodes from CDS

To reduce the size of CDS

Marking Process

Define a network as a graph G = (V,E) Initially, all nodes are unmarked Every v exchanges its N(v) with all its neig

hbors Mark v if there exists 2 unconnected neigh

bors

Example

A B C E

D

Open neighbors set of all nodes:

N(A) = {B,D}

N(B) = {A,C,D}

N(C) = {B, E}

N(D) = {A, B}

N(E) = {C}

After step 2:

A: N(B), N(D)

B: N(A), N(C), N(D)

C: N(B), N(E)

D: N(A), N(B)

E: N(C)

Prune redundant nodes from CDS Assign a distinct id, id(v) to each vertex v i

n G Define N[v] as a closed neighbor set of v

Prune redundant nodes from CDS Rule 1: Considers two vertices v and u in G’.

If N[v] N[u] in G, and id(v) < id(u),change the marker of v to F if node v is marded

Prune redundant nodes from CDS Rule 2: Assume u and w are two marked neighb

ors of marked vertex v in G’. If N(v) N(u) U N(w) in G and id(v) = min{id(v), id(u), id(w)}, then unmark v.

DS-based clustering AlgorithmChen’s WCDS Algorithm Reduce the number of clusters by relaxing the

connectivity requirement The subgraph weakly induced by S(S⊆V) is the

graph <S>w=(N [S], E ∩ (N [S]×S)). <S>w includes the vertices in S and all of their

neighbors as vertex set The edges of <S>w are all edges of G which have

at least one end point in S

Weakly induced subgraph (example)

Vertex set: black vertices

Edge set: black lines

Weakly-connected dominating set

A vertex subset S is a weakly-connected dominating set (WCDS), if S is a dominating set and <S>w is connected

Algorithms for finding small WCDS

Algorithm I and II: Two centralized algorithms

Algorithm III and IV: Distributed Implementations of Algorithm I and II

Algorithm V: Distributed Asynchronous Approach

Chen’s WCDS Algo I (overview)

Given a graph G=(V,E), each vertex is associated with a color (white, gray, or black)

All vertices are initially colored white In each iteration, the algorithm color a white or

gray vertex black and all its neighboring white vertices gray

At the end, the black vertices form a weakly-connected dominating set

Term: piece Piece refers to a particular substructure of the graph A white piece is simply

a white vertex A black piece contains a

maximal set of black

vertices whose weakly

induced subgraph is

connected plus any

adjacent gray vertices

The pieces are indicated by dotted regions

Term: improvement

The improvement of a (non-black) vertex u is the number of pieces that would be merged into a single black piece if u were to be dyed black

In last example, dying vertex 5 black would merge 4 piece, while dying vertex 4 would merge 3 pieces

Chen’s WCDS Algo I(detail)

In each iteration, the algorithm choose a single white or gray vertex to dye black

The vertex is chosen greedily: a vertex with maximum improvement is chosen

Until there is only one piece left

Initially, all nodes are white

7

7

4

5

3

33

5

5

4

3

5

5

4

4

4

7

3

5

6

First Iteration

7

7

4

5

3

33

5

5

4

3

5

4

4

4

7

3

5

5 6

2

3

33

5

5

4

3

5

4

4

4

3

3

5 2

Second Iteration

2

3

3

5

5

4

3

5

4

4

4

3

3

5 2

2

3

3

3

2

5

4

4

4

3

3

5 2

Third Iteration

2

3

3

3

2

5

4

4

4

3

3

5 2

2

3

3

3

4

3

3

Fourth Iteration

2

3

3

3

4

3

3

2

3

3

2

Last Iteration

Summary of DS-based Clustering

Summary of DS-based Clustering

References

J. Y. YU and P. H. J. CHONG, "A Survey of Clustering Schemes for Mobile Ad Hoc Networks," IEEE Communications Surveys and Tutorials, First Quarter 2005, Vol. 7, No. 1, pp. 32--48.

J. Wu and H. L. Li, “On Calculating Connected Dominating Set for Efficient Routing in Ad Hoc Wireless Networks,” Proc. 3rd Int’l. Wksp. Discrete Algorithms and Methods for Mobile Comp. and Commun., 1999, pp. 7–14

Y.-Z. P. Chen and A. L. Liestman, “Approximating Minimum Size Weakly-Connected Dominating Sets for Clustering Mobile Ad Hoc Networks,” in Proc. 3rd ACM Int’l. Symp. Mobile Ad Hoc Net. & Comp., June 2002, pp. 165–72.