Algorithms for Minimum m-Connected k-Dominating Set Problem

1
Algorithms for Minimum m-Connected k-Dominating
Set Problem
W. Shang, F. Yao, P. Wang and X. Hu 2007
2
Introduction

• In many existing schemes virtual backbone nodes
  form a Connected Dominating Set of the WSN.
• How to construct a fault tolerant virtual
  backbone that continues to function when some
  nodes or links break down is an important
  research problem.

3
Introduction

• In this paper, a WSN can be modelled as a Unit
  Disk Graph (UDG) that consists of all nodes in
  the WSN and there exists an edge between two
  nodes if the distance between them is at most 1.
• M-connected k-dominating set
• Each node u in V \ S is dominated by at least k
  nodes in S
• There are at least m disjoint paths between each
  pair of nodes in S

4
Preliminaries

• maximal independent set (MIS) S if each vertex V
  \ S is adjacent to at least one vertex in S
• Connected dominating set (CDS) C C is the MIS
  also induces a connected subgraph

5
Preliminaries

• Cut-vertex if the graph G \ v is disconnected.
• Block is a maximal connected subgraph having no
  cut-vertex.
• 2-connected graph is a graph without
  cut-vertices.
• Leaf block is a subgraph of which is a block
  with only one cut-vertex.

6
Approximation Algorithm
So
S
D
T
v
u
X
Y
7
(1,k)-CDS
8
(1,k)-CDS

• Proof

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(2,k)-CDS

• Basic Idea

10
(2,k)-CDS
11
(2,k)-CDS
y
x
D
S
u
v
12
(2,k)-CDS
13
(2,1)-CDS
14
(m,k)-CDS for 3lt m lt k
15
Conclusion

• Centralized approximation algorithms for minimum
  m-connected k-dominating set problem for m 1,2
• Discuss the relation between (m,k)-CDS and
  (m,m)-CDS.

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• Q A