# A New Constant Factor Approximation to Construct Highly Fault-Tolerant Connected Dominating Set in Unit Disk Graph

## Department

Computer Science

## Document Type

Article

## Publication Date

5-17-2016

## Abstract

This paper proposes a new polynomial time constant factor approximation algorithm for a more-a-decade-long open NP-hard problem, the minimum four-connected m-dominating set problem in unit disk graph (UDG) with any positive integer m ≥ 1 for the first time in the literature. We observe that it is difficult to modify the existing constant factor approximation algorithm for the minimum three-connected m-dominating set problem to solve the minimum four-connected m-dominating set problem in UDG due to the structural limitation of Tutte decomposition, which is the main graph theory tool used by Wang et al. to design their algorithm. To resolve this issue, we first reinvent a new constant factor approximation algorithm for the minimum three-connected m-dominating set problem in UDG and later use this algorithm to design a new constant factor approximation algorithm for the minimum four-connected m-dominating set problem in UDG.

## Journal Title

IEEE/ACM Transactions on Networking

## Journal ISSN

1558-2566

## Volume

PP

## Issue

99

## First Page

1

## Last Page

11

## Digital Object Identifier (DOI)

10.1109/TNET.2016.2561901