Performance Guaranteed Evolutionary Algorithm for Minimum Connected Dominating Set

TL;DR

This paper presents a new evolutionary algorithm for the minimum connected dominating set problem in wireless sensor networks, with proven performance guarantees in terms of runtime and approximation ratio.

Contribution

It introduces a performance-guaranteed evolutionary algorithm for MinCDS with theoretical bounds on time and approximation ratio.

Findings

Expected runtime of $O(n^3)$ for finding a CDS.

Approximation ratio within $(2+ ext{ln}\Delta)$ of optimal.

Algorithm's performance is theoretically proven.

Abstract

A connected dominating set is a widely adopted model for the virtual backbone of a wireless sensor network. In this paper, we design an evolutionary algorithm for the minimum connected dominating set problem (MinCDS), whose performance is theoretically guaranteed in terms of both computation time and approximation ratio. Given a connected graph $G=(V,E)$, a connected dominating set (CDS) is a subset $C\subseteq V$ such that every vertex in $V\setminus C$ has a neighbor in $C$, and the subgraph of $G$ induced by $C$ is connected. The goal of MinCDS is to find a CDS of $G$ with the minimum cardinality. We show that our evolutionary algorithm can find a CDS in expected $O(n^3)$ time which approximates the optimal value within factor $(2+\ln\Delta)$, where $n$ and $\Delta$ are the number of vertices and the maximum degree of graph $G$, respectively.