Algorithms for connected set cover problem and fault-tolerant connected set cover problem

Abstract

Given a set V of elements, S a family of subsets of V , and G a connected graph on vertex set S ,a connected set cover (CSC) is a subfamily R of S such that every element in V is covered by at least one set of R , and the subgraph G [ R ] of G induced by R is connected. If furthermore G [ R ] is k -connected and every element in V is covered by at least m sets in R , then R is a ( k , m ) -CSC. In this paper, we present two approximation algorithms for the minimum CSC problem, and one approximation algorithm for the minimum ( 2 , m ) -CSC problem. Performance ratios are analyzed. These are the first approximation algorithms for CSC problems in general graphs with guaranteed performance ratios.