Approximation Algorithms for a Network Design Problem

Abstract

A class of network design problems, including the k-path/ tree/cycle covering problems and some location-routing problems, can be modeled by downwards monotone functions [5]. We consider a class of network design problems, called the p-constrained path/tree/cycle covering problems, obtained by introducing an additional constraint to these problems; i.e., we require that the number of connected components in the optimal solution be at most p for some integer p. The p-constrained path/tree/cycle covering problems cannot be modeled by downwards monotone functions. In this paper, we present a different analysis for the performance guarantee of the algorithm in [5]. As a result of the analysis, we are able to tackle p-constrained path/tree/cycle covering problems, and show the performance bounds of 2 and 4 for p-constrained tree/cycle problems and p-constrained path covering problems respectively.