Path Hitting in Acyclic Graphs

An instance of the path hitting problem consists of two families of paths, D and H, in a common undirected graph, where each path in H is associated with a non-negative cost. We refer to D and H as the sets of demand and hitting paths, respectively. When p H and q D share at least one mutual edge, we say that p hits q. The objective is to find a minimum cost subset of H whose members collectively hit those of D. In this paper we provide constant factor approximation algorithms for path hitting, confined to instances in which the underlying graph is a tree, a spider, or a star. Although such restricted settings may appear to be very simple, we demonstrate that they still capture some of the most basic covering problems in graphs. Our approach combines several novel ideas: We extend the algorithm of Garg, Vazirani and Yannakakis [Algorithmica, 18:3

• Type: Conference
• Year: 2006
• Where: ESA
• Authors: Ojas Parekh, Danny Segev
• Keywords: Algorithms, Common Undirected Graph, ESA 2006, Hitting Paths, Path Hitting Problem