Path Hitting in Acyclic Graphs

  • Ojas Parekh
  • Danny Segev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4168)


An instance of the path hitting problem consists of two families of paths, \({\cal D}\) and \({\cal H}\), in a common undirected graph, where each path in \({\cal H}\) is associated with a non-negative cost. We refer to \({\cal D}\) and \({\cal H}\) as the sets of demand and hitting paths, respectively. When \(p \in {\cal H}\) and \(q \in {\cal D}\) share at least one mutual edge, we say that phits q. The objective is to find a minimum cost subset of \({\cal H}\) whose members collectively hit those of \({\cal D}\).

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.


Vertex Cover Edge Cost Edge Cover Assignment Cost Complementary Slackness Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ojas Parekh
    • 1
  • Danny Segev
    • 2
  1. 1.Department of Mathematics and Computer ScienceEmory UniversityUSA
  2. 2.School of Mathematical SciencesTel-Aviv UniversityIsrael

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