Table of Contents
ISRN Discrete Mathematics
Volume 2012, Article ID 347430, 11 pages
http://dx.doi.org/10.5402/2012/347430
Research Article

Spider Covers and Their Applications

1Dipartimento di Informatica, Università di Salerno, 84084 Fisciano, Italy
2Research and Development, Apptus Technologies AB, Ideon, 223 70 Lund, Sweden

Received 27 September 2012; Accepted 19 October 2012

Academic Editors: G. Hahn and W. F. Klostermeyer

Copyright © 2012 Filomena De Santis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce two new combinatorial optimization problems: the Maximum Spider Problem and the Spider Cover Problem; we study their approximability and illustrate their applications. In these problems we are given a directed graph , a distinguished vertex , and a family D of subsets of vertices. A spider centered at vertex s is a collection of arc-disjoint paths all starting at s but ending into pairwise distinct vertices. We say that a spider covers a subset of vertices X if at least one of the endpoints of the paths constituting the spider other than s belongs to X. In the Maximum Spider Problem the goal is to find a spider centered at s that covers the maximum number of elements of the family D. Conversely, the Spider Cover Problem consists of finding the minimum number of spiders centered at s that covers all subsets in D. We motivate the study of the Maximum Spider and Spider Cover Problems by pointing out a variety of applications. We show that a natural greedy algorithm gives a 2-approximation algorithm for the Maximum Spider Problem and a -approximation algorithm for the Spider Cover Problem.