On the Covering Steiner Problem
 Anupam Gupta,
 Aravind Srinivasan
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Abstract
The Covering Steiner problem is a common generalization of the kMST and Group Steiner problems. An instance of the Covering Steiner problem consists of an undirected graph with edgecosts, and some subsets of vertices called groups, with each group being equipped with a nonnegative integer value (called its requirement); the problem is to find a minimumcost tree which spans at least the required number of vertices from every group. When all requirements are equal to 1, this is the Group Steiner problem.
While many covering problems (e.g., the covering integer programs such as set cover) become easier to approximate as the requirements increase, the Covering Steiner problem remains at least as hard to approximate as the Group Steiner problem; in fact, the best guarantees previously known for the Covering Steiner problem were worse than those for Group Steiner as the requirements became large. In this work, we present an improved approximation algorithm whose guarantee equals the best known guarantee for the Group Steiner problem.
 Title
 On the Covering Steiner Problem
 Book Title
 FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science
 Book Subtitle
 23rd Conference, Mumbai, India, December 1517, 2003. Proceedings
 Pages
 pp 244251
 Copyright
 2003
 DOI
 10.1007/9783540245971_21
 Print ISBN
 9783540206804
 Online ISBN
 9783540245971
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 2914
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
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 Editors

 Paritosh K. Pandya ^{(4)}
 Jaikumar Radhakrishnan ^{(5)}
 Editor Affiliations

 4. Tata Institute of Fundamental Research
 5. Tata Institute of Fundamental Research, School of Technology and Computer Science
 Authors

 Anupam Gupta ^{(6)}
 Aravind Srinivasan ^{(7)}
 Author Affiliations

 6. Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA, 15232, USA
 7. Department of Computer Science and University of Maryland Institute for Advanced Computer Studies, University of Maryland at College Park, College Park, MD, 20742, USA
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