On the Covering Steiner Problem

TitleOn the Covering Steiner Problem
Publication TypeBook Chapters
Year of Publication2003
AuthorsGupta A, Srinivasan A
EditorPandya P, Radhakrishnan J
Book TitleFST TCS 2003: Foundations of Software Technology and Theoretical Computer ScienceFST TCS 2003: Foundations of Software Technology and Theoretical Computer Science
Series TitleLecture Notes in Computer Science
Pagination244 - 251
PublisherSpringer Berlin / Heidelberg
ISBN Number978-3-540-20680-4

The Covering Steiner problem is a common generalization of the k -MST and Group Steiner problems. An instance of the Covering Steiner problem consists of an undirected graph with edge-costs, and some subsets of vertices called groups , with each group being equipped with a non-negative integer value (called its requirement ); the problem is to find a minimum-cost 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.