Multi-rooted greedy approximation of directed steiner trees with applications

Authors:
Tomoya Hibi;Toshihiro Fujito
Affiliations:
Department of Computer Science and Engineering, Toyohashi University of Technology, Tempaku, Toyohashi, Japan;Department of Computer Science and Engineering, Toyohashi University of Technology, Tempaku, Toyohashi, Japan
Venue:
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2012

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Abstract

We present a greedy algorithm for the directed Steiner tree problem (DST), where any tree rooted at any (uncovered) terminal can be a candidate for greedy choice. It will be shown that the algorithm, running in polynomial time for any constant l, outputs a directed Steiner tree of cost no larger than 2(l−1)(ln n+1) times the cost of the minimum l-restricted Steiner tree. We derive from this result that 1) DST for a class of graphs, including quasi-bipartite graphs, in which the length of paths induced by Steiner vertices is bounded by some constant can be approximated within a factor of O(logn), and 2) the tree cover problem on directed graphs can also be approximated within a factor of O(logn).