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Multi-rooted Greedy Approximation of Directed Steiner Trees with Applications

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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 any \(l\)-restricted Steiner tree, which is such a Steiner tree in which every terminal is at most \(l\) arcs away from the root or another terminal. 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 \(O(\log n)\), and (2) the tree cover problem on directed graphs can also be approximated within a factor of \(O(\log n)\).

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  1. Tomoya Hibi

    Present address: NTT corporation, Kanagawa, Japan

Authors and Affiliations

  1. Department of Computer Science and Engineering, Toyohashi University of Technology, Toyohashi, 441-8580, Japan

    Tomoya Hibi & Toshihiro Fujito

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  1. Tomoya Hibi
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  2. Toshihiro Fujito
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Correspondence to Toshihiro Fujito.

Additional information

A preliminary version of this work appeared in Proceedings of 38th WG (International Workshop on Graph Theoretic Concepts in Computer Science), 2012. Supported in part by the Kayamori Foundation of Informational Science Advancement and a Grant in Aid for Scientific Research of the Ministry of Education, Science, Sports and Culture of Japan.

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Hibi, T., Fujito, T. Multi-rooted Greedy Approximation of Directed Steiner Trees with Applications. Algorithmica 74, 778–786 (2016). https://doi.org/10.1007/s00453-015-9973-1

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