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An Algorithm for Minimum Cost Arc-Connectivity Orientations

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Abstract

Given a 2k-edge-connected undirected graph, we consider to find a minimum cost orientation that yields a k-arc-connected directed graph. This minimum cost k-arc-connected orientation problem is a special case of the submodular flow problem. Frank (1982) devised a combinatorial algorithm that solves the problem in O(k 2 n 3 m) time, where n and m are the numbers of vertices and edges, respectively. Gabow (1995) improved Frank’s algorithm to run in O(kn 2 m) time by introducing a new sophisticated data structure. We describe an algorithm that runs in O(k 3 n 3+kn 2 m) time without using sophisticated data structures. In addition, we present an application of the algorithm to find a shortest dijoin in O(n 2 m) time, which matches the current best bound.

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    Satoru Iwata

  2. Graduate School of Information Science and Technology, University of Tokyo, Bunkyo-ku, Tokyo, 113-8656, Japan

    Yusuke Kobayashi

Authors
  1. Satoru Iwata
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  2. Yusuke Kobayashi
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Correspondence to Satoru Iwata.

Additional information

The research of S. Iwata was supported in part by a Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science.

The research of Y. Kobayashi was supported by the Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.

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Iwata, S., Kobayashi, Y. An Algorithm for Minimum Cost Arc-Connectivity Orientations. Algorithmica 56, 437–447 (2010). https://doi.org/10.1007/s00453-008-9179-x

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  • DOI: https://doi.org/10.1007/s00453-008-9179-x

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