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Minimax Regret 1-Median Problem in Dynamic Path Networks

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Abstract

This paper considers the minimax regret 1-median problem in dynamic path networks. In our model, we are given a dynamic path network consisting of an undirected path with positive edge lengths, uniform positive edge capacity, and nonnegative vertex supplies. Here, each vertex supply is unknown but only an interval of supply is known. A particular assignment of supply to each vertex is called a scenario. Given a scenario s and a sink location x in a dynamic path network, let us consider the evacuation time to x of a unit supply given on a vertex by s. The cost of x under s is defined as the sum of evacuation times to x for all supplies given by s, and the median under s is defined as a sink location which minimizes this cost. The regret for x under s is defined as the cost of x under s minus the cost of the median under s. Then, the problem is to find a sink location such that the maximum regret for all possible scenarios is minimized. We propose an O(n 3) time algorithm for the minimax regret 1-median problem in dynamic path networks with uniform capacity, where n is the number of vertices in the network.

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Acknowledgments

This work is supported by JST CREST (JPMJCR1402) and partially supported by JSPS KAKENHI Grant-in-Aid for Young Scientists (B) (17K12641).

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Authors and Affiliations

  1. Department of Information and System Engineering, Chuo University, Tokyo, Japan

    Yuya Higashikawa

  2. Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong

    Siu-Wing Cheng

  3. School of Computing Science, Simon Fraser University, Burnaby, BC, Canada

    Tsunehiko Kameda

  4. Department of Informatics, Kwansei Gakuin University, Hyogo, Japan

    Naoki Katoh

  5. Department of Architecture and Architectural Engineering, Kyoto University, Kyoto, Japan

    Shun Saburi

Authors
  1. Yuya Higashikawa
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  2. Siu-Wing Cheng
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  3. Tsunehiko Kameda
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  4. Naoki Katoh
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  5. Shun Saburi
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Corresponding author

Correspondence to Yuya Higashikawa.

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This article is part of the Topical Collection on Special Issue on Combinatorial Algorithms

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Higashikawa, Y., Cheng, SW., Kameda, T. et al. Minimax Regret 1-Median Problem in Dynamic Path Networks. Theory Comput Syst 62, 1392–1408 (2018). https://doi.org/10.1007/s00224-017-9783-8

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  • DOI: https://doi.org/10.1007/s00224-017-9783-8

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