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Minsum k-Sink Problem on Dynamic Flow Path Networks

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Combinatorial Algorithms (IWOCA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10979))

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Abstract

In emergencies such as earthquakes, nuclear accidents, etc., we need an evacuation plan. We model a street, a building corridor, etc. by a path network, and consider the problem of locating a set of k sinks on a dynamic flow path network with n vertices, where people are located, that minimizes the sum of the evacuation times of all evacuees. Our minsum model is more difficult to deal with than the minmax model, because the cost function is not monotone along the path. We present an \(O(kn^2\log ^2 n)\) time algorithm for solving this problem, which is the first polynomial time result. If the edge capacities are uniform, we give an \(O(kn\log ^3 n)\) time algorithm.

This work was supported in part by NSERC Discovery Grants, awarded to R. Benkoczi and B. Bhattacharya, in part by JST CREST Grant Number JPMJCR1402 held by N. Katoh and Y. Higashikawa, and in part by JSPS Kakenhi Grant-in-Aid for Young Scientists (B) (17K12641) given to Y. Higashikawa.

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Notes

  1. 1.

    In Sects. 3 and 4, for simplicity, we will often identify a vertex with its index, referring to vertex i, instead of vertex \(v_i\).

  2. 2.

    We use the term “node” for \(\mathcal T\) to distinguish them from the vertices of P.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Canada

    Robert Benkoczi

  2. School of Computing Science, Simon Fraser University, Burnaby, Canada

    Binay Bhattacharya & Tsunehiko Kameda

  3. School of Business Administration, University of Hyogo, Kobe, Japan

    Yuya Higashikawa

  4. School of Science and Technology, Kwansei Gakuin University, Sanda, Japan

    Naoki Katoh

Authors
  1. Robert Benkoczi
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  2. Binay Bhattacharya
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  3. Yuya Higashikawa
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  4. Tsunehiko Kameda
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  5. Naoki Katoh
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Corresponding author

Correspondence to Tsunehiko Kameda .

Editor information

Editors and Affiliations

  1. Department of Informatics, King’s College London, London, United Kingdom

    Costas Iliopoulos

  2. Department of Computer Science, School of Computing, National University of Singapore, Singapore, Singapore

    Hon Wai Leong

  3. Department of Computer Science, School of Computing, National University of Singapore, Singapore, Singapore

    Wing-Kin Sung

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Benkoczi, R., Bhattacharya, B., Higashikawa, Y., Kameda, T., Katoh, N. (2018). Minsum k-Sink Problem on Dynamic Flow Path Networks. In: Iliopoulos, C., Leong, H., Sung, WK. (eds) Combinatorial Algorithms. IWOCA 2018. Lecture Notes in Computer Science(), vol 10979. Springer, Cham. https://doi.org/10.1007/978-3-319-94667-2_7

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  • DOI: https://doi.org/10.1007/978-3-319-94667-2_7

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  • Online ISBN: 978-3-319-94667-2

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