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Locating Evacuation Centers Optimally in Path and Cycle Networks

Authors Robert Benkoczi, Binay Bhattacharya, Yuya Higashikawa, Tsunehiko Kameda, Naoki Katoh, Junichi Teruyama

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Author Details

Robert Benkoczi
  • Department of Mathematics and Computer Science, University of Lethbridge, Canada
Binay Bhattacharya
  • School of Computing Science, Simon Fraser University, Burnaby, Canada
Yuya Higashikawa
  • Graduate School of Information Science, University of Hyogo, Kobe, Japan
Tsunehiko Kameda
  • School of Computing Science, Simon Fraser University, Burnaby, Canada
Naoki Katoh
  • Graduate School of Information Science, University of Hyogo, Kobe, Japan
Junichi Teruyama
  • Graduate School of Information Science, University of Hyogo, Kobe, Japan

Funding

  • Benkoczi, Robert: Partially supported by a Discovery Grant from NSERC of Canada.
  • Bhattacharya, Binay: Partially supported by a Discovery Grant from NSERC of Canada.
  • Higashikawa, Yuya: Partially supported by JSPS KAKENHI Grant Number 20K19746 and JSPS KAKENHI Grant Number 19H04068.
  • Katoh, Naoki: Partially supported by JSPS KAKENHI Grant Number 19H04068.
  • Teruyama, Junichi: Partially supported by JSPS KAKENHI Grant Number 19H04068.

Cite AsGet BibTex

Robert Benkoczi, Binay Bhattacharya, Yuya Higashikawa, Tsunehiko Kameda, Naoki Katoh, and Junichi Teruyama. Locating Evacuation Centers Optimally in Path and Cycle Networks. In 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021). Open Access Series in Informatics (OASIcs), Volume 96, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/OASIcs.ATMOS.2021.13

Abstract

We present dynamic flow algorithms to solve the k-sink problem whose aim is to locate k sinks (evacuation centers) in such a way that the evacuation time of the last evacuee is minimized. In the confluent model, the evacuees originating from or passing through a vertex must evacuate to the same sink, and most known results on the k-sink problem adopt the confluent model. When the edge capacities are uniform (resp. general), our algorithms for non-confluent flow in the path networks run in O(n + k² log² n) (resp. O(n log(n) + k² log⁵ n)) time, where n is the number of vertices. Our algorithms for cycle networks run in O(k²n log² n) (resp. O(k²n log⁵ n)) time, when the edge capacities are uniform (resp. general).

Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • Efficient algorithms
  • facility location
  • minmax sink
  • evacuation problem
  • dynamic flow in network

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