Document Open Access Logo

Submodularity Property for Facility Locations of Dynamic Flow Networks

Authors Peerawit Suriya, Vorapong Suppakitpaisarn , Supanut Chaidee , Phapaengmueng Sukkasem

PDF
Thumbnail PDF

File

OASIcs.ATMOS.2023.10.pdf
  • Filesize: 3.52 MB
  • 13 pages

Document Identifiers

Author Details

Peerawit Suriya
  • Department of Mathematics, Faculty of Science, Chiang Mai University, Thailand
Vorapong Suppakitpaisarn
  • Graduate School of Information Science and Technology, The University of Tokyo, Japan
Supanut Chaidee
  • Department of Mathematics, Faculty of Science, Chiang Mai University, Thailand
Phapaengmueng Sukkasem
  • Department of Mathematics, Faculty of Science, Chiang Mai University, Thailand

Funding

This research is partially supported by Chiang Mai University as a part of the One Faculty One MoU Project.
  • Suriya, Peerawit: Supported by the Development and Promotion of Science and Technology Talents Project (DPST) under The Institute for the Promotion of Teaching Science and Technology (IPST), Ministry of Education, Thailand.
  • Suppakitpaisarn, Vorapong: Supported by JSPS Grant-in-Aid for Transformative Research Areas A grant number JP21H05845, and also by JST SICORP Grant Number JPMJSC2208, Japan.

Cite As Get BibTex

Peerawit Suriya, Vorapong Suppakitpaisarn, Supanut Chaidee, and Phapaengmueng Sukkasem. Submodularity Property for Facility Locations of Dynamic Flow Networks. In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/OASIcs.ATMOS.2023.10

Abstract

This paper considers facility location problems within dynamic flow networks, shifting the focus from minimizing evacuation time to handling situations with a constrained evacuation timeframe. Our study sets two main goals: 1) Determining a fixed-size set of locations that can maximize the number of evacuees, and 2) Identifying the smallest set of locations capable of accommodating all evacuees within the time constraint. We introduce flow_t(S) to represent the number of evacuees for given locations S within a fixed time limit t. We prove that flow_t functions is a monotone submodular function, which allows us to apply an approximation algorithm specifically designed for maximizing such functions with size restrictions. For the second objective, we implement an approximation algorithm tailored to solving the submodular cover problem. We conduct experiments on the real datasets of Chiang Mai, and demonstrate that the approximation algorithms give solutions which are close to optimal for all of the experiments we have conducted.

Subject Classification

ACM Subject Classification
  • Theory of computation → Network flows
  • Theory of computation → Dynamic graph algorithms
  • Theory of computation → Routing and network design problems
Keywords
  • Approximation Algorithms
  • Dynamic Networks
  • Facility Location
  • Submodular Function Optimization

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Rémy Belmonte, Yuya Higashikawa, Naoki Katoh, and Yoshio Okamoto. Polynomial-time approximability of the k-sink location problem. arXiv preprint arXiv:1503.02835, 2015. Google Scholar
  2. Fabián A Chudak and David B Shmoys. Improved approximation algorithms for the uncapacitated facility location problem. SIAM Journal on Computing, 33(1):1-25, 2003. Google Scholar
  3. Yefim Dinitz. Dinitz’ algorithm: The original version and Even’s version. In Theoretical Computer Science: Essays in Memory of Shimon Even, pages 218-240. Springer, 2006. Google Scholar
  4. Yefim A Dinitz. An algorithm for the solution of the problem of maximal flow in a network with power estimation. In Doklady Akademii nauk, volume 194, pages 754-757. Russian Academy of Sciences, 1970. Google Scholar
  5. Jack Edmonds and Richard M Karp. Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the ACM (JACM), 19(2):248-264, 1972. Google Scholar
  6. Lester Randolph Ford and Delbert R Fulkerson. Maximal flow through a network. Canadian Journal of Mathematics, 8:399-404, 1956. Google Scholar
  7. Lester R Ford Jr and Delbert Ray Fulkerson. Constructing maximal dynamic flows from static flows. Operations research, 6(3):419-433, 1958. Google Scholar
  8. Norie Fu and Vorapong Suppakitpaisarn. Clustering 1-dimensional periodic network using betweenness centrality. Computational Social Networks, 3(1):1-20, 2016. Google Scholar
  9. Satoru Fujishige. Submodular functions and optimization. Elsevier, 2005. Google Scholar
  10. Yuya Higashikawa, Mordecai J. Golin, and Naoki Katoh. Multiple sink location problems in dynamic path networks. Theoretical Computer Science, 607:2-15, 2015. Google Scholar
  11. Yuya Higashikawa and Naoki Katoh. A survey on facility location problems in dynamic flow networks. The Review of Socionetwork Strategies, 13:163-208, 2019. Google Scholar
  12. Dorit S Hochbaum. Heuristics for the fixed cost median problem. Mathematical programming, 22:148-162, 1982. Google Scholar
  13. Satoko Mamada, Takeaki Uno, Kazuhisa Makino, and Satoru Fujishige. An O(nlog²n) algorithm for the optimal sink location problem in dynamic tree networks. Discrete Applied Mathematics, 154(16):2387-2401, 2006. Google Scholar
  14. George L Nemhauser, Laurence A Wolsey, and Marshall L Fisher. An analysis of approximations for maximizing submodular set functions—i. Mathematical programming, 14:265-294, 1978. Google Scholar
  15. Jorge Qüense, Carolina Martínez, Jorge León, Rafael Aránguiz, Simón Inzunza, Nikole Guerrero, Alondra Chamorro, and Malcom Bonet. Land cover and potential for tsunami evacuation in rapidly growing urban areas. the case of Boca Sur (San Pedro de la Paz, Chile). International Journal of Disaster Risk Reduction, 69:102747, 2022. Google Scholar
  16. Maxim Sviridenko. An improved approximation algorithm for the metric uncapacitated facility location problem. In International Conference on Integer Programming and Combinatorial Optimization, pages 240-257. Springer, 2002. Google Scholar
  17. Lucia Williams, Alexandru I Tomescu, and Brendan Mumey. Flow decomposition with subpath constraints. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 20(1):360-370, 2022. Google Scholar
  18. Laurence A Wolsey. An analysis of the greedy algorithm for the submodular set covering problem. Combinatorica, 2(4):385-393, 1982. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact