Submodularity Property for Facility Locations of Dynamic Flow Networks
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.
Approximation Algorithms
Dynamic Networks
Facility Location
Submodular Function Optimization
Theory of computation~Network flows
Theory of computation~Dynamic graph algorithms
Theory of computation~Routing and network design problems
10:1-10:13
Regular Paper
This research is partially supported by Chiang Mai University as a part of the One Faculty One MoU Project.
Peerawit
Suriya
Peerawit Suriya
Department of Mathematics, Faculty of Science, Chiang Mai University, Thailand
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.
Vorapong
Suppakitpaisarn
Vorapong Suppakitpaisarn
Graduate School of Information Science and Technology, The University of Tokyo, Japan
https://orcid.org/0000-0002-7020-395X
Supported by JSPS Grant-in-Aid for Transformative Research Areas A grant number JP21H05845, and also by JST SICORP Grant Number JPMJSC2208, Japan.
Supanut
Chaidee
Supanut Chaidee
Department of Mathematics, Faculty of Science, Chiang Mai University, Thailand
https://orcid.org/0000-0002-2314-1397
Phapaengmueng
Sukkasem
Phapaengmueng Sukkasem
Department of Mathematics, Faculty of Science, Chiang Mai University, Thailand
10.4230/OASIcs.ATMOS.2023.10
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Peerawit Suriya, Vorapong Suppakitpaisarn, Supanut Chaidee, and Phapaengmueng Sukkasem
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