Faster algorithms for evacuation problems in networks with a single sink of small degree and bounded capacitated edges

Yuya Higashikawa (), Naoki Katoh (), Junichi Teruyama () and Yuki Tokuni ()
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Yuya Higashikawa: University of Hyogo
Naoki Katoh: University of Hyogo
Junichi Teruyama: University of Hyogo
Yuki Tokuni: University of Hyogo

Journal of Combinatorial Optimization, 2024, vol. 48, issue 3, No 3, 22 pages

Abstract: Abstract In this paper, we propose new algorithms for evacuation problems defined on dynamic flow networks. A dynamic flow network is a directed graph in which source nodes are given supplies and a single sink node is given a demand. The evacuation problem seeks a dynamic flow that sends all supplies from sources to the sink such that its demand is satisfied in the minimum feasible time horizon. For this problem, the current best algorithms are developed by Schlöter (2018) and Kamiyama (2019), which run in strongly polynomial time but with high-order polynomial time complexity because they use submodular function minimization as a subroutine. In this paper, we propose new algorithms that do not explicitly execute submodular function minimization, and we prove that they are faster than the current best algorithms when an input network is restricted such that the sink has a small in-degree and every edge has the same capacity.

Keywords: Dynamic flow; Evacuation problem; Quickest transshipment problem; Polynomial-time algorithm; Base polytope (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10878-024-01213-y

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