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DOI: 10.4230/LIPIcs.ESA.2025.112

A Faster Parametric Search for the Integral Quickest Transshipment Problem

Authors: Mariia Anapolska, Dario van den Boom, Christina Büsing, and Timo Gersing

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract

Algorithms for computing fractional solutions to the quickest transshipment problem have been significantly improved since Hoppe and Tardos first solved the problem in strongly polynomial time. For integral solutions, however, no structural improvements on their algorithm itself have yet been proposed. Runtime improvements are limited to general progress on submodular function minimization (SFM), which is an integral part of Hoppe and Tardos' algorithm. In fact, SFM constitutes the main computational load of the algorithm, as the runtime is blown up by using it within Megiddo’s parametric search algorithm. We replace this part of Hoppe and Tardos' algorithm with a more efficient routine that solves only a linear number of SFM and, in contrast to previous techniques, exclusively uses minimum cost flow algorithms within Megiddo’s parametric search. Our approach improves the state-of-the-art runtime from 𝒪̃(m⁴ k^15) down to 𝒪̃(m²k⁵ + m⁴ k²), where k is the number of terminals and m is the number of arcs.

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Mariia Anapolska, Dario van den Boom, Christina Büsing, and Timo Gersing. A Faster Parametric Search for the Integral Quickest Transshipment Problem. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 112:1-112:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{anapolska_et_al:LIPIcs.ESA.2025.112,
  author =	{Anapolska, Mariia and van den Boom, Dario and B\"{u}sing, Christina and Gersing, Timo},
  title =	{{A Faster Parametric Search for the Integral Quickest Transshipment Problem}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{112:1--112:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.112},
  URN =		{urn:nbn:de:0030-drops-245817},
  doi =		{10.4230/LIPIcs.ESA.2025.112},
  annote =	{Keywords: Flow over time, dynamic transshipment, quickest transshipment, parametric submodular functions, efficient algorithms}
}

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A Faster Parametric Search for the Integral Quickest Transshipment Problem

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