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A Faster Parametric Search for the Integral Quickest Transshipment Problem

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

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ACM Subject Classification
  • Theory of computation → Network flows
Keywords
  • Flow over time
  • dynamic transshipment
  • quickest transshipment
  • parametric submodular functions
  • efficient algorithms

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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) https://doi.org/10.4230/LIPIcs.ESA.2025.112

Author Details

Mariia Anapolska
  • Combinatorial Optimization, RWTH Aachen University, Germany
Dario van den Boom
  • Combinatorial Optimization, RWTH Aachen University, Germany
Christina Büsing
  • Combinatorial Optimization, RWTH Aachen University, Germany
Timo Gersing
  • Combinatorial Optimization, RWTH Aachen University, Germany

Funding

This work is co-funded by the German research council (DFG) - project number 442047500 - Collaborative Research Center Sparsity and Singular Structures (SFB 1481) and by the German research council (DFG) Research Training Group 2236 UnRAVeL.

Acknowledgements

We would like to express our gratitude to the anonymous reviewers for their valuable feedback and constructive comments, which have greatly contributed to improving the presentation of this paper.

References

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