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Unsplittable Transshipments

Authors Srinwanti Debgupta , Sarah Morell , Martin Skutella

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LIPIcs.ICALP.2026.74.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
  • Mathematics of computing → Network flows
Keywords
  • Network flow
  • unsplittable flow
  • flow augmentation

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Abstract

We introduce the Unsplittable Transshipment Problem in directed graphs with multiple sources and sinks. An unsplittable transshipment routes given supplies and demands using at most one path for each source-sink pair. Although they are a natural generalization of single source unsplittable flows, unsplittable transshipments raise interesting new challenges and require novel algorithmic techniques. As our main contribution, we give a nontrivial generalization of a seminal result of Dinitz, Garg, and Goemans (1999) by showing how to efficiently turn a given transshipment x into an unsplittable transshipment y with y_a < x_a+d_max for all arcs a, where d_max is the maximum demand (or supply) value. Further results include bounds on the number of rounds required to satisfy all demands, where each round consists of an unsplittable transshipment that routes a subset of the demands while respecting arc capacity constraints.

Cite As Get BibTex

Srinwanti Debgupta, Sarah Morell, and Martin Skutella. Unsplittable Transshipments. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 74:1-74:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.74

Author Details

Srinwanti Debgupta
  • Institute of Mathematics, TU Berlin, Germany
Sarah Morell
  • Faculty of Mathematics and Computer Science, University of Bremen, Germany
Martin Skutella
  • Institute of Mathematics, TU Berlin, Germany

Funding

The first and third author are funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - The Berlin Mathematics Research Center MATH+ (EXC-2046/1, EXC-2046/2, project ID: 390685689).

Acknowledgements

We want to thank the anonymous referees for their thoughtful comments that helped to improve the presentation of the paper.

References

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