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DOI: 10.4230/LIPIcs.ICALP.2026.74

Unsplittable Transshipments

Authors: Srinwanti Debgupta, Sarah Morell, and Martin Skutella

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

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.

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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)

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@InProceedings{debgupta_et_al:LIPIcs.ICALP.2026.74,
  author =	{Debgupta, Srinwanti and Morell, Sarah and Skutella, Martin},
  title =	{{Unsplittable Transshipments}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{74:1--74:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.74},
  URN =		{urn:nbn:de:0030-drops-264634},
  doi =		{10.4230/LIPIcs.ICALP.2026.74},
  annote =	{Keywords: Network flow, unsplittable flow, flow augmentation}
}

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Unsplittable Transshipments

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