Unsplittable Transshipments
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914312128299008 |
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| author | Debgupta, Srinwanti Morell, Sarah Skutella, Martin |
| author_facet | Debgupta, Srinwanti Morell, Sarah Skutella, Martin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07230 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unsplittable Transshipments Debgupta, Srinwanti Morell, Sarah Skutella, Martin Data Structures and Algorithms Discrete Mathematics Combinatorics 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. |
| title | Unsplittable Transshipments |
| topic | Data Structures and Algorithms Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2602.07230 |