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Strongly Polynomial Algorithms for the Unsplittable Flow Problem

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Integer Programming and Combinatorial Optimization (IPCO 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2081))

Abstract

We provide the first strongly polynomial algorithms with the best approximation ratio for all three variants of the unsplittable flow problem (UFP). In this problem we are given a (possibly directed) capacitated graph with n vertices and m edges, and a set of terminal pairs each with its own demand and profit. The objective is to connect a subset of the terminal pairs each by a single flow path as to maximize the total profit of the satisfied terminal pairs subject to the capacity constraints. Classical UFP, in which demands must be lower than edge capacities, is known to have an Om approximation algorithm. We provide the same result with a strongly polynomial combinatorial algorithm. The extended UFP case is when some demands might be higher than edge capacities. For that case we both improve the current best approximation ratio and use strongly polynomial algorithms. We also use a lower bound to show that the extended case is provably harder than the classical case. The last variant is the bounded UFP where demands are at most 1/K of the minimum edge capacity. Using strongly polynomial algorithms here as well, we improve the currently best known algorithms. Specifically, for K = 2 our results are better than the lower bound for classical UFP thereby separating the two problems.

Research supported in part by the Israel Science Foundation and by the US-Israel Binational Science Foundation (BSF).

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© 2001 Springer-Verlag Berlin Heidelberg

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Azar, Y., Regev, O. (2001). Strongly Polynomial Algorithms for the Unsplittable Flow Problem. In: Aardal, K., Gerards, B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2001. Lecture Notes in Computer Science, vol 2081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45535-3_2

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  • DOI: https://doi.org/10.1007/3-540-45535-3_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42225-9

  • Online ISBN: 978-3-540-45535-6

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