Abstract
We consider the unsplittable flow problem (UFP) and the closely related column-restricted packing integer programs (CPIPs). In UFP we are given an edge-capacitated graph Gā=ā(V,E) and k request pairs R 1, ā¦, R k , where each R i consists of a source-destination pair (s i ,t i ), a demand d i and a weight w i . The goal is to find a maximum weight subset of requests that can be routed unsplittably in G. Most previous work on UFP has focused on the no-bottleneck case in which the maximum demand of the requests is at most the smallest edge capacity. Inspired by the recent work of Bansal et al. [3] on UFP on a path without the above assumption, we consider UFP on paths as well as trees. We give a simple O(logn) approximation for UFP on trees when all weights are identical; this yields an O(log2 n) approximation for the weighted case. These are the first non-trivial approximations for UFP on trees. We develop an LP relaxation for UFP on paths that has an integrality gap of O(log2 n); previously there was no relaxation with o(n) gap. We also consider UFP in general graphs and CPIPs without the no-bottleneck assumption and obtain new and useful results.
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Chekuri, C., Ene, A., Korula, N. (2009). Unsplittable Flow in Paths and Trees and Column-Restricted Packing Integer Programs. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2009 2009. Lecture Notes in Computer Science, vol 5687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03685-9_4
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DOI: https://doi.org/10.1007/978-3-642-03685-9_4
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