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WAOA
2005
Springer

Approximation and Complexity of k-Splittable Flows

13 years 8 months ago
Approximation and Complexity of k-Splittable Flows
Given a graph with a source and a sink node, the NP–hard maximum k–splittable flow (MkSF) problem is to find a flow of maximum value with a flow decomposition using at most k paths [6]. The multicommodity variant of this problem is a natural generalization of disjoint paths and unsplittable flow problems. Constructing a k–splittable flow requires two interdepending decisions. One has to decide on k paths (routing) and on the flow values on these paths (packing). We give efficient algorithms for computing exact and approximate solutions by decoupling the two decisions into a first packing step and a second routing step. Our main contributions are as follows: (i) We show that for constant k a polynomial number of packing alternatives containing at least one packing used by an optimal MkSF solution can be constructed in polynomial time. If k is part of the input, we obtain a slightly weaker result. In this case we can guarantee that, for any fixed > 0, the computed set o...
Ronald Koch, Martin Skutella, Ines Spenke
Added 28 Jun 2010
Updated 28 Jun 2010
Type Conference
Year 2005
Where WAOA
Authors Ronald Koch, Martin Skutella, Ines Spenke
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