A polynomial time approximation algorithm for the two-commodity splittable flow problem

Elke Eisenschmidt () and Utz-Uwe Haus ()

Mathematical Methods of Operations Research, 2013, vol. 77, issue 3, 391 pages

Abstract: We consider a generalization of the unsplittable maximum two-commodity flow problem on undirected graphs where each commodity $${i \in \{1, 2\}}$$ can be split into a bounded number k i of equally-sized chunks that can be routed on different paths. We show that in contrast to the single-commodity case this problem is NP-hard, and hard to approximate to within a factor of α > 1/2. We present a polynomial time 1/2-approximation algorithm for the case of uniform chunk size over both commodities and show that for even k i and a mild cut condition it can be modified to yield an exact method. The uniform case can be used to derive a 1/4-approximation for the maximum concurrent (k 1 , k 2 )-splittable flow without chunk size restrictions for fixed demand ratios. Copyright Springer-Verlag 2013

Keywords: Splittable flow; 2-commodity flow; Approximation algorithm (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s00186-012-0402-9

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