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

We consider a generalization of the unsplittable maximum two-commodity flow problem on undirected graphs where each commodity 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...

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Bibliographic Details
Published in:Mathematical methods of operations research (Heidelberg, Germany) Vol. 77; no. 3; pp. 381 - 391
Main Authors: Eisenschmidt, Elke, Haus, Utz-Uwe
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2013
Springer
Springer Nature B.V
Subjects:
Algorithms
Approximation
Business and Management
Calculus of Variations and Optimal Control; Optimization
Commodities
Graphs
Marketing
Mathematical analysis
Mathematics
Mathematics and Statistics
Operations research
Operations Research/Decision Theory
Original Article
Restrictions
Studies
Surface hardness
Splittable flow
Approximation algorithm
2-commodity flow
ISSN:1432-2994, 1432-5217
Online Access:Get full text
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Summary:We consider a generalization of the unsplittable maximum two-commodity flow problem on undirected graphs where each commodity 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.
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ISSN:1432-2994
1432-5217
DOI:10.1007/s00186-012-0402-9