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Approximating Fractional Multicommodity Flow Independent of the Number of Commodities

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Fleischer, Lisa K.
Copyright Year	2000
Abstract	We describe fully polynomial time approximation schemes for various multicommodity flow problems in graphs with m edges and n vertices. We present the first approximation scheme for maximum multicommodity flow that is independent of the number of commodities k, and our algorithm improves upon the run time of previous algorithms by this factor of k, running in ${{\cal O}^*(\epsilon^{-2}m^2)}$ time. For maximum concurrent flow and minimum cost concurrent flow, we present algorithms that are faster than the current known algorithms when the graph is sparse or the number of commodities k is large, i.e., k > m/n. Our algorithms build on the framework proposed by Garg and Knemann [Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science, IEEE, New York, 1998, pp. 300--309]. They are simple, deterministic, and for the versions without costs, they are strongly polynomial. The approximation guarantees are obtained by comparison with dual feasible solutions found by our algorithm.Our maximum multicommodity flow algorithm extends to an approximation scheme for the maximum weighted multicommodity flow, which is faster than those implied by previous algorithms by a factor of k/log W, where W is the maximum weight of a commodity.
Starting Page	505
Ending Page	520
Page Count	16
File Format	PDF
ISSN	08954801
DOI	10.1137/S0895480199355754
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	4
Volume Number	13
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-01
Access Restriction	Subscribed
Subject Keyword	VLSI routing Analysis of algorithms and problem complexity Special problems of linear programming concurrent flow Approximation methods and heuristics approximation algorithm multicommodity flow Combinatorial optimization Programming involving graphs or networks
Content Type	Text
Resource Type	Article
Subject	Mathematics

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