Faster approximation schemes for fractional multicommodity flow problems via dynamic graph algorithms

Authors:
Aleksander Madry
Affiliations:
Massachusetts Institute of Technology, Cambridge, MA, USA
Venue:
Proceedings of the forty-second ACM symposium on Theory of computing
Year:
2010

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Abstract

We combine the work of Garg and Konemann, and Fleischer with ideas from dynamic graph algorithms to obtain faster (1-ε)-approximation schemes for various versions of the multicommodity flow problem. In particular, if ε is moderately small and the size of every number used in the input instance is polynomially bounded, the running times of our algorithms match -- up to poly-logarithmic factors and some provably optimal terms -- the Ω(mn) flow-decomposition barrier for single-commodity flow.