Faster approximate multicommodity flow using quadratically coupled flows
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Kelner_Faster approximate.pdf
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331.58 KB
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Author(s)
Miller, Gary L.
Peng, Richard
Kelner, Jonathan Adam
Date Issued
May 2012
Journal
Proceedings of the 44th symposium on Theory of Computing (STOC '12)
Publisher
Association for Computing Machinery (ACM)
Citation
Jonathan A. Kelner, Gary L. Miller, and Richard Peng. 2012. Faster approximate multicommodity flow using quadratically coupled flows. In Proceedings of the 44th symposium on Theory of Computing (STOC '12). ACM, New York, NY, USA, 1-18.
Version
Original manuscript
Abstract
The maximum multicommodity flow problem is a natural generalization of the maximum flow problem to route multiple distinct flows. Obtaining a 1-ε approximation to the multicommodity flow problem on graphs is a well-studied problem. In this paper we present an adaptation of recent advances in single-commodity flow algorithms to this problem. As the underlying linear systems in the electrical problems of multicommodity flow problems are no longer Laplacians, our approach is tailored to generate specialized systems which can be preconditioned and solved efficiently using Laplacians. Given an undirected graph with m edges and k commodities, we give algorithms that find 1-ε approximate solutions to the maximum concurrent flow problem and maximum weighted multicommodity flow problem in time O(m[superscript 4/3]poly(k,ε[superscript -1])).
Description
Original manuscript May 8, 2012
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1145/2213977.2213979
