Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms

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Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms (1999)

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by Tom Leighton , Satish Rao

Venue:	J. ACM
Citations:	356 - 6 self

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@ARTICLE{Leighton99multicommoditymax-flow,
    author = {Tom Leighton and Satish Rao},
    title = {Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms},
    journal = {J. ACM},
    year = {1999}
}

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Abstract

In this paper, we establish max-flow min-cut theorems for several important classes of multicommodity flow problems. In particular, we show that for any n-node multicommodity flow problem with uniform demands, the max-flow for the problem is within an O(log n) factor of the upper bound implied by the min-cut. The result (which is existentially optimal) establishes an important analogue of the famous 1-commodity max-flow min-cut theorem for problems with multiple commodities. The result also has substantial applications to the field of approximation algorithms. For example, we use the flow result to design the first polynomial-time (polylog n-times-optimal) approximation algorithms for well-known NP-hard optimization problems such as graph partitioning, min-cut linear arrangement, crossing number, VLSI layout, and minimum feedback arc set. Applications of the flow results to path routing problems, network reconfiguration, communication in distributed networks, scientific computing and rapidly mixing Markov chains are also described in the paper.

Keyphrases

approximation algorithm multicommodity max-flow min-cut theorem flow result first polynomial-time minimum feedback arc several important class network reconfiguration well-known np-hard optimization problem markov chain famous 1-commodity max-flow min-cut theorem max-flow min-cut theorem uniform demand scientific computing vlsi layout multiple commodity graph partitioning important analogue substantial application n-node multicommodity flow problem multicommodity flow problem upper bound min-cut linear arrangement distributed network

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