An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms

A multicommodity flow problem is considered where for each pair of vertices (u, v) it is required to send f half-units of commodity (u, v) from u to v and f half-units of commodity (v, u) from v to u without violating capacity constraints. The main result is an algorithm for performing the task prov...

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Bibliographic Details
Published in[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science pp. 422 - 431
Main Authors Leighton, T., Rao, S.
Format Conference Proceeding
LanguageEnglish
Published IEEE 1988
Subjects
Application software
Approximation algorithms
Bifurcation
Computer science
Constraint theory
Contracts
Laboratories
Linear programming
Mathematics
Particle separators
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Summary:A multicommodity flow problem is considered where for each pair of vertices (u, v) it is required to send f half-units of commodity (u, v) from u to v and f half-units of commodity (v, u) from v to u without violating capacity constraints. The main result is an algorithm for performing the task provided that the capacity of each cut exceeds the demand across the cut by a Theta (log n) factor. The condition on cuts is required in the worst case, and is trivially within a Theta (log n) factor of optimal for any flow problem. The result can be used to construct the first polylog-times optimal approximation algorithms for a wide variety of problems, including minimum quotient separators, 1/3-2/3 separators, bifurcators, crossing number, and VLSI layout area. It can also be used to route packets efficiently in arbitrary distributed networks.< >
ISBN:9780818608773
0818608773
DOI:10.1109/SFCS.1988.21958