Fast Approximation Algorithms for Multicommodity Flow Problems
Abstract
In this paper, we describe the first polynomial-time combinatorial algorithms for approximately solving the multicommodity flow problem. Our algorithms are significantly faster than the best previously known algorithms, that were based on linear programming. For a k-commodity multicommodity flow problem, the running time of our randomized algorithm is (up to log factors) the same as the time needed to solve k single-commodity flow problems, thus giving the surprising result that approximately computing a k-commodity maximum-flow is not much harder than computing about k single-commodity maximum-flows iii isolation. Given any multicommodity flow problem as input, our algorithm is guaranteed to provide a feasible solution to a modified flow problem in which all capacities are increased by a (1 + e)-factor, or to provide a proof that there is no feasible solution to the original problem. We also describe faster approximation algorithms for multicommodity flow problems with a special structure, such as those that arise in the sparsest cut problems and the uniform concurrent flow problems if k < or - m.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1991
- Accession Number
- ADA254048
Entities
People
- Clifford Stein
- Fillia Makedon
- Serge Plotkin
- Spyros Tragoudas
- Tom Leighton
- Éva Tardos
Organizations
- Stanford University