Fast Augmenting Paths by Random Sampling from Residual Graphs

Author(s)
Karger, David R.; Levine, Matthew S.
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Abstract
Consider an n-vertex, m-edge, undirected graph with integral capacities and max-flow value v. We give a new [~ over O](m + nv)-time maximum flow algorithm. After assigning certain special sampling probabilities to edges in [~ over O](m)$ time, our algorithm is very simple: repeatedly find an augmenting path in a random sample of edges from the residual graph. Breaking from past work, we demonstrate that we can benefit by random sampling from directed (residual) graphs. We also slightly improve an algorithm for approximating flows of arbitrary value, finding a flow of value (1 - ε) times the maximum in [~ over O](m√n/ε) time.
Date issued
2015-03
URI
http://hdl.handle.net/1721.1/97225
Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Journal
SIAM Journal on Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Karger, David R., and Matthew S. Levine. “Fast Augmenting Paths by Random Sampling from Residual Graphs.” SIAM Journal on Computing 44, no. 2 (January 2015): 320–339.
Version: Final published version
ISSN
0097-5397
1095-7111
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