Randomized Approximation Schemes for Cuts and Flows in Capacitated Graphs

Details Randomized Approximation Schemes for Cuts and Flows in Capacitated Graphs Randomized Approximation Schemes for Cuts and Flows in Capacitated Graphs

2002-07-23

arxiv.org/abs/cs/0207078v1

Computer Science

Data Structures and Algorithms

Draft journal version combining conference publications in STOC '96 and SODA '98

Scientific paper

We improve on random sampling techniques for approximately solving problems that involve cuts and flows in graphs. We give a near-linear-time construction that transforms any graph on n vertices into an O(n\log n)-edge graph on the same vertices whose cuts have approximately the same value as the original graph's. In this new graph, for example, we can run the O(m^{3/2})-time maximum flow algorithm of Goldberg and Rao to find an s--t minimum cut in O(n^{3/2}) time. This corresponds to a (1+epsilon)-times minimum s--t cut in the original graph. In a similar way, we can approximate a sparsest cut to within O(log n) in O(n^2) time using a previous O(mn)-time algorithm. A related approach leads to a randomized divide and conquer algorithm producing an approximately maximum flow in O(m sqrt{n}) time.

Affiliated with

Also associated with

No associations

Rating

Randomized Approximation Schemes for Cuts and Flows in Capacitated Graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Randomized Approximation Schemes for Cuts and Flows in Capacitated Graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Randomized Approximation Schemes for Cuts and Flows in Capacitated Graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-469161