Randomized Approximation Schemes for Cuts and Flows in Capacitated Graphs

dc.creatorBenczur, Andras
dc.creatorKarger, David R.
dc.date2002-07-23
dc.date.accessioned2026-07-25T16:35:30Z
dc.descriptionWe 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.
dc.descriptionDraft journal version combining conference publications in STOC '96 and SODA '98
dc.identifierhttps://arxiv.org/abs/cs/0207078
dc.identifierhttp://arxiv.org/abs/cs/0207078
dc.identifier.urihttps://dspace.dare.co.zw/handle/123456789/42429
dc.subjectData Structures and Algorithms
dc.subjectDiscrete Mathematics
dc.subjectF.2.2; G.2.1;G.2.2
dc.titleRandomized Approximation Schemes for Cuts and Flows in Capacitated Graphs
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