Randomized Approximation Schemes for Cuts and Flows in Capacitated Graphs
| dc.creator | Benczur, Andras | |
| dc.creator | Karger, David R. | |
| dc.date | 2002-07-23 | |
| dc.date.accessioned | 2026-07-25T16:35:30Z | |
| dc.description | 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. | |
| dc.description | Draft journal version combining conference publications in STOC '96 and SODA '98 | |
| dc.identifier | https://arxiv.org/abs/cs/0207078 | |
| dc.identifier | http://arxiv.org/abs/cs/0207078 | |
| dc.identifier.uri | https://dspace.dare.co.zw/handle/123456789/42429 | |
| dc.subject | Data Structures and Algorithms | |
| dc.subject | Discrete Mathematics | |
| dc.subject | F.2.2; G.2.1;G.2.2 | |
| dc.title | Randomized Approximation Schemes for Cuts and Flows in Capacitated Graphs | |
| dc.type | text |