Minimum cuts in near-linear timeMinimum cuts in near-linear time

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 Author Karger, David R. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2000 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Monte Carlo algorithm ♦ Connectivity ♦ Min-cut ♦ Optimization ♦ Tree packing Abstract We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a "semiduality" between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling techniques. We give a randomized (Monte Carlo) algorithm that finds a minimum cut in an $\textit{m}-edge,$ $\textit{n}-vertex$ graph with high probability in $\textit{O}(m$ log3 $\textit{n})$ time. We also give a simpler randomized algorithm that finds $\textit{all}$ minimum cuts with high probability in $O(\textit{m}$ log3 $\textit{n})$ time. This variant has an optimal $\textit{RNC}$ parallelization. Both variants improve on the previous best time bound of O(n2 log3 n). Other applications of the tree-packing approach are new, nearly tight bounds on the number of $\textit{near-minimum}$ cuts a graph may have and a new data structure for representing them in a space-efficient manner. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2000-01-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 47 Issue Number 1 Page Count 31 Starting Page 46 Ending Page 76

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Source: ACM Digital Library