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Algorithms for connectivity problems in undirected graphs : maximum flow and minimun [kappa]-way cut.

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dc.contributor.advisor David R. Karger. en_US
dc.contributor.author Levine, Matthew S. (Matthew Steven) en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. en_US
dc.date.accessioned 2005-10-14T19:21:03Z
dc.date.available 2005-10-14T19:21:03Z
dc.date.copyright 2002 en_US
dc.date.issued 2002 en_US
dc.identifier.uri http://hdl.handle.net/1721.1/29234
dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002. en_US
dc.description In title on t.p., "[kappa]" apears as lower-case Greek letter. en_US
dc.description Includes bibliographical references (p. [69]-72). en_US
dc.description.abstract We consider two connectivity problems on undirected graphs: maximum flow and minimum k-way cut. The maximum flow problem asks about the connectivity between two specified nodes. A traditional approach is to search for augmenting paths. We explore the possibility of restricting the set of edges in which we search for an augmenting path, so that we can find each flow path in sub-linear time. Consider an n-vertex, m-edge, undirected graph with maximum flow value v. We give two methods for finding augmenting paths in such a graph in amortized sub-linear time, based on the idea that undirected graphs have sparse subgraphs that capture connectivity information. The first method sparsifies unused edges by using a spanning forest. It is deterministic and takes ... time per path on average. The second method sparsifies the entire residual graph by taking random samples of the edges. It takes O(n) time per path on average. These results let us improve the O(mv) time bound of the classic augmenting path algorithm to O(m + nv3/2) (deterministic) and O(m + nv) (randomized). For simple graphs, the addition of a blocking flow subroutine yields a deterministic O (nm2/3vl/6)-time algorithm. A minimum k-way cut of an n-vertex, m-edge, weighted, undirected graph is a partition of the vertices into k sets that minimizes the total weight of edges with endpoints in different sets. We give new randomized algorithms to find minimum 3-way and 4-way cuts, which lead to time bounds of O(mnk-2 log3 n) for k =/< 6. Our key insight is that two different structural properties of k-way cuts, both exploited by previous algorithms, can be exploited simultaneously to avoid the bottleneck operations in both prior algorithms. The result is that we improve on the best previous time bounds by a factor of O(n2). en_US
dc.format.extent 72 p. en_US
dc.format.extent 3419122 bytes
dc.format.extent 3418927 bytes
dc.format.mimetype application/pdf
dc.format.mimetype application/pdf
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri http://dspace.mit.edu/handle/1721.1/7582
dc.subject Electrical Engineering and Computer Science. en_US
dc.title Algorithms for connectivity problems in undirected graphs : maximum flow and minimun [kappa]-way cut. en_US
dc.type Thesis en_US
dc.description.degree Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. en_US
dc.identifier.oclc 51458636 en_US


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