Please use this identifier to cite or link to this item: doi:10.22028/D291-26130
Title: Can a maximum flow be computed in o(nm) time?
Author(s): Cheriyan, Joseph
Hagerup, Torben
Mehlhorn, Kurt
Language: English
Year of Publication: 1990
OPUS Source: Kaiserslautern ; Saarbrücken : DFKI, 1990
DDC notations: 004 Computer science, internet
Publikation type: Report
Abstract: We show that a maximum flow in a network with n vertices can be computed deterministically in O(n^{3}/logn) time on a uniform-cost RAM. For dense graphs, this improves the previous best bound of O(n^{3}). The bottleneck in our algorithm is a combinatorial problem on (unweighted) graphs. The number of operations executed on flow variables is O(n^{8/3}(log n)^{4/3}), in contrast with Omega(nm) flow operations for all previous algorithms, where m denotes the number of edges in the network. A randomized version of our algorithm executes O(n^{3/2}m^{1/2}(log n)^{3/2}+n^{2}(log n)^{2}) flow operations with high probability. Specializing to the case in which all capacities are integers bounded by U, we show that a maximum flow can be computed using O(n^{3/2}m^{1/2}+n^{2}(log U)^{1/2}) flow operations. Finally, we argue that several of our results yield optimal parallel algorithms.
Link to this record: urn:nbn:de:bsz:291-scidok-41970
Series name: Technischer Bericht / A / Fachbereich Informatik, Universität des Saarlandes
Series volume: 1990/07
Date of registration: 6-Sep-2011
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Informatik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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