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 hdl:20.500.11880/26186 http://dx.doi.org/10.22028/D291-26130 |
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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fb14_1990_07.pdf | 4,57 MB | Adobe PDF | View/Open |
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