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Report (Bericht) zugänglich unter
Can a maximum flow be computed in o(nm) time?
URN: urn:nbn:de:bsz:291-scidok-41970
URL: http://scidok.sulb.uni-saarland.de/volltexte/2011/4197/
Quelle:
(1990) Kaiserslautern ; Saarbrücken : DFKI, 1990
pdf-Format:
Dokument 1.pdf (4.572 KB)
Institut:
Fachrichtung 6.2 - Informatik
DDC-Sachgruppe:
Informatik
Dokumentart:
Report (Bericht)
Schriftenreihe:
Technischer Bericht / A / Fachbereich Informatik, Universität des Saarlandes
Bandnummer:
1990/07
Sprache:
Englisch
Erstellungsjahr:
1990
Publikationsdatum:
06.09.2011
Kurzfassung auf Englisch:
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.
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