TY - RPRT
T1 - Can a maximum flow be computed in o(nm) time?
T3 - Kaiserslautern ; Saarbrücken : DFKI, 1990
A1 - Cheriyan,Joseph
A1 - Hagerup,Torben
A1 - Mehlhorn,Kurt
Y1 - 2011/09/06
N2 - 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.
CY - Saarbrücken
PB - Saarländische Universitäts- und Landesbibliothek
AD - Postfach 151141, 66041 Saarbrücken
UR - http://scidok.sulb.uni-saarland.de/volltexte/2011/4197
ER -