A Fast Parallel Algorithm for Minimum-Cost Small Integral Flows

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A Fast Parallel Algorithm for Minimum-Cost Small Integral Flows

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Publication Article, peer reviewed scientific
Title A Fast Parallel Algorithm for Minimum-Cost Small Integral Flows
Author Lingas, Andrzej ; Persson, Mia
Date 2015
English abstract
We present a new approach to the minimum-cost integral flow problem for small values of the flow. It reduces the problem to the tests of simple multivariate polynomials over a finite field of characteristic two for non-identity with zero. In effect, we show that a minimum-cost flow of value k in a network with n vertices, a sink and a source, integral edge capacities and positive integral edge costs polynomially bounded in n can be found by a randomized PRAM, with errors of exponentially small probability in n, running in O(klog(kn)+log(2)(kn)) time and using 2 (k) (kn) (O(1)) processors. Thus, in particular, for the minimum-cost flow of value O(logn), we obtain an RNC2 algorithm, improving upon time complexity of earlier NC and RNC algorithms.
DOI http://dx.doi.org/10.1007/s00453-013-9865-1 (link to publisher's fulltext)
Publisher Springer
Host/Issue Algorithmica;2
Volume 72
ISSN 0178-4617
Pages 607-619
Language eng (iso)
Subject Maximum integral flow
Minimum-cost flow
Polynomial verification
Parallel algorithms
Randomized algorithms
Time complexity
Processor
complexity
Technology
Research Subject Categories::TECHNOLOGY
Handle http://hdl.handle.net/2043/20002 Permalink to this page
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