NDLI: Very Simple Methods for All Pairs Network Flow Analysis

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Gusfield, Dan
Copyright Year	1990
Abstract	A very simple algorithm for the classical problem of computing the maximum network flow value between every pair of nodes in an undirected, capacitated n node graph is presented; as in the well-known GomoryHu method, the method given here uses only $n - 1$ maximum flow computations. Our algorithm is implemented by adding only five simple lines of code to any program that produces a minimum cut; a program to produce an equivalent flow tree, which is a compact representation of the flow values, is obtained by adding only three simple lines of code to any program producing a minimum cut. A very simple version of the GomoryHu cut tree method that finds one minimum cut for every pair of nodes is also derived, and it is shown that the seemingly fundamental operation of that method, node contraction, is not needed, nor must crossing cuts be avoided. As a result, this version of the GomoryHu method is implemented by adding less than ten simple lines of code to any program that produces a minimum cut. The algorithms in this paper demonstrate that a cut tree of graph G can be computed with $n - 1$ calls to an oracle that alone knows G, and that, when given two nodes s and t, returns any arbitrary minimum $(s, t)$ cut and its value.
Starting Page	143
Ending Page	155
Page Count	13
File Format	PDF
ISSN	00975397
DOI	10.1137/0219009
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	1
Volume Number	19
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-31
Access Restriction	Subscribed
Subject Keyword	combinatorial optimization Analysis of algorithms and problem complexity network flow Network models, deterministic Scheduling theory, deterministic Programming involving graphs or networks
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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