Edge-disjoint paths in expander graphs

Given a graph G=(V,E)and a set of $\kappa$ pairs of vertices in V, we are interested in finding, for each pair (ai, bi), a path connecting ai to bi such that the set of $\kappa$ paths so found is edge-disjoint. For arbitrary graphs the problem is ${\cal NP}$-complete, although it is in ${\cal P}$ if...

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Bibliographic Details
Published inSIAM journal on computing Vol. 30; no. 6; pp. 1790 - 1801
Main Author FRIEZE, Alan M
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2001
Subjects
Algorithms
Approximation
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Graphs
Mathematics
Sciences and techniques of general use
Polynomial
Graph path
Random walk
Graph theory
Randomized algorithm
Algorithm
Polynomial time
Edge disjoint path
Graph partitioning
Randomization
Algorithm complexity
NP complete problem
Edge
Regular graph
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Summary:Given a graph G=(V,E)and a set of $\kappa$ pairs of vertices in V, we are interested in finding, for each pair (ai, bi), a path connecting ai to bi such that the set of $\kappa$ paths so found is edge-disjoint. For arbitrary graphs the problem is ${\cal NP}$-complete, although it is in ${\cal P}$ if $\kappa$ is fixed. We present a polynomial time randomized algorithm for finding edge-disjoint paths in an r-regular expander graph G. We show that if G has sufficiently strong expansion properties and r is sufficiently large, then all sets of $\kappa=\Omega(n/\log n)$ pairs of vertices can be joined. This is within a constant factorof best possible.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0097-5397
1095-7111
DOI:10.1137/S0097539700366103