Multi-terminal multipath flows: synthesis

Given an undirected network G≡[ N, E], a source–sink pair of nodes ( s, t) in N, a non-negative number u i, j representing the capacity of edge ( i, j) for each ( i, j)∈ E, and a positive integer q, an “elementary q-path flow” from s to t is defined as a flow of q units from s to t, with one unit of...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 143; no. 1; pp. 182 - 193
Main Authors: Chandrasekaran, R., Nair, K.P.K., Aneja, Y.P., Kabadi, S.N.
Format: Journal Article
Language:English
Published: Lausanne Elsevier B.V 30.09.2004
Amsterdam Elsevier
New York, NY
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Exact sciences and technology
Mathematics
Multipath flows
Network synthesis
q-capacity of a cut
Sciences and techniques of general use
Strongly polynomial algorithm
Theoretical computing
Strongly polynomial algorithm
q-capacity of a cut
Multipath flows
Network synthesis
Integer
Linear combination
Computer theory
Network
Combinatorial algorithm
Multipath flow
Edge set
Optimization
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary:Given an undirected network G≡[ N, E], a source–sink pair of nodes ( s, t) in N, a non-negative number u i, j representing the capacity of edge ( i, j) for each ( i, j)∈ E, and a positive integer q, an “elementary q-path flow” from s to t is defined as a flow of q units from s to t, with one unit of flow along each path in a set of q edge-disjoint s– t paths. A q-path flow from s to t is a non-negative linear combination of elementary q-path flows from s to t. In this paper we provide a strongly polynomial combinatorial algorithm for designing an undirected network with minimum total edge capacity which is capable of meeting, non-simultaneously, a given set of symmetric q-path flow requirements between all pairs of nodes. This extends the previous work on network synthesis.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2004.02.014