Edge-packing of graphs and network reliability

Charles J. Colbourn

doi:10.1016/0012-365X(88)90193-8

Edge-packing of graphs and network reliability

Charles J. Colbourn

Computing, Informatics and Decision Systems Engineering, School of (CIDSE)

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

The reliability of a network can be efficiently bounded using graph-theoretical techniques based on edge-packing. We examine the application of combinatorial theorems on edge-packing spanning trees, s, t-paths, and s, t-cuts to the determination of reliability bounds. The application of spanning trees has been studied by Polesskii, and the application of s, t-paths has been studied by Brecht and Colbourn. The use of edge-packings of s, t-cutsets has not been previously examined. We compare the resulting bounds with known bounds produced by different techniques, and establish that the edge-packing bounds often produce a substantial improvement. We also establish that three other edge-packing problems arising in reliability bounding are NP-complete, namely edge-packing by network cutsets, Steiner trees, and Steiner cutsets.

Original language	English (US)
Pages (from-to)	49-61
Number of pages	13
Journal	Discrete Mathematics
Volume	72
Issue number	1-3
DOIs	https://doi.org/10.1016/0012-365X(88)90193-8
State	Published - Dec 1988

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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title = "Edge-packing of graphs and network reliability",

abstract = "The reliability of a network can be efficiently bounded using graph-theoretical techniques based on edge-packing. We examine the application of combinatorial theorems on edge-packing spanning trees, s, t-paths, and s, t-cuts to the determination of reliability bounds. The application of spanning trees has been studied by Polesskii, and the application of s, t-paths has been studied by Brecht and Colbourn. The use of edge-packings of s, t-cutsets has not been previously examined. We compare the resulting bounds with known bounds produced by different techniques, and establish that the edge-packing bounds often produce a substantial improvement. We also establish that three other edge-packing problems arising in reliability bounding are NP-complete, namely edge-packing by network cutsets, Steiner trees, and Steiner cutsets.",

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note = "Funding Information: Thanks to University of Auckland and University of Toronto for hospitality while this paper was written, and to NSERC Canadaf or financial support.",

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