Edge-Packings of Graphs and Network Reliability

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 edgepacking 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 languageEnglish (US)
Pages (from-to)49-61
Number of pages13
JournalAnnals of Discrete Mathematics
Volume38
Issue numberC
DOIs
StatePublished - 1988
Externally publishedYes

Fingerprint

Network Reliability
Packing
Cutset
Graph in graph theory
Spanning tree
Reliability Bounds
Steiner Tree
Path
Packing Problem
NP-complete problem
Theorem

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

Edge-Packings of Graphs and Network Reliability. / Colbourn, Charles.

In: Annals of Discrete Mathematics, Vol. 38, No. C, 1988, p. 49-61.

Research output: Contribution to journalArticle

@article{43f7d8a343dd4631b6fec777b750d4b7,
title = "Edge-Packings 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 edgepacking 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.",
author = "Charles Colbourn",
year = "1988",
doi = "10.1016/S0167-5060(08)70770-2",
language = "English (US)",
volume = "38",
pages = "49--61",
journal = "Annals of Discrete Mathematics",
issn = "0167-5060",
publisher = "Elsevier",
number = "C",

}

TY - JOUR

T1 - Edge-Packings of Graphs and Network Reliability

AU - Colbourn, Charles

PY - 1988

Y1 - 1988

N2 - 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 edgepacking 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.

AB - 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 edgepacking 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.

UR - http://www.scopus.com/inward/record.url?scp=77957056904&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957056904&partnerID=8YFLogxK

U2 - 10.1016/S0167-5060(08)70770-2

DO - 10.1016/S0167-5060(08)70770-2

M3 - Article

VL - 38

SP - 49

EP - 61

JO - Annals of Discrete Mathematics

JF - Annals of Discrete Mathematics

SN - 0167-5060

IS - C

ER -