TY - JOUR
T1 - Edge-Packings of Graphs and Network Reliability
AU - Colbourn, Charles J.
N1 - Funding Information:
Thanks to University of Auckland and University of Toronto for hospitality while this paper was written, and to NSERC Canada for financial support.
PY - 1988/1/1
Y1 - 1988/1/1
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.
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U2 - 10.1016/S0167-5060(08)70770-2
DO - 10.1016/S0167-5060(08)70770-2
M3 - Article
AN - SCOPUS:77957056904
VL - 38
SP - 49
EP - 61
JO - Annals of Discrete Mathematics
JF - Annals of Discrete Mathematics
SN - 0167-5060
IS - C
ER -