TY - JOUR
T1 - Edge-packing 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 Canadaf or financial support.
PY - 1988/12
Y1 - 1988/12
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 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.
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 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.
UR - http://www.scopus.com/inward/record.url?scp=38249028177&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=38249028177&partnerID=8YFLogxK
U2 - 10.1016/0012-365X(88)90193-8
DO - 10.1016/0012-365X(88)90193-8
M3 - Article
AN - SCOPUS:38249028177
VL - 72
SP - 49
EP - 61
JO - Discrete Mathematics
JF - Discrete Mathematics
SN - 0012-365X
IS - 1-3
ER -