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 language | English (US) |
|---|---|
| Pages (from-to) | 49-61 |
| Number of pages | 13 |
| Journal | Annals of Discrete Mathematics |
| Volume | 38 |
| Issue number | C |
| DOIs | |
| State | Published - 1988 |
| Externally published | Yes |
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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 journal › Article
}
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 -