Proceedings ArticleDOI
A new bounding procedure for the network reliability problem
C.L. Suffel
- pp 688-693
TLDR
A description is given of a way to obtain bounds which will be tight over the class of networks for all possible values of the edge failure rate, which have been shown to be valid for a certain range of edge failure rates.Abstract:
A description is given of a way to obtain bounds which will be tight over the class of networks for all possible values of the edge failure rate. These bounds have been shown to be valid for a certain range of edge failure rates. The author discusses the known bounding methods before proposing the new approach. >read more
Citations
More filters
Combinational properties of directed graphs useful in computing network reliability
A. Satyanarayana,J.N. Hagstrom +1 more
TL;DR: In this paper, the problem of computing the probability that a root vertex can communicate with all other vertices in a probabilistic directed graph is discussed, and one method is to apply the inclusion-exclusion principle of probability theory to the event at least one rooted spanning tree of the graph is working.
References
More filters
Journal ArticleDOI
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Jack Edmonds,Richard M. Karp +1 more
TL;DR: New algorithms for the maximum flow problem, the Hitchcock transportation problem, and the general minimum-cost flow problem are presented, and Dinic shows that, in a network with n nodes and p arcs, a maximum flow can be computed in 0 (n2p) primitive operations by an algorithm which augments along shortest augmenting paths.
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems.
Jack Edmonds,Richard M. Karp +1 more
TL;DR: In this article, the authors presented new algorithms for the maximum flow problem, the Hitchcock transportation problem and the general minimum-cost flow problem and derived upper bounds on the number of steps in these algorithms.
Journal ArticleDOI
Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird
Journal ArticleDOI
The Complexity of Counting Cuts and of Computing the Probability that a Graph is Connected
J. Scott Provan,Michael O. Ball +1 more
TL;DR: Several enumeration and reliability problems are shown to be # P-complete, and hence, at least as hard as NP-complete problems.