ylfink@water.UUCP (ylfink) (12/15/86)
DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF WATERLOO SEMINAR ACTIVITIES COMPUTER NETWORKS SEMINAR - Tuesday, December 16, 1986. Miss Aparna Ramanathan a graduate student of this department will speak on ``Improving Bounds on All- terminal Network Reliability''. TIME: 3:30 PM ROOM: MC 5158 ABSTRACT A standard model of a network is a graph in which nodes represent communication centers and edges represent links between these centers. Edges are assumed to have statistically independent probabilities of failure, and nodes are assumed to be perfectly reliable. The all- terminal reliability of the network is defined to be the probability that all the communication centers in the network are able to communicate with each other in an environment of random link failures. Exact calcula- tion of the all-terminal reliability for general graphs is known to be #P-complete. As a result, much research has been done in obtaining upper and lower bounds for all-terminal reliability that avoid the exponential computation likely to be required by the exact algo- rithms. In this talk, two different methods are developed to improve on the existing bounds. Firstly, a new polyno- mial time algorithm to count almost minimal cutsets provides immediate improvement on all of the subgraph counting bounds. Improvements on the bounds for planar networks ar also derived. The second method uses arc-disjoint rooted subdigraphs of a network to improve on existing lower bounds and arc-disjoint s-directed cuts for upper bounds. The - lower bounds obtained from an arc-packing of acyclic rooted subdigraphs are shown to be competitive both with the Kruskal-Katona and Lomonosov-Polesskii bounds.