Computing Terminal Reliability Of Multi-Tolerance Graphs

Let G be a probabilistic graph, in which the vertices fail independently with known probabilities. Let K represent a specified subset of vertices. The K-terminal reliability of G is defined as the probability that all vertices in K are connected. When broken vertical bar K broken vertical bar = 2, the K-terminal reliability is called the 2-terminal reliability, which is the probability that the source vertex is connected to the destination vertex. The problems of computing K-terminal reliability and 2-terminal reliability have been proven to be #P-complete in general. This work demonstrates that on multi-tolerance graphs, the 2-terminal reliability problem can be solved in polynomial-time and the results can be extended to the K-terminal reliability problem on bounded multi-tolerance graphs.