Estimating the Number of s-t Paths in a Graph
Ben Roberts, Dirk P. Kroese · Journal of Graph Algorithms and Applications · 2007
Abstract. The problem of counting the number of s-t paths in a graph is #P-complete. We provide an algorithm to estimate the solution stochastically, using sequential importance sampling. We show that the method works effectively for both graphs and digraphs. We also use the method to investigate the expected number of s-t paths in a random graph of size n and density d, and develop a model that shows how this quantity behaves when n and d are varied. Key words. Counting s-t paths, #P-completeness, random graphs, Monte Carlo simulation, sequential importance sampling. 1.