Sequential Importance Sampling Algorithms for Estimating the All-Terminal Reliability Polynomial of Sparse Graphs

The all-terminal reliability polynomial of a graph counts its connected subgraphs of various sizes. Algorithms based on sequential importance sampling (SIS) have been proposed to estimate a graph’s reliability polynomial. We show upper bounds on the relative error of three sequential importance sampling algorithms. We use these to create a hybrid algorithm, which selects the best SIS algorithm for a particular graph G and particular coefficient of the polynomial. This hybrid algorithm is particularly effective when G has low degree. For graphs of average degree ≤ 11, it is the fastest known algorithm; for graphs of average degree ≤ 45 it is the fastest known polynomial-space algorithm. For example, when a graph has average degree 3, this

• Type: Journal
• Year: 2015
• Where: APPROX
• Authors: David G. Harris, Francis Sullivan
• Keywords: Algorithms, APPROX 2015