Simple Counting and Sampling Algorithms for Graphs with Bounded Pathwidth
Christine T. Cheng,
Will Rosenbaum
Abstract:In this paper, we consider the problem of counting and sampling structures in graphs. We define a class of "edge universal labeling problems"-which include proper k-colorings, independent sets, and downsets-and describe simple algorithms for counting and uniformly sampling valid labelings of graphs, assuming a path decomposition is given. Thus, we show that several well-studied counting and sampling problems are fixed parameter tractable (FPT) when parameterized by the pathwidth of the input graph. We discuss … Show more
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