Compression with wildcards: All induced metric subgraphs
Abstract
Driven by applications in the natural, social and computer sciences several algorithms have been proposed to enumerate all sets X V of vertices of a graph G=(V,E) that induce a connected subgraph. We offer two algorithms for enumerating all X's that induce (more exquisite) metric subgraphs. Specifically, the first algorithm, called AllMetricSets, generates these X's in a compressed format. The second algorithm generates all (accessible) metric sets one-by-one but is provably output-polynomial. Mutatis mutandis the same holds for the geodesically-convex sets X V, this being a natural strengthening of "metric". The Mathematica command BooleanConvert features prominently.
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