Compression with wildcards: All induced metric subgraphs

Marcel Wild

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arXiv · 2409.08363

Compression with wildcards: All induced metric subgraphs

Marcel Wild

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Abstract

Driven by applications in the natural, social and computer sciences several algorithms have been proposed to enumerate all sets $X\s V$ of vertices of a graph $G=(V,E)$ that induce a {\it connected} subgraph. We offer two algorithms for enumerating all $X$'s that induce (more exquisite) {\it metric} subgraphs. Specifically, the first algorithm, called {\tt 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 $X\s V$, this being a natural strengthening of "metric". The Mathematica command {\tt BooleanConvert} features prominently.

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Marcel Wild. 2024-09-12. Compression with wildcards: All induced metric subgraphs. https://arxiv.org/abs/2409.08363

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