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arXiv · 0901.4417

ALLSAT compressed with wildcards: All, or all maximum independent sets

Marcel Wild
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Abstract

An odd cycle cover is a vertex set whose removal makes a graph bipartite. We show that if a $k$-element odd cycle cover of a graph with w vertices is known then all $N$ maximum anticliques (= independent sets) can be generated in time $O(2^k w^3 + N w^2))$. Generating ${\it all}\ N'$ anticliques (maximum or not) is easier and works for arbitrary graphs in time $O(N'w^2)$. In fact the use of wildcards allows to compactly generate the anticliques in clusters.

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Marcel Wild. 2009-01-28. ALLSAT compressed with wildcards: All, or all maximum independent sets. https://arxiv.org/abs/0901.4417

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