ALLSAT compressed with wildcards: Partitionings and face-numbers of simplicial complexes

12/06/2018

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by   Marcel Wild, et al.

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Given the facets of a finite simplicial complex, we use wildcards to enumerate its faces in compressed fashion. Our algorithm, coded in high-level Mathematica code, compares favorably to the hardwired Mathematica command BooleanConvert (=exclusive sums of products). As to running time, depending on the particular shape of the problem, either method can excel. When our method excels it may not just beat BooleanConvert but also SatisfiabilityCount by orders of magnitude. Independent of running time, our compression rate is always higher.