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arXiv · 1812.02570

Compression with wildcards: Abstract simplicial complexes

Marcel Wild
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Abstract

Despite the more handy terminology of abstract simplicial complexes SC, in its core this article is about antitone Boolean functions. Given the maximal faces (=facets) of SC, our main algorithm, called Facets-To-Faces, outputs SC in a compressed format. The degree of compression of Facets-To-Faces, which is programmed in high-level Mathematica code, compares favorably to both the Mathematica command BooleanConvert, and to the BDD's provided by Python. A novel way to calculate the face-numbers from the facets is also presented. Both algorithms can be parallelized and are applicable (e.g.) to reliability analysis, combinatorial topology, and frequent set mining.

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Marcel Wild. 2018-12-06. Compression with wildcards: Abstract simplicial complexes. https://arxiv.org/abs/1812.02570

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