2018/12/06 by Wild, Marcel
#Combinatorics (math.CO) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.1812.02570
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.