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Complexity and Algorithms for Euler Characteristic of Simplicial Complexes (1112.4523v1)
Published 19 Dec 2011 in cs.CG, cs.CC, cs.DS, cs.MS, cs.SC, math.AC, and math.CO
Abstract: We consider the problem of computing the Euler characteristic of an abstract simplicial complex given by its vertices and facets. We show that this problem is #P-complete and present two new practical algorithms for computing Euler characteristic. The two new algorithms are derived using combinatorial commutative algebra and we also give a second description of them that requires no algebra. We present experiments showing that the two new algorithms can be implemented to be faster than previous Euler characteristic implementations by a large margin.