Complexity and Algorithms for Euler Characteristic of Simplicial Complexes

Details Complexity and Algorithms for Euler Characteristic of Simplicial Complexes Complexity and Algorithms for Euler Characteristic of Simplicial Complexes

2011-12-19

arxiv.org/abs/1112.4523v1

Computer Science

Computational Geometry

28 pages

Scientific paper

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.

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