Complexity and Algorithms for Euler Characteristic of Simplicial Complexes
Computational Geometry
2011-12-21 v1 Computational Complexity
Data Structures and Algorithms
Mathematical Software
Symbolic Computation
Commutative Algebra
Combinatorics
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.
Cite
@article{arxiv.1112.4523,
title = {Complexity and Algorithms for Euler Characteristic of Simplicial Complexes},
author = {Bjarke Hammersholt Roune and Eduardo Sáenz de Cabezón},
journal= {arXiv preprint arXiv:1112.4523},
year = {2011}
}
Comments
28 pages