English

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.

Keywords

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

R2 v1 2026-06-21T19:54:06.816Z