A presentation of general multipersistence modules computable in polynomial time?
Algebraic Topology
2015-12-22 v2 Computational Geometry
Commutative Algebra
Abstract
Multipersistence homology modules were introduced by G.Carlsson and A.Zomorodian which gave, together with G.Singh, an algorithm to compute their Groebner bases. Although their algorithm has polynomial complexity when the chain modules are free, i.e. in the one-critical case, it might be exponential in general. We give a new presentation of multipersistence homology modules, which allows us to design an algorithm to compute their Groebner bases always in polynomial time by avoiding the mapping telescope.
Keywords
Cite
@article{arxiv.1210.1932,
title = {A presentation of general multipersistence modules computable in polynomial time?},
author = {Antonio Patriarca and Martina Scolamiero and Francesco Vaccarino},
journal= {arXiv preprint arXiv:1210.1932},
year = {2015}
}
Comments
This paper has been overcome by Combinatorial presentation of multidimensional persistent homology. Wojciech Chacholski, Martina Scolamiero, Francesco Vaccarino. arXiv:1409.7936