Homology Localization Through the Looking-Glass of Parameterized Complexity Theory
Computational Geometry
2020-12-01 v1 Computational Complexity
Algebraic Topology
Abstract
Finding a cycle of lowest weight that represents a homology class in a simplicial complex is known as homology localization (HL). Here we address this NP-complete problem using parameterized complexity theory. We show that it is W[1]-hard to approximate the HL problem when it is parameterized by solution size. We have also designed and implemented two algorithms based on treewidth solving the HL problem in FPT-time. Both algorithms are ETH-tight but our results shows that one outperforms the other in practice.
Keywords
Cite
@article{arxiv.2011.14490,
title = {Homology Localization Through the Looking-Glass of Parameterized Complexity Theory},
author = {Nello Blaser and Erlend Raa Vågset},
journal= {arXiv preprint arXiv:2011.14490},
year = {2020}
}
Comments
30 pages, 19 figures