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arXiv · 2011.14490

Homology Localization Through the Looking-Glass of Parameterized Complexity Theory

Nello Blaser·Erlend Raa Vågset
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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.

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Nello Blaser, Erlend Raa Vågset. 2020-11-30. Homology Localization Through the Looking-Glass of Parameterized Complexity Theory. https://arxiv.org/abs/2011.14490

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