Homology Localization Through the Looking-Glass of Parameterized Complexity Theory

11/30/2020
by   Nello Blaser, et al.
0

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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset