ETHtight algorithms for finding surfaces in simplicial complexes of bounded treewidth
Abstract
Given a simplicial complex with $n$ simplices, we consider the Connected Subsurface Recognition (cSR) problem of finding a subcomplex that is homeomorphic to a given connected surface with a fixed boundary. We also study the related SumofGenus Subsurface Recognition (SoG) problem, where we instead search for a surface whose boundary, number of connected components, and total genus are given. For both of these problems, we give parameterized algorithms with respect to the treewidth $k$ of the Hasse diagram that run in $2^{O(k \log k)}n^{O(1)}$ time. For the SoG problem, we also prove that our algorithm is optimal assuming the exponentialtime hypothesis. In fact, we prove the stronger result that our algorithm is ETHtight even without restriction on the total genus.
 Publication:

arXiv eprints
 Pub Date:
 March 2022
 DOI:
 10.48550/arXiv.2203.07566
 arXiv:
 arXiv:2203.07566
 Bibcode:
 2022arXiv220307566B
 Keywords:

 Computer Science  Computational Geometry
 EPrint:
 This paper contains some material that previously appeared at arXiv:2107.10339. The split into two papers reflects new material and a change in authorship in this version. Accepted to SoCG 2022