eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-06-01
17:1
17:16
10.4230/LIPIcs.SoCG.2022.17
article
ETH-Tight Algorithms for Finding Surfaces in Simplicial Complexes of Bounded Treewidth
Black, Mitchell
1
Blaser, Nello
2
https://orcid.org/0000-0001-9489-1657
Nayyeri, Amir
1
Vågset, Erlend Raa
2
https://orcid.org/0000-0003-2289-2268
School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR, USA
Department of Informatics, University of Bergen, Norway
Given a simplicial complex with n simplices, we consider the Connected Subsurface Recognition (c-SR) problem of finding a subcomplex that is homeomorphic to a given connected surface with a fixed boundary. We also study the related Sum-of-Genus 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 exponential-time hypothesis. In fact, we prove the stronger result that our algorithm is ETH-tight even without restriction on the total genus.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol224-socg2022/LIPIcs.SoCG.2022.17/LIPIcs.SoCG.2022.17.pdf
Computational Geometry
Surface Recognition
Treewidth
Hasse Diagram
Simplicial Complexes
Low-Dimensional Topology
Parameterized Complexity
Computational Complexity