ETH-Tight Algorithms for Finding Surfaces in Simplicial Complexes of Bounded Treewidth
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Date
2022Metadata
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- Department of Informatics [978]
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Original version
Leibniz International Proceedings in Informatics. 2022, 224, 17. 10.4230/LIPIcs.SoCG.2022.17Abstract
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.