Tight Bounds for Connectivity Problems Parameterized by Cutwidth ...

• Main Authors: Bojikian, Narek, Chekan, Vera, Hegerfeld, Falko, Kratsch, Stefan
• Format: Conference Object
• Language: English
• Published: Schloss Dagstuhl – Leibniz-Zentrum für Informatik 2023
• Subjects: Parameterized complexity; connectivity problems; cutwidth; Theory of computation → Parameterized complexity and exact algorithms; Groenland
• Online Access: https://dx.doi.org/10.4230/lipics.stacs.2023.14; https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.14

In this work we start the investigation of tight complexity bounds for connectivity problems parameterized by cutwidth assuming the Strong Exponential-Time Hypothesis (SETH). Van Geffen et al. [Bas A. M. van Geffen et al., 2020] posed this question for Odd Cycle Transversal and Feedback Vertex Set. We answer it for these two and four further problems, namely Connected Vertex Cover, Connected Dominating Set, Steiner Tree, and Connected Odd Cycle Transversal. For the latter two problems it sufficed to prove lower bounds that match the running time inherited from parameterization by treewidth; for the others we provide faster algorithms than relative to treewidth and prove matching lower bounds. For upper bounds we first extend the idea of Groenland et al. [Carla Groenland et al., 2022] to solve what we call coloring-like problems. Such problems are defined by a symmetric matrix M over ????₂ indexed by a set of colors. The goal is to count the number (modulo some prime p) of colorings of a graph such that M has a ... : LIPIcs, Vol. 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023), pages 14:1-14:16 ...