2026-07-28T19:12:39Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12251 2024-03-06T10:49:27Z ddc:004 open_access

Parameter Analysis for Guarding Terrains Agrawal, Akanksha Kolay, Sudeshna Zehavi, Meirav Terrain Guarding Reflex Vertices Terrain Minima FPT Algorithm XP Algorithm Kernelization The Terrain Guarding problem is a well-known variant of the famous Art Gallery problem. Only second to Art Gallery, it is the most well-studied visibility problem in Discrete and Computational Geometry, which has also attracted attention from the viewpoint of Parameterized complexity. In this paper, we focus on the parameterized complexity of Terrain Guarding (both discrete and continuous) with respect to two natural parameters. First we show that, when parameterized by the number r of reflex vertices in the input terrain, the problem has a polynomial kernel. We also show that, when parameterized by the number c of minima in the terrain, Discrete Orthogonal Terrain Guarding has an XP algorithm. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Akanksha Agrawal and Sudeshna Kolay and Meirav Zehavi 2020 Is Part Of LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SWAT.2020.4 urn:nbn:de:0030-drops-122514 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.4 eng https://creativecommons.org/licenses/by/3.0/legalcode