Parameter analysis for guarding terrains

Akanksha Agrawal, Sudeshna Kolay, Meirav Zehavi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

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.

Original languageEnglish
Title of host publication17th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2020
EditorsSusanne Albers
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771504
DOIs
StatePublished - 1 Jun 2020
Event17th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2020 - Torshavn, Faroe Islands
Duration: 22 Jun 202024 Jun 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume162
ISSN (Print)1868-8969

Conference

Conference17th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2020
Country/TerritoryFaroe Islands
CityTorshavn
Period22/06/2024/06/20

Keywords

  • FPT Algorithm
  • Kernelization
  • Reflex Vertices
  • Terrain Guarding
  • Terrain Minima
  • XP Algorithm

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