Parameter Analysis for Guarding Terrains

Authors Akanksha Agrawal, Sudeshna Kolay, Meirav Zehavi

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Akanksha Agrawal
  • Ben-Gurion University of the Negev, Beersheba, Israel
Sudeshna Kolay
  • Ben-Gurion University of the Negev, Beersheba, Israel
Meirav Zehavi
  • Ben-Gurion University of the Negev, Beersheba, Israel


The second author would like to thank Prof. Mark de Berg for very insightful preliminary discussions for the second problem. The first and third authors are thankful to Prof. Saket Saurabh for helpful discussions.

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Akanksha Agrawal, Sudeshna Kolay, and Meirav Zehavi. Parameter Analysis for Guarding Terrains. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Terrain Guarding
  • Reflex Vertices
  • Terrain Minima
  • FPT Algorithm
  • XP Algorithm
  • Kernelization


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