research-article

Parameterized Hardness of Art Gallery Problems

Authors:

Édouard Bonnet,

Tillmann MiltzowAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 16, Issue 4

Article No.: 42, Pages 1 - 23

https://doi.org/10.1145/3398684

Published: 21 June 2020 Publication History

Abstract

Given a simple polygon P on n vertices, two points x, y in P are said to be visible to each other if the line segment between x and y is contained in P. The Point Guard Art Gallery problem asks for a minimum set S such that every point in P is visible from a point in S. The Vertex Guard Art Gallery problem asks for such a set S subset of the vertices of P. A point in the set S is referred to as a guard. For both variants, we rule out any f(k)n^{o(k / log k)} algorithm, where k := |S| is the number of guards, for any computable function f, unless the exponential time hypothesis fails. These lower bounds almost match the n^O(k) algorithms that exist for both problems.

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Cited By

Dumitrescu ATóth C(2024)Observation routes and external watchman routesTheoretical Computer Science10.1016/j.tcs.2024.1148181019(114818)Online publication date: Dec-2024
https://doi.org/10.1016/j.tcs.2024.114818
Agrawal AKnudsen KLokshtanov DSaurabh SZehavi M(2023)The Parameterized Complexity of Guarding Almost Convex PolygonsDiscrete & Computational Geometry10.1007/s00454-023-00569-y71:2(358-398)Online publication date: 5-Dec-2023
https://doi.org/10.1007/s00454-023-00569-y
Bertschinger DEl Maalouly NMiltzow TSchnider PWeber S(2023)Topological Art in Simple GalleriesDiscrete & Computational Geometry10.1007/s00454-023-00540-x71:3(1092-1130)Online publication date: 27-Aug-2023
https://doi.org/10.1007/s00454-023-00540-x
Show More Cited By

Index Terms

Parameterized Hardness of Art Gallery Problems
1. Networks
  1. Network algorithms
2. Theory of computation
  1. Theory and algorithms for application domains

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 16, Issue 4

October 2020

404 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/3407674

Editor:
Aravind Srinivasan
University of Maryland, USA

Issue’s Table of Contents

Copyright © 2020 ACM.

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Association for Computing Machinery

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Publication History

Published: 21 June 2020

Online AM: 13 May 2020

Accepted: 01 May 2020

Revised: 01 May 2020

Received: 01 April 2019

Published in TALG Volume 16, Issue 4

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Cited By

Dumitrescu ATóth C(2024)Observation routes and external watchman routesTheoretical Computer Science10.1016/j.tcs.2024.1148181019(114818)Online publication date: Dec-2024
https://doi.org/10.1016/j.tcs.2024.114818
Agrawal AKnudsen KLokshtanov DSaurabh SZehavi M(2023)The Parameterized Complexity of Guarding Almost Convex PolygonsDiscrete & Computational Geometry10.1007/s00454-023-00569-y71:2(358-398)Online publication date: 5-Dec-2023
https://doi.org/10.1007/s00454-023-00569-y
Bertschinger DEl Maalouly NMiltzow TSchnider PWeber S(2023)Topological Art in Simple GalleriesDiscrete & Computational Geometry10.1007/s00454-023-00540-x71:3(1092-1130)Online publication date: 27-Aug-2023
https://doi.org/10.1007/s00454-023-00540-x
Dumitrescu ATóth C(2023)Observation Routes and External Watchman RoutesAlgorithms and Data Structures10.1007/978-3-031-38906-1_26(401-415)Online publication date: 31-Jul-2023
https://dl.acm.org/doi/10.1007/978-3-031-38906-1_26
Agrawal AKolay SZehavi M(2022)Parameter Analysis for Guarding TerrainsAlgorithmica10.1007/s00453-021-00913-984:4(961-981)Online publication date: 1-Apr-2022
https://dl.acm.org/doi/10.1007/s00453-021-00913-9
Kratsch SMasařík TMuzi IPilipczuk MSorge MMarx D(2021)Optimal discretization is fixed-parameter tractableProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458167(1702-1719)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458167
Abrahamsen MAdamaszek AMiltzow T(2021)The Art Gallery Problem is ∃ℝ-completeJournal of the ACM10.1145/348622069:1(1-70)Online publication date: 7-Dec-2021
https://dl.acm.org/doi/10.1145/3486220

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