Guarding Polyominoes Under k-Hop Visibility

Omrit Filtser, Erik Krohn, Bengt J. Nilsson, Christian Rieck, Christiane Schmidt

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


We study the Art Gallery Problem under k-hop visibility in polyominoes. In this visibility model, two unit squares of a polyomino can see each other if and only if the shortest path between the respective vertices in the dual graph of the polyomino has length at most k. In this paper, we show that the VC dimension of this problem is 3 in simple polyominoes, and 4 in polyominoes with holes. Furthermore, we provide a reduction from Planar Monotone 3Sat, thereby showing that the problem is NP-complete even in thin polyominoes (i.e., polyominoes that do not a contain a 2×2 block of cells). Complementarily, we present a linear-time 4-approximation algorithm for simple 2-thin polyominoes (which do not contain a 3×3 block of cells) for all k∈N.

Original languageEnglish
Title of host publicationLATIN 2024
Subtitle of host publicationTheoretical Informatics - 16th Latin American Symposium, 2024, Proceedings
EditorsJosé A. Soto, Andreas Wiese
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages15
ISBN (Print)9783031555978
StatePublished - 2024
Event16th Latin American Symposium on Theoretical Informatics, LATIN 2042 - Puerto Varas, Chile
Duration: 18 Mar 202422 Mar 2024

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14578 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th Latin American Symposium on Theoretical Informatics, LATIN 2042
CityPuerto Varas

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.


  • approximation
  • Art Gallery problem
  • k-hop dominating set
  • k-hop visibility
  • polyominoes
  • VC dimension


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