An Approximation Algorithm for the Art Gallery Problem

Édouard Bonnet, Till Miltzow

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

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-size set S such that every point in P is visible from a point in S. The set S is referred to as guards. Assuming integer coordinates and a specific general position on the vertices of P, we present the first O(log OPT)-approximation algorithm for the point guard problem. This algorithm combines ideas in papers of Efrat and Har-Peled and Deshpande et al. We also point out a mistake in the latter.
Original languageEnglish
Title of host publication33rd International Symposium on Computational Geometry, SoCG 2017, July 4-7, 2017, Brisbane, Australia
EditorsBoris Aronov, Matthew J. Katz
PublisherSchloss Dagstuhl – Leibniz-Zentrum für Informatik GmbH
Pages20:1-20:15
DOIs
Publication statusPublished - 2017

Publication series

NameLIPIcs
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Volume77

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