eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-06-20
20:1
20:15
10.4230/LIPIcs.SoCG.2017.20
article
An Approximation Algorithm for the Art Gallery Problem
Bonnet, Édouard
Miltzow, Tillmann
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol077-socg2017/LIPIcs.SoCG.2017.20/LIPIcs.SoCG.2017.20.pdf
computational geometry
art gallery
approximation algorithm