eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-08-18
19:1
19:17
10.4230/LIPIcs.ESA.2016.19
article
Parameterized Hardness of Art Gallery Problems
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 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 a f(k)*n^{o(k/log k)} algorithm, for any computable function f, where k := |S| is the number of guards, unless the Exponential Time Hypothesis fails. These lower bounds almost match the n^{O(k)} algorithms that exist for both problems.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol057-esa2016/LIPIcs.ESA.2016.19/LIPIcs.ESA.2016.19.pdf
art gallery problem
computational geometry
parameterized complexity
ETH-based lower bound
geometric set cover/hitting set