How to place efficiently guards and paintings in an art gallery

Fragoudakis, C; Markou, E; Zachos, S

dc.contributor.author	Fragoudakis, C	en
dc.contributor.author	Markou, E	en
dc.contributor.author	Zachos, S	en
dc.date.accessioned	2014-03-01T02:43:22Z
dc.date.available	2014-03-01T02:43:22Z
dc.date.issued	2005	en
dc.identifier.issn	0302-9743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/31359
dc.subject	Approximate Algorithm	en
dc.subject	Art Gallery Problem	en
dc.subject	Computational Geometry	en
dc.subject	Research Paper	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.other	Art gallery	en
dc.subject.other	Constant ratios	en
dc.subject.other	Polygon	en
dc.subject.other	Algorithms	en
dc.subject.other	Approximation theory	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Decoration	en
dc.subject.other	Polynomials	en
dc.subject.other	Problem solving	en
dc.subject.other	Painting	en
dc.title	How to place efficiently guards and paintings in an art gallery	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1007/11573036_14	en
heal.identifier.secondary	http://dx.doi.org/10.1007/11573036_14	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	In the art gallery problem the goal is to place guards (as few as possible) in a polygon so that a maximal area of the polygon is covered. We address here a closely related problem: how to place paintings and guards in an art gallery so that the total value of guarded paintings is a maximum. More formally, a simple polygon is given along with a set of paintings. Each painting, has a length and a value. We study how to place at the same time: i) a given number of guards on the boundary of the polygon and ii) paintings on the boundary of the polygon so that the total value of guarded paintings is maximum. We investigate this problem for a number of cases depending on: i) where the guards can be placed (vertices, edges), ii) whether the polygon has holes or not and iii) whether the goal is to oversee the placed paintings (every point of a painting is seen by at least one guard), or to watch the placed paintings (at least one point of a painting is seen by at least one guard). We prove that the problem is NP-hard in all the above cases and we present polynomial time approximation algorithms for all cases, achieving constant ratios. © Springer-Verlag Berlin Heidelberg 2005.	en
heal.publisher	SPRINGER-VERLAG BERLIN	en
heal.journalName	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	en
heal.bookName	LECTURE NOTES IN COMPUTER SCIENCE	en
dc.identifier.doi	10.1007/11573036_14	en
dc.identifier.isi	ISI:000233675500014	en
dc.identifier.volume	3746 LNCS	en
dc.identifier.spage	145	en
dc.identifier.epage	154	en