Maximizing the guarded boundary of an art gallery is APX-complete

Markou, E; Zachos, S; Fragoudakis, C

dc.contributor.author	Markou, E	en
dc.contributor.author	Zachos, S	en
dc.contributor.author	Fragoudakis, C	en
dc.date.accessioned	2014-03-01T01:19:13Z
dc.date.available	2014-03-01T01:19:13Z
dc.date.issued	2003	en
dc.identifier.issn	0302-9743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15391
dc.subject	Art Gallery Problem	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.title	Maximizing the guarded boundary of an art gallery is APX-complete	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/3-540-44849-7_10	en
heal.identifier.secondary	http://dx.doi.org/10.1007/3-540-44849-7_10	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	In the Art Gallery problem, given is a polygonal gallery and the goal is to guard the gallery's interior or walls with a number of guards that must be placed strategically in the interior, on walls or on corners of the gallery. Here we consider a more realistic version: exhibits now have size and may have different costs. Moreover the meaning of guarding is relaxed: we use a new concept, that of watching an expensive art item, i.e. overseeing a part of the item. The main result of the paper is that the problem of maximizing the total value of a guarded weighted boundary is APX-complete. This is shown by an appropriate gap-preserving reduction from the MAX-5-OCCURRENCE-3-SAT problem. We also show that this technique can be applied to a number of maximization variations of the art gallery problem. In particular we consider the following problems: given a polygon with or without holes and k available guards, maximize a) the length of walls guarded and b) the total cost of paintings watched or overseen. We prove that all the above problems are APX-complete. © Springer-Verlag Berlin Heidelberg 2003.	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	10.1007/3-540-44849-7_10	en
dc.identifier.isi	ISI:000184834000010	en
dc.identifier.volume	2653	en
dc.identifier.spage	24	en
dc.identifier.epage	35	en