Maximizing the guarded boundary of an Art Gallery is APX-complete

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	2014-03-01T01:26:34Z
dc.date.available	2014-03-01T01:26:34Z
dc.date.issued	2007	en
dc.identifier.issn	0925-7721	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18141
dc.subject	Approximation algorithms	en
dc.subject	Art gallery	en
dc.subject	Visibility	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.title	Maximizing the guarded boundary of an Art Gallery is APX-complete	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.comgeo.2006.12.001	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.comgeo.2006.12.001	en
heal.language	English	en
heal.publicationDate	2007	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. (C) 2006 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Computational Geometry: Theory and Applications	en
dc.identifier.doi	10.1016/j.comgeo.2006.12.001	en
dc.identifier.isi	ISI:000249488900004	en
dc.identifier.volume	38	en
dc.identifier.issue	3	en
dc.identifier.spage	170	en
dc.identifier.epage	180	en