URL - Presentation file, Visit http://pefprints.pef.uni-lj.si/3661/

Abstract
Obravnavamo osnovni problem varovanja galerij, katerih tlorisi so enostavni poligoni z n oglišči, varnostnike pa postavljamo v oglišča. Preko primera poligona z n oglišči pokažemo, da obstaja poligon, ki za nadzor potrebuje floor(n / 3) varnostnikov. S triangulacijo poligona in 3-barvanjem podamo algoritem, ki nam najde postavitev varnostnikov pri kateri floor(n / 3) varnostnikov zadosti za nadzor celotne galerije. Obravnavamo tudi delitev poligona na y-monotone dele in njihovo triangulacijo. Delovanje algoritmov ponazorimo na primerih.

Language: Slovenian problem galerije Undergraduate thesis (m5) 2.11 - Undergraduate Thesis PEF - Faculty of Education 2016 11134793 805 152 (0 votes) Voting is allowed only to logged in users. AddThis uses cookies that require your consent. Edit consent...

## Secondary language

Language: English Guarding art galleries We present the classical art gallery problem where the floor is a simple polygon with n vertices and we guard it by vertex guards. With an example which needs floor(n / 3) vertex guards, we proof that floor(n / 3) vertex guards might be necessary. By a triangulation of polygon and 3-coloring we give an algorithm which finds a placement for vertex guards where floor(n / 3) guards are sufficient to cover the entire polygon. We continue with presenting a division of the polygon into y-monotone pieces which we further triangulate. We simulate algoritms on examples. art gallery problem