Open guard edges and edge guards in simple polygons

Csaba D. Tóth, Godfried Toussaint, Andrew Winslow

Research output: Contribution to conferencePaper

Abstract

An open edge of a simple polygon is the set of points in the relative interior of an edge. We revisit several art gallery problems, previously considered for closed edge guards, using open edge guards. A guard edge of a poly- gon is an edge that sees every point inside the polygon. We show that every simple non-starshaped polygon ad- mits at most one open guard edge, and give a simple new proof that it admits at most three closed guard edges. We characterize open guard edges, and derive an algorithm that finds all open guard edges of a simple n-gon in O(n) time in the RAM model of computation. Finally, we present lower bound constructions for simple polygons with n vertices that require [n/3] open edge guards, and conjecture that this bound is tight.

Original languageEnglish (US)
Pages54-64
Number of pages11
DOIs
StatePublished - Dec 1 2011
Event23rd Annual Canadian Conference on Computational Geometry, CCCG 2011 - Toronto, ON, Canada
Duration: Aug 10 2011Aug 12 2011

Other

Other23rd Annual Canadian Conference on Computational Geometry, CCCG 2011
CountryCanada
CityToronto, ON
Period8/10/118/12/11

Fingerprint

Simple Polygon
Random access storage
Polygon
Art Gallery Problem
n-gon
Closed
Models of Computation
Set of points
Interior
Lower bound

Keywords

  • art gallery
  • illumination
  • mobile guards
  • visibility

ASJC Scopus subject areas

  • Computational Mathematics
  • Geometry and Topology

Cite this

Tóth, C. D., Toussaint, G., & Winslow, A. (2011). Open guard edges and edge guards in simple polygons. 54-64. Paper presented at 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011, Toronto, ON, Canada. https://doi.org/10.1007/978-3-642-34191-5_5

Open guard edges and edge guards in simple polygons. / Tóth, Csaba D.; Toussaint, Godfried; Winslow, Andrew.

2011. 54-64 Paper presented at 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011, Toronto, ON, Canada.

Research output: Contribution to conferencePaper

Tóth, CD, Toussaint, G & Winslow, A 2011, 'Open guard edges and edge guards in simple polygons' Paper presented at 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011, Toronto, ON, Canada, 8/10/11 - 8/12/11, pp. 54-64. https://doi.org/10.1007/978-3-642-34191-5_5
Tóth CD, Toussaint G, Winslow A. Open guard edges and edge guards in simple polygons. 2011. Paper presented at 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011, Toronto, ON, Canada. https://doi.org/10.1007/978-3-642-34191-5_5
Tóth, Csaba D. ; Toussaint, Godfried ; Winslow, Andrew. / Open guard edges and edge guards in simple polygons. Paper presented at 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011, Toronto, ON, Canada.11 p.
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