Illumination of polygons with vertex lights
Information Processing Letters
Pseudo-triangulations: theory and applications
Proceedings of the twelfth annual symposium on Computational geometry
Art gallery problem with guards whose range of vision is 180°
Computational Geometry: Theory and Applications
ACM SIGACT News
Computational geometry column 43
ACM SIGACT News
Illuminating Polygons with Vertex pi-Floodlights
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
A combinatorial approach to planar non-colliding robot arm motion planning
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Planar minimally rigid graphs and pseudo-triangulations
Proceedings of the nineteenth annual symposium on Computational geometry
Kinetic collision detection between two simple polygons
Computational Geometry: Theory and Applications
The polytope of non-crossing graphs on a planar point set
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Convexity minimizes pseudo-triangulations
Computational Geometry: Theory and Applications - Special issue on the 14th Canadian conference on computational geometry — CCCG02
Energy-aware stage illumination
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Planar minimally rigid graphs and pseudo-triangulations
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
Computational geometry column 48
ACM SIGACT News
Minimum weight pseudo-triangulations
Computational Geometry: Theory and Applications
Planar minimally rigid graphs and pseudo-triangulations
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
The stochastic walk algorithms for point location in pseudo-triangulations
Advances in Engineering Software
Construction of pseudo-triangulation by incremental insertion
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
Parallel-redrawing mechanisms, pseudo-triangulations and kinetic planar graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
Minimum weight pseudo-triangulations
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
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We use the concept of pointed pseudo-triangulations to establish new upper and lower bounds on a well known problem from the area of art galleries: What is the worst case optimal number of vertex π-guards that collectively monitor a simple polygon with n vertices?Our results are as follows:1. Any simple polygon with n vertices can be mon- itored by at most [n/2] general vertex π-guards. This bound is tight up to an additive constant of 1.2. Any simple polygon with n vertices, k of which are convex, can be monitored by at most [(2n -- k)/3] edge-aligned vertex π-guards. This is the first non- trivial upper bound for this problem and it is tight for the worst case families of polygons known so far.