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» On empty convex polygons in a planar point set
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CCCG
2006
15 years 1 months ago
An O(n log n) Algorithm for the All-Farthest-Segments Problem for a Planar Set of Points
In this paper, we propose an algorithm for computing the farthest-segment Voronoi diagram for the edges of a convex polygon and apply this to obtain an O(n log n) algorithm for th...
Asish Mukhopadhyay, Robert L. Scot Drysdale
SIGACT
2008
103views more  SIGACT 2008»
14 years 11 months ago
Computational geometry column 50
Two long-open problems have been solved: (1) every sufficiently large planar point set in general position contains the vertices of an empty hexagon; (2) every finite collection o...
Joseph O'Rourke
CCCG
2008
15 years 1 months ago
Recognition of Largest Empty Orthoconvex Polygon in a Point Set
An algorithm for computing the maximum area empty isothetic orthoconvex polygon among a set of n points in a rectangular region, is presented. The worst case time and space comple...
Subhas C. Nandy, Krishnendu Mukhopadhyaya, Bhargab...
CCCG
2009
15 years 21 days ago
Optimal Empty Pseudo-Triangles in a Point Set
Given n points in the plane, we study three optimization problems of computing an empty pseudo-triangle: we consider minimizing the perimeter, maximizing the area, and minimizing ...
Hee-Kap Ahn, Sang Won Bae, Iris Reinbacher