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COCOON
2005
Springer
13 years 11 months ago
An Upper Bound on the Number of Rectangulations of a Point Set
Abstract. We consider the number of different ways to divide a rectangle containing n noncorectilinear points into smaller rectangles by n non-intersecting axis-parallel segments,...
Eyal Ackerman, Gill Barequet, Ron Y. Pinter
JCT
2006
60views more  JCT 2006»
13 years 5 months ago
On the number of rectangulations of a planar point set
We investigate the number of different ways in which a rectangle containing a set of n noncorectilinear points can be partitioned into smaller rectangles by n (non-intersecting) s...
Eyal Ackerman, Gill Barequet, Ron Y. Pinter
JCT
2011
108views more  JCT 2011»
13 years 8 days ago
The number of extreme points of tropical polyhedra
The celebrated upper bound theorem of McMullen determines the maximal number of extreme points of a polyhedron in terms of its dimension and the number of constraints which define...
Xavier Allamigeon, Stéphane Gaubert, Ricard...
DAM
2006
124views more  DAM 2006»
13 years 5 months ago
Coloring copoints of a planar point set
To a set of n points in the plane, one can associate a graph that has less than n2 vertices and has the property that k-cliques in the graph correspond vertex sets of convex k-gon...
Walter Morris
CORR
2002
Springer
86views Education» more  CORR 2002»
13 years 5 months ago
Small Strictly Convex Quadrilateral Meshes of Point Sets
In this paper we give upper and lower bounds on the number of Steiner points required to construct a strictly convex quadrilateral mesh for a planar point set. In particular, we sh...
David Bremner, Ferran Hurtado, Suneeta Ramaswami, ...