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COCOON
2005
Springer
13 years 10 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 4 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»
12 years 12 months 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 4 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 4 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, ...