131views more  JDA 2010»
9 years 8 months ago
Convex drawings of hierarchical planar graphs and clustered planar graphs
: Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in VLSI design, CASE tools, soft...
Seok-Hee Hong, Hiroshi Nagamochi
81views more  DCG 1999»
9 years 10 months ago
Properties of Random Triangulations and Trees
Let Tn denote the set of triangulations of a convex polygon K with n sides. We study functions that measure very natural "geometric" features of a triangulation Tn, fo...
Luc Devroye, Philippe Flajolet, Ferran Hurtado, Ma...
75views more  JCIT 2007»
9 years 10 months ago
A Method for Classification of Convex Polygons
Based on the planar polygon shape classification, we propose a method—Standardized Binary String Descriptor of Convex Polygon—for classification of convex polygons, making it ...
Ping Guo, Yan-Xia Wang
9 years 10 months ago
Dyck paths with coloured ascents
We introduce a notion of Dyck paths with coloured ascents. For several ways of colouring, when the set of colours is itself some class of lattice paths, we establish bijections be...
Andrei Asinowski, Toufik Mansour
113views Education» more  CORR 2010»
9 years 10 months ago
Opaque sets
The problem of finding "small" sets that meet every straight-line which intersects a given convex region was initiated by Mazurkiewicz in 1916. We call such a set an opa...
Adrian Dumitrescu, János Pach
121views Algorithms» more  SODA 1996»
9 years 11 months ago
Optimal Placement of Convex Polygons to Maximize Point Containment
Given a convex polygon P with m vertices and a set S of n points in the plane, we consider the problem of nding a placement of P that contains the maximum number of points in S. W...
Matthew Dickerson, Daniel Scharstein
9 years 11 months ago
An algorithm for the MaxMin area triangulation of a convex polygon
Given a convex polygon in the plane, we are interested in triangulations of its interior, i.e. maximal sets of nonintersecting diagonals that subdivide the interior of the polygon...
J. Mark Keil, Tzvetalin S. Vassilev
9 years 11 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
9 years 11 months ago
On Computing Shortest External Watchman Routes for Convex Polygons
We study the relationship between the interior angles of a convex polygon and the lengths of external watchman routes.
Rafa Absar, Sue Whitesides
9 years 12 months ago
Hausdorff core of a one reflex vertex polygon
In this paper we present a polynomial time algorithm for computing a Hausdorff core of a polygon with a single reflex vertex. A Hausdorff core of a polygon P is a convex polygon Q...
Robert Fraser, Patrick K. Nicholson