Browsing by Author "Bose, Prosenjit"

A polynomial bound for untangling geometric planar graphs
Bose, Prosenjit; Dujmovic, Vida; Hurtado Díaz, Fernando Alfredo; Langerman, Stefan; Morin, Pat; Wood, David (200912)
Article
Open AccessTo untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings. Pach and Tardos (Discrete Comput. Geom. 28(4): 585–592, 2002) asked if every nvertex geometric planar ... 
Connectivitypreserving transformations of binary images
Bose, Prosenjit; Dujmovic, Vida; Hurtado Díaz, Fernando Alfredo; Morin, Pat (200910)
Article
Open AccessA binary image $\emph{I}$ is $B_a$, $W_b$connected, where $\emph{a,b}$ ∊ {4,8}, if its foreground is $\emph{a}$connected and its background is $\emph{b}$connected. We consider a local modification of a $B_a$, $W_b$connected ... 
Every large point set contains many collinear points or an empty pentagon
Wood, David; Por, Attila; Abel, Zachary; Ballinger, Brad; Bose, Prosenjit; Collette, Sébastien; Dujmovic, Vida; Hurtado Díaz, Fernando Alfredo; Kominers, Scott Duke; Langerman, Stefan (201101)
Article
Restricted access  publisher's policyWe prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next ... 
On computing enclosing isosceles triangles and related problems
Bose, Prosenjit; Mora Giné, Mercè; Seara Ojea, Carlos; Sethia, Saurabh (201102)
Article
Open AccessGiven a set of n points in the plane, we show how to compute various enclosing isosceles triangles where different parameters such as area or perimeter are optimized. We then study a 3dimensional version of the problem ... 
On structural and graph theoretic properties of higher order Delaunay graphs
Abellanas, Manuel; Bose, Prosenjit; García López de Lacalle, Jesús; Hurtado Díaz, Fernando Alfredo; Nicolás, Carlos M.; Ramos, Pedro A. (200912)
Article
Open AccessGiven a set $\emph{P}$ of $\emph{n}$ points in the plane, the order$\emph{k}$ Delaunay graph is a graph with vertex set $\emph{P}$ and an edge exists between two points p,q ∊ $\emph{P}$ when there is a circle through ... 
Pole Dancing: 3D Morphs for Tree Drawings
Arseneva, Elena; Bose, Prosenjit; Cano Vila, María del Pilar; D'Angelo, Anthony; Dujmovic, Vida; Frati, Fabrizio; Langerman, Stefan; Tappini, Alessandra
Conference report
Restricted access  publisher's policyWe study the question whether a crossingfree 3D morph between two straightline drawings of an nvertex tree can be constructed consisting of a small number of linear morphing steps. We look both at the case in which the ... 
Sequences of spanning trees for Linfinity Delaunay triangulations
Bose, Prosenjit; Cano Vila, María del Pilar; Silveira, Rodrigo Ignacio (2018)
Conference report
Open AccessWe extend a known result about L2Delaunay triangulations to L∞Delaunay. Let TS be the set of all noncrossing spanning trees of a planar npoint set S. We prove that for each element T of TS, there exists a lengthdecreasing ... 
Some properties of higher order delaunay and gabriel graphs
Bose, Prosenjit; Collette, Sébastien; Hurtado Díaz, Fernando Alfredo; Korman, Matias; Langerman, Stefan; Sacristán Adinolfi, Vera; Saumell Mendiola, Maria (2010)
Conference report
Open AccessWe consider two classes of higher order proximity graphs defined on a set of points in the plane, namely, the kDelaunay graph and the kGabriel graph. We give bounds on the following combinatorial and geometric properties ...