Browsing by Author "Bose, Prosenjit"
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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 ... 
Affine invariant triangulations
Bose, Prosenjit; Cano Vila, María del Pilar; Silveira, Rodrigo Ignacio (2019)
Conference report
Restricted access  publisher's policyWe study affine invariant 2D triangulation methods. That is, methods that produce the same triangulation for a point set S for any (unknown) affine transformation of S. Our work is based on a method by Nielson [A ... 
Affine invariant triangulations
Bose, Prosenjit; Cano Vila, Pilar; Silveira, Rodrigo Ignacio (20211101)
Article
Restricted access  publisher's policyWe study affine invariant 2D triangulation methods. That is, methods that produce the same triangulation for a point set S for any (unknown) affine transformation of S. Our work is based on a method by Nielson (1993) that ... 
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 ... 
Flips in higher order Delaunay triangulations
Arseneva, Elena; Bose, Prosenjit; Cano Vila, María del Pilar; Silveira, Rodrigo Ignacio (2021)
Conference report
Restricted access  publisher's policyWe study the flip graph of higher order Delaunay triangulations. A triangulation of a set S of n points in the plane is orderk Delaunay if for every triangle its circumcircle encloses at most k points of S. The flip graph ... 
Hamiltonicity for convex shape Delaunay and Gabriel graphs
Bose, Prosenjit; Cano Vila, María del Pilar; Saumell Mendiola, Maria; Silveira, Rodrigo Ignacio (2019)
Conference report
Restricted access  publisher's policyWe study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Let S be a point set in the plane. The korder Delaunay graph of S, denoted kDGC(S), has vertex set S and edge pq provided ... 
Hamiltonicity for convex shape Delaunay and Gabriel graphs
Bose, Prosenjit; Cano Vila, María del Pilar; Saumell Mendiola, Maria; Silveira, Rodrigo Ignacio (202008)
Article
Open AccessWe study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Instead of defining these proximity graphs using circles, we use an arbitrary convex shape \(\mathcal {C}\) . Let S be a point ... 
Hamiltonicity for convex shape Delaunay and Gabriel Graphs
Bose, Prosenjit; Cano Vila, María del Pilar; Saumell Mendiola, Maria; Silveira, Rodrigo Ignacio (Springer, 2019)
Conference report
Restricted access  publisher's policyWe study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Instead of defining these proximity graphs using circles, we use an arbitrary convex shape C. Let S be a point set in the plane. ... 
On approximating shortest paths in weighted triangular tessellations
Bose, Prosenjit; Esteban Pascual, Guillermo; Orden Martin, David; Silveira, Rodrigo Ignacio (Springer, 2022)
Conference report
Open AccessWe study the quality of weighted shortest paths when a continuous 2dimensional space is discretized by a weighted triangular tessellation. In order to evaluate how well the tessellation approximates the 2dimensional ... 
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 (Springer, 2018)
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 ... 
Spanning ratio of shortest paths in weighted square tessellations
Bose, Prosenjit; Esteban Pascual, Guillermo; Orden Martin, David; Silveira, Rodrigo Ignacio (2022)
Conference report
Restricted access  publisher's policyContinuous 2dimensional space is often discretized by considering a grid of weighted square cells. In this work we study how well a weighted tessellation approximates the space, with respect to shortest paths. In particular, ...