Now showing items 1-14 of 14

    • A polynomial bound for untangling geometric planar graphs 

      Bose, Prosenjit; Dujmovic, Vida; Hurtado Díaz, Fernando Alfredo; Langerman, Stefan; Morin, Pat; Wood, David (2009-12)
      Article
      Open Access
      To 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 n-vertex geometric planar ...
    • Affine invariant triangulations 

      Bose, Prosenjit; Cano Vila, María del Pilar; Silveira, Rodrigo Ignacio (2019)
      Conference report
      Restricted access - publisher's policy
      We 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 (2021-11-01)
      Article
      Restricted access - publisher's policy
      We 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 ...
    • Connectivity-preserving transformations of binary images 

      Bose, Prosenjit; Dujmovic, Vida; Hurtado Díaz, Fernando Alfredo; Morin, Pat (2009-10)
      Article
      Open Access
      A 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 (2011-01)
      Article
      Restricted access - publisher's policy
      We 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
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      We study the flip graph of higher order Delaunay triangulations. A triangulation of a set S of n points in the plane is order-k 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
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      We study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Let S be a point set in the plane. The k-order Delaunay graph of S, denoted k-DGC(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 (2020-08)
      Article
      Open Access
      We 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 policy
      We 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 computing enclosing isosceles triangles and related problems 

      Bose, Prosenjit; Mora Giné, Mercè; Seara Ojea, Carlos; Sethia, Saurabh (2011-02)
      Article
      Open Access
      Given 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 3-dimensional 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. (2009-12)
      Article
      Open Access
      Given 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 policy
      We study the question whether a crossing-free 3D morph between two straight-line drawings of an n-vertex 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 L-infinity Delaunay triangulations 

      Bose, Prosenjit; Cano Vila, María del Pilar; Silveira, Rodrigo Ignacio (2018)
      Conference report
      Open Access
      We extend a known result about L2-Delaunay triangulations to L∞-Delaunay. Let TS be the set of all non-crossing spanning trees of a planar n-point set S. We prove that for each element T of TS, there exists a length-decreasing ...
    • 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 Access
      We consider two classes of higher order proximity graphs defined on a set of points in the plane, namely, the k-Delaunay graph and the k-Gabriel graph. We give bounds on the following combinatorial and geometric properties ...