Now showing items 1-8 of 8

  • 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 ...
  • Computing a visibility polygon using few variables 

    Barba, Luis; Korman Cozzetti, Matías; Langerman, Stefan; Silveira, Rodrigo Ignacio (2014-10-01)
    Article
    Restricted access - publisher's policy
    We present several algorithms for computing the visibility polygon of a simple polygon P of n vertices (out of which r are reflex) from a viewpoint inside P, when P resides in read-only memory and only few working variables ...
  • 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 ...
  • Matching points with things 

    Taslakian, Perouz; Seara Ojea, Carlos; Saumell Mendiola, Maria; Langerman, Stefan; Hurtado Díaz, Fernando Alfredo; Aloupis, Greg; Cardinal, Jean; Collette, Sébastien; Demaine, Erik D.; Demaine, Martin L.; Dulieu, Muriel; Fabila Monroy, Ruy; Hart, Vi (Springer Verlag, 2010)
    Conference report
    Restricted access - publisher's policy
    Given an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a non-crossing matching between point-object pairs. We show that when the objects we match the points to ...
  • Necklaces, convolutions, and X plus Y 

    Bremner, David; Chan, Timothy M.; Demaine, Erik D.; Erickson, Jeff; Hurtado Díaz, Fernando Alfredo; Iacono, John; Langerman, Stefan; Patrascu, Mihai; Taslakian, Perouz (2014-06-01)
    Article
    Restricted access - publisher's policy
    We give subquadratic algorithms that, given two necklaces each with n beads at arbitrary positions, compute the optimal rotation of the necklaces to best align the beads. Here alignment is measured according to the ℓ p ...
  • Realistic reconfiguration of crystalline (and telecube) robots 

    Wuhrer, Stefanie; Sacristán Adinolfi, Vera; Ramaswami, Suneeta; Pinciu, Val; Aloupis, Greg; Collette, Sébastien; Damian, Mirela; Demaine, Erik D.; El-Khechen, Dania; Flatland, Robin; Langerman, Stefan; O'Rourke, Joseph (CIMAT, 2008)
    Conference report
    Open Access
    In this paper we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or ...
  • Reconfiguration of cube-style modular robots using O(logn) parallel moves 

    Aloupis, Greg; Collette, Sébastien; Demaine, Erik D.; Langerman, Stefan; Sacristán Adinolfi, Vera; Wuhrer, Stefanie (Lecture Notes in Computer Science LNCS 5369, Springer-Verlag, 2008)
    Conference report
    Restricted access - publisher's policy
    We consider a model of reconfigurable robot, introduced and prototyped by the robotics community. The robot consists of independently manipulable unit-square atoms that can extend/contract arms on each side and attach/detach ...
  • 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 ...