Now showing items 1-5 of 5

  • 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
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    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 ...
  • 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 ...