• 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
    Accés restringit per política de l'editorial
    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)
    Text en actes de congrés
    Accés restringit per política de l'editorial
    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)
    Text en actes de congrés
    Accés obert
    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)
    Text en actes de congrés
    Accés restringit per política de l'editorial
    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)
    Text en actes de congrés
    Accés obert
    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 ...