Browsing by Author "Langerman, Stefan"

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 ... 
Computing a visibility polygon using few variables
Barba, Luis; Korman Cozzetti, Matías; Langerman, Stefan; Silveira, Rodrigo Ignacio (20141001)
Article
Restricted access  publisher's policyWe 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 readonly 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 (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 ... 
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 policyGiven an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a noncrossing matching between pointobject 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 (20140601)
Article
Restricted access  publisher's policyWe 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.; ElKhechen, Dania; Flatland, Robin; Langerman, Stefan; O'Rourke, Joseph (CIMAT, 2008)
Conference report
Open AccessIn 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 cubestyle 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, SpringerVerlag, 2008)
Conference report
Restricted access  publisher's policyWe consider a model of reconfigurable robot, introduced and prototyped by the robotics community. The robot consists of independently manipulable unitsquare 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 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 ...