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- Prosenjit Bose, Pat Morin, Ivan Stojmenovic, Jorge Urrutia
- Wireless Networks
- 1999

We consider routing problems in ad hoc wireless networks modeled as unit graphs in which nodes are points in the plane and two nodes can communicate if the distance between them is less than some fixed unit. We describe the first distributed algorithms for routing that do not require duplication of packets or memory at the nodes and yet guarantee that a… (More)

- Evangelos Kranakis, Harvinder Singh, Jorge Urrutia
- CCCG
- 1999

Suppose that a traveler arrives in the city of Toronto, and wants to walk to the famous CN Tower, one of the tallest free-standing structures in the world. Our visitor, lacking a map of Toronto, is standing at an intersection fromwhich he can see the CN Tower, and several streets S1; : : : ; Sm from which he can choose to start his walk. A natural (and most… (More)

- Jorge Urrutia
- 2000

How many guards are necessary, and how many are sufficient to patrol the paintings and works of art in an art gallery with n walls? This wonderfully na¨ıve question of combinatorial geometry has, since its formulation, stimulated an increasing number of of papers and surveys. In 1987, J. O'Rourke published his book Art Gallery Theorems and Algorithms which… (More)

- Ferran Hurtado, Marc Noy, Jorge Urrutia
- Discrete & Computational Geometry
- 1996

In this paper we study the problem of flipping edges in triangulations of polygons and point sets. One of the main results is that any triangulation of a set of n points in general position contains at least d(n − 4)/2e edges that can be flipped. We also prove that O(n + k2) flips are sufficient to transform any triangulation of an n-gon with k reflex… (More)

- Martin Charles Golumbic, Doron Rotem, Jorge Urrutia
- Discrete Mathematics
- 1983

A function diagram (f-diagram) D consists of the family of curves {i, . . . , ii} obtained from n continuous functions fi : [O, 1] -B R (1 G i d n). We call the intersection graph of D a function graph (f-graph). It is shown that a graph G is an f-graph if and only if its complement 0 is a comparability graph. An f-diagram generalizes the notion cf a… (More)

- Jurek Czyzowicz, Evangelos Kranakis, +6 authors Mohammadreza Yazdani
- ADHOC-NOW
- 2010

A set of sensors establishes barrier coverage of a given line segment if every point of the segment is within the sensing range of a sensor. Given a line segment I, n mobile sensors in arbitrary initial positions on the line (not necessarily inside I) and the sensing ranges of the sensors, we are interested in finding final positions of sensors which… (More)

- Manuel Abellanas, Alfredo García Olaverri, Ferran Hurtado, Javier Tejel, Jorge Urrutia
- Comput. Geom.
- 2008

Let G be a connected plane geometric graph with n vertices. In this paper, we study bounds on the number of edges required to be added to G to obtain 2-vertex or 2-edge connected plane geometric graphs. In particular, we show that for G to become 2-edge connected, 2n 3 additional edges are required in some cases and that 6n 7 additional edges are always… (More)

- Jérôme Galtier, Ferran Hurtado, Marc Noy, Stéphane Pérennes, Jorge Urrutia
- Int. J. Comput. Geometry Appl.
- 2003

We generalize the operation of flipping an edge in a triangulation to that of flipping several edges simultaneously. Our main result is an optimal upper bound on the number of simultaneous flips that are needed to transform a triangulation into another. Our results hold for triangulations of point sets and for polygons.

- Jurek Czyzowicz, Evangelos Kranakis, +6 authors Mohammadreza Yazdani
- ADHOC-NOW
- 2009

We consider n mobile sensors located on a line containing a barrier represented by a finite line segment. Sensors form a wireless sensor network and are able to move within the line. An intruder traversing the barrier can be detected only when it is within the sensing range of at least one sensor. The sensor network establishes barrier coverage of the… (More)

We study a generalization of the classical problem of illumination of polygons. Instead of modeling a light source we model a wireless device whose radio signal can penetrate a given number k of walls. We call these objects k-modems and study the minimum number of k-modems necessary to illuminate monotone and monotone orthogonal polygons. We show that every… (More)