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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)

- Oswin Aichholzer, Ruy Fabila Monroy, David Flores-Peñaloza, Thomas Hackl, Clemens Huemer, Jorge Urrutia
- Comput. Geom.
- 2008

We consider a variation of a problem stated by Erdös and Guy in 1973 about the number of convex k-gons determined by any set S of n points in the plane. In our setting the points of S are colored and we say that a spanned polygon is monochromatic if all its points are colored with the same color. As a main result we show that any bi-colored set of n points… (More)

- Bernardo M. Ábrego, Ruy Fabila Monroy, +4 authors Maria Saumell
- Comput. Geom.
- 2011

Let P be a set of n points in the plane. A geometric proximity graph on P is a graph where two points are connected by a straight-line segment if they satisfy some prescribed proximity rule. We consider four classes of higher order proximity graphs, namely, the k-nearest neighbor graph, the k-relative neighborhood graph, the k-Gabriel graph and the… (More)

In 1926, Jarník introduced the problem of drawing a convex n-gon with vertices having integer coordinates. He constructed such a drawing in the grid [1, c · n 3/2 ] 2 for some constant c > 0, and showed that this grid size is optimal up to a constant factor. We consider the analogous problem for drawing the double circle, and prove that it can be done… (More)

- José Miguel Díaz-Báñez, Ruy Fabila Monroy, David Flores-Peñaloza, Marco A. Heredia, Jorge Urrutia
- J. Comb. Optim.
- 2012

This paper concerns about energy-efficient broadcasts in mobile ad hoc networks, yet in a model where each station moves on the plane with uniform rec-tilinear motion. Such restriction is imposed to discern which issues arise from the introduction of movement in the wireless ad hoc networks. Given a transmission range assignment for a set of n stations S,… (More)

- Bernardo M. Ábrego, Ruy Fabila Monroy, +5 authors Maria Saumell
- Networks
- 2013

Given a large weighted graph G = (V, E) and a subset U of V , we define several graphs with vertex set U in which two vertices are adjacent if they satisfy some prescribed proximity rule. These rules use the shortest path distance in G and generalize the proximity rules that generate some of the most common proximity graphs in Euclidean spaces. We prove… (More)

- Crevel Bautista-Santiago, Javier Cano, +5 authors Jorge Urrutia
- Discrete Mathematics & Theoretical Computer…
- 2013

Let P be a set of n points in general position in the plane. A subset I of P is called an island if there exists a convex set C such that I = P ∩ C. In this paper we define the generalized island Johnson graph of P as the graph whose vertex consists of all islands of P of cardinality k, two of which are adjacent if their intersection consists of exactly l… (More)

We prove that a graph is 4-colorable if and only if it can be drawn with vertices in the integer lattice, using as edges only line segments not containing a third point of the lattice.

- Oswin Aichholzer, Sergio Cabello, +5 authors David R. Wood
- Discrete Mathematics & Theoretical Computer…
- 2010

A geometric graph is a graph G = (V, E) drawn in the plane, such that V is a point set in general position and E is a set of straight-line segments whose endpoints belong to V. We study the following extremal problem for geometric graphs: How many arbitrary edges can be removed from a complete geometric graph with n vertices such that the remaining graph… (More)

- Sergio Rajsbaum, Armando Castañeda, David Flores-Peñaloza, Manuel Alcantara
- 2017 IEEE International Parallel and Distributed…
- 2017

The LOOK-COMPUTE-MOVE model for a set of autonomous robots has been thoroughly studied for over two decades. Each robot repeatedly LOOKS at its surroundings and obtains a snapshot containing the positions of all robots; based on this information, the robot COMPUTES a destination and then MOVES to it. Previous work assumed all robots are present at the… (More)