Ruy Fabila-Monroy

Learn More
Resumen In this paper we review recent results on a new variation of the Art Gallery problem. A common problem we face nowadays, is that of placing a set of wireless modems in a building in such a way that a computer placed anywhere within the building receives a signal strong enough to connect to the Web. In most buildings, the main limitation for this(More)
We study a geometric Ramsey type problem where the vertices of the complete graph K n are placed on a set S of n points in general position in the plane, and edges are drawn as straight-line segments. We define the empty convex polygon Ramsey number R EC (k, k) as the smallest number n such that for every set S of n points and for every two-coloring of the(More)
Let S be a 2-colored (red and blue) set of n points in the plane. A subset I of S is an island if there exits a convex set C such that I = C ∩ S. The discrepancy of an island is the absolute value of the number of red minus the number of blue points it contains. A convex partition of S is a partition of S into islands with pairwise disjoint convex hulls.(More)
Let S be a 2-colored (red and blue) set of n points in the plane. A subset I of S is an island if there exits a convex set C such that I = C ∩S. The discrepancy of an island is the absolute value of the number of red minus the number of blue points it contains. A convex partition of S is a partition of S into islands with pairwise disjoint convex hulls. The(More)
This paper concerns about mobile ad-hoc wireless networks, but with the added restriction that each radio station has a rectilinear trajectory. We focus on the problem of computing an optimal range assignment for the stations, which allows to perform a broadcast operation from a source station, while the overall energy deployed is minimized. An O(n 3 log(More)
Citation Aloupis, Greg et al. " Matching Points with Things. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract. 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(More)
We study the number of crossings among edges of some higher order proximity graphs of the family of the Delaunay graph. That is, given a set P of n points in the Euclidean plane, we give lower and upper bounds on the minimum and the maximum number of crossings that these geometric graphs defined on P have.
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)
This paper studies the chromatic number of the following four flip graphs (under suitable definitions of a flip): • the flip graph of perfect matchings of a complete graph of even order, • the flip graph of triangulations of a convex polygon (the associahedron), • the flip graph of non-crossing Hamiltonian paths of a convex point set, and • the flip graph(More)
  • 1