Jorge Urrutia

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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)
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)
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)
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)
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)
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)
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.
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)