Author

# Jorge Urrutia

Other affiliations: University of Waterloo, University of Ottawa, Universidad Autónoma Metropolitana

Bio: Jorge Urrutia is an academic researcher from National Autonomous University of Mexico. The author has contributed to research in topics: Convex hull & General position. The author has an hindex of 32, co-authored 290 publications receiving 8296 citations. Previous affiliations of Jorge Urrutia include University of Waterloo & University of Ottawa.

##### Papers published on a yearly basis

##### Papers

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01 Aug 1999

TL;DR: The first distributed algorithms for routing that do not require duplication of packets or memory at the nodes and yet guarantee that a packet is delivered to its destination are described.

Abstract: 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 packet is delivered to its destination. These algorithms can be extended to yield algorithms for broadcasting and geocasting that do not require packet duplication. A byproduct of our results is a simple distributed protocol for extracting a planar subgraph of a unit graph. We also present simulation results on the performance of our algorithms.

1,537 citations

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TL;DR: The first distributed algorithms for routing that do not require duplication of packets or memory at the nodes and yet guarantee that a packet is delivered to its destination are described.

Abstract: 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 packet is delivered to its destination. These algorithms can be extended to yield algorithms for broadcasting and geocasting that do not require packet duplication. A by product of our results is a simple distributed protocol for extracting a planar subgraph of a unit graph. We also present simulation results on the performance of our algorithms.

1,234 citations

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01 Jan 1999

TL;DR: A close look at maps of numerous cities around the world, show that the previous way to explore a new, and unknown city will in general yield walks that will be close to the optimal ones to travel from one location to another.

Abstract: Suppose that a traveler arrives to the City of Toronto, and wants to walk to the famous CN-Tower, one of the tallest free-standing structures in the world. Assume now that our visitor, lacking a map of Toronto, is standing at a crossing from which he can see the CN-tower, and several streets S1, . . . , Sm that he can choose to start his walk. A natural (and most likely safe assumption), is that our visitor must choose to walk first along the road that points closest in the direction of the CN-tower, see Figure 1. A close look at maps of numerous cities around the world, show us that the previous way to explore a new, and unknown city will in general yield walks that will be close enough to the optimal ones to travel from one location to another. In mathematical terms, we can model the map of many cities by geometric graphs in which street intersections are represented by the vertices of our graphs, and streets by straight line segments. Compass routing on geometric networks, in its most elemental form yields the following algorithm:

964 citations

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01 Jan 2000

TL;DR: The Davenport-Schinzel sequences and their geometric applications, as well as randomizedalgorithms in computaional geometry, are described.

Abstract: reface. List of contrinbutors. 1. Davenport-Schinzel sequences and their geometric applications (P.K. Agarwal and M. Sharir). 2. Arrangements and their applications (P.K. Agarwal and M. Sharir). 3. Discrete geometric shapes: Matching, interpolation, and approximation (H. Alt and L.J. Guibas). 4. Deterministic parallel computational geometry (M.J. Attalah and D.Z. Chen). 5. Voronoi diagrams (F. Aurenhammer and R. Klein). 6. Mesh generation (M. Bern and P. Plassmann). 7. Applications of computational geometry to geographic information systems (L. de Floriani, P. Magillo and E. Puppo). 8. Making geometry visible: An introduction to the animation of geometric algorithms (A. Hausner and D.P. Dobkin). 9. Spanning trees and spanners (D. Eppstein). 10. Geometric data structures (M.T. Goodrich and K. Ramaiyer). 11. Polygon decomposition (J.M. Keil). 12. Link distance problems (A. Maheshwari, J.-R. Sack and H. N. Djidjev). 13. Derandomization in computational geometry (J. Matousek). 14. Robustness and precision issues in geometric computation (S. Schirra). 15. Geometric shortest paths and network optimization (J.S.B. Mitchell). 16. Randomizedalgorithms in computaional geometry (K. Mulmuley).

688 citations

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01 Jan 2000TL;DR: Since Victor Klee's question, numerous variations on the art gallery problem have been studied, including mobile guards, guards with limited visibility or mobility, illumination of families of convex sets on the plane, guarding of rectilinear polygons, and others.

Abstract: In 1973, Victor Klee posed the following question: 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 naive question of combinatorial geometry has, since its formulation, stimulated a plethora of papers, surveys and a book, most of them written in the last fifteen years. The first result in this area, due to V. Chvatal, asserts that n 3 guards are occasionally necessary and always sufficient to guard an art gallery represented by a simple polygon with n vertices. Since ChvataFs result, numerous variations on the art gallery problem have been studied, including mobile guards, guards with limited visibility or mobility, illumination of families of convex sets on the plane, guarding of rectilinear polygons, and others. In this paper, we survey most of these results.

474 citations

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[...]

TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.
Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

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01 Aug 2000TL;DR: Greedy Perimeter Stateless Routing is presented, a novel routing protocol for wireless datagram networks that uses the positions of routers and a packet's destination to make packet forwarding decisions and its scalability on densely deployed wireless networks is demonstrated.

Abstract: We present Greedy Perimeter Stateless Routing (GPSR), a novel routing protocol for wireless datagram networks that uses the positions of routers and a packet's destination to make packet forwarding decisions. GPSR makes greedy forwarding decisions using only information about a router's immediate neighbors in the network topology. When a packet reaches a region where greedy forwarding is impossible, the algorithm recovers by routing around the perimeter of the region. By keeping state only about the local topology, GPSR scales better in per-router state than shortest-path and ad-hoc routing protocols as the number of network destinations increases. Under mobility's frequent topology changes, GPSR can use local topology information to find correct new routes quickly. We describe the GPSR protocol, and use extensive simulation of mobile wireless networks to compare its performance with that of Dynamic Source Routing. Our simulations demonstrate GPSR's scalability on densely deployed wireless networks.

7,384 citations

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TL;DR: This paper presents a detailed study on recent advances and open research issues in WMNs, followed by discussing the critical factors influencing protocol design and exploring the state-of-the-art protocols for WMNs.

4,205 citations

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01 May 2005TL;DR: In this paper, several fundamental key aspects of underwater acoustic communications are investigated and a cross-layer approach to the integration of all communication functionalities is suggested.

Abstract: Underwater sensor nodes will find applications in oceanographic data collection, pollution monitoring, offshore exploration, disaster prevention, assisted navigation and tactical surveillance applications. Moreover, unmanned or autonomous underwater vehicles (UUVs, AUVs), equipped with sensors, will enable the exploration of natural undersea resources and gathering of scientific data in collaborative monitoring missions. Underwater acoustic networking is the enabling technology for these applications. Underwater networks consist of a variable number of sensors and vehicles that are deployed to perform collaborative monitoring tasks over a given area. In this paper, several fundamental key aspects of underwater acoustic communications are investigated. Different architectures for two-dimensional and three-dimensional underwater sensor networks are discussed, and the characteristics of the underwater channel are detailed. The main challenges for the development of efficient networking solutions posed by the underwater environment are detailed and a cross-layer approach to the integration of all communication functionalities is suggested. Furthermore, open research issues are discussed and possible solution approaches are outlined. � 2005 Published by Elsevier B.V.

2,864 citations