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The city Voronoi diagram is induced by quickest paths, in the <i>L</i> <inf>1</inf> plane speeded up by an isothetic transportation network. We investigate the rich geometric and algorithmic properties of city Voronoi diagrams, and report on their use in processing quickest-path queries.In doing so, we revisit the fact that not every Voronoi-type diagram(More)
Suppose there are k types of facilities, e. g. schools, post offices, supermarkets , modeled by n colored points in the plane, each type by its own color. One basic goal in choosing a residence location is in having at least one representative of each facility type in the neighborhood. In this paper we provide algorithms that may help to achieve this goal(More)
A highway H is a line in the plane on which one can travel at a greater speed than in the remaining plane. One can choose to enter and exit H at any point. The highway time distance between a pair of points is the minimum time required to move from one point to the other, with optional use of H. The highway hull H(S, H) of a point set S is the minimal set(More)
Scheduling for speculative parallelization is a problem that remained unsolved despite its importance. Simple methods such as Fixed-Size Chunking (FSC) need several 'dry-runs' before an acceptable chunk size is found. Other traditional scheduling methods were originally designed for loops with no dependences, so they are primarily focused in the problem of(More)
We are given a transportation line where displacements happen at a bigger speed than in the rest of the plane. A shortest time path is a path between two points which takes less than or equal time to any other. We consider the time to follow a shortest time path to be the time distance between the two points. In this paper, we give a simple algorithm for(More)
We consider algorithms for finding the optimal location of a simple transportation device, that we call a moving walkway, consisting of a pair of points in the plane between which the travel speed is high. More specifically, one can travel from one endpoint of the walkway to the other at speed v > 1, but can only travel at unit speed between any other pair(More)
We propose algorithms for pricing a transportation network in such a way that the profit generated by the customers is maximized. We model the transportation network as a subset of the plane and take into account the fact that the customers minimize their own transportation cost. The underlying theory is a two-player game model called Stackel-berg games. We(More)
Finding the fastest algorithm to solve a problem is one of the main issues in Computational Geometry. Focusing only on worst case analysis or asymptotic computations leads to the development of complex data structures or hard to implement algorithms. Randomized algorithms appear in this scenario as a very useful tool in order to obtain easier(More)