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)
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)
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)
Motivated by questions in location planning, we show for a set of colored point sites in the plane how to compute the smallest (by perimeter or area) axis-parallel rectangle, the narrowest strip, and other smallest objects enclosing at least one site of each color.
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)
We study a simple geometric model of transportation facility that consists of two points between which the travel speed is high. This elementary definition can model shuttle services, tunnels, bridges, teleportation devices, escalators or moving walkways. The travel time between a pair of points is defined as a time distance, in such a way that a customer… (More)
We study a new family of geometric graphs that interpolate between the Delaunay triangulation and the Gabriel graph. These graphs share many properties with β-skeletons for β ∈ [0, 1] (such as sublinear spanning ratio) with the added benefit of planarity (and consequently linear size and local routability).
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)
In this work we address the problem of scheduling loops with dependences in the context of speculative paralleliza-tion. We show that scheduling alternatives are highly influenced by the dependence violation pattern presented in the code. We center our analysis in those algorithms where dependences are less likely to appear as the execution proceeds , like… (More)