Belén Palop

Quickest Paths, Straight Skeletons, and the City Voronoi Diagram

Abstract The city Voronoi diagram is induced by quickest paths in the L1plane, made faster 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 has interpretations in both the distance model and the wavefront model. Especially, straight skeletons are a relevant example where an interpretation in the former model is lacking. We clarify the relationship between these models, and further draw a connection to the bisector-defined abstract Voronoi diagram model, with the particular goal of computing the city Voronoi diagram efficiently.

Voronoi Diagram for services neighboring a highway

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 computing the Time Voronoi Diagram, that is, the Voronoi Diagram of a set of points using the time distance.

Smallest Color-Spanning Objects

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 and the narrowest strip enclosing at least one site of each color.

Quickest paths, straight skeletons, and the city Voronoi diagram

The city Voronoi diagram is induced by quickest paths, in the L 1 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 has interpretations in both the distance model and the wavefront model. Especially, straight skeletons are a relevant example where an interpretation in the former model is lacking. We clarify the relation between these models, and further draw a connection to the bisector-defined abstract Voronoi diagram model, with the particular goal of computing the city Voronoi diagram efficiently.

TPCC-UVa: an open-source TPC-C implementation for parallel and distributed systems

This paper presents TPCC-UVa, an open-source implementation of the TPC-C benchmark intended to be used in parallel and distributed systems. TPCC-UVa is written entirely in C language and it uses the Post-greSQL database engine. This implementation includes all the functionalities described by the TPC-C standard specification for the measurement of both uni- and multiprocessor systems performance. The major characteristics of the TPC-C specification are discussed, together with a description of the TPCC-UVa implementation and architecture and real examples of performance measurements

Pricing geometric transportation networks

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 Stackelberg games. We propose algorithms for the cases where the fare does and does not depend on the distance traveled, in the L1 or L2 metrics. In particular, we propose an O(n log n) algorithm for optimal pricing of a highway under the L2 metric, and an O(nk log n log3 k) algorithm for orthogonally convex networks of complexity O(k) under the L1 metric.

Optimal location of transportation devices

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 of points. The travel time between any two points in the plane is the minimum between the actual geometric distance, and the time needed to go from one point to the other using the walkway. A location for a walkway is said to be optimal with respect to a given finite set of points if it minimizes the maximum travel time between any two points of the set. We give a simple linear-time algorithm for finding an optimal location in the case where the points are on a line. We also give an @W(nlogn) lower bound for the problem of computing the travel time diameter of a set of n points on a line with respect to a given walkway. Then we describe an O(nlogn) algorithm for locating a walkway with the additional restriction that the walkway must be horizontal. This algorithm is based on a recent generic method for solving quasiconvex programs with implicitly defined constraints. It is used in a (1+@e)-approximation algorithm for optimal location of a walkway of arbitrary orientation.

New Scheduling Strategies for Randomized Incremental Algorithms in the Context of Speculative Parallelization

In this work, we address the problem of scheduling loops with dependences in the context of speculative parallelization. We show that the scheduling alternatives are highly influenced by the dependence violation pattern the code presents. We center our analysis in those algorithms where dependences are less likely to appear as the execution proceeds. Particularly, we focus on randomized incremental algorithms, widely used as a much more efficient solution to many problems than their deterministic counterparts. These important algorithms are, in general, hard to parallelize by hand and represent a challenge for any automatic parallelization scheme. Our analysis led us to the development of MESETA, a new scheduling strategy that takes into account the probability of a dependence violation to determine the number of iterations being scheduled. MESETA is compared with existing techniques, including fixed-size chunking (FSC), the only scheduling alternative used so far in the context of speculative parallelization. Our experimental results show a 5.5 percent to 36.25 percent speedup improvement over FSC, leading to a better extraction of the parallelism inherent to randomized incremental algorithms. Moreover, when the cost of dependence violations is too high to obtain speedups, MESETA curves the performance degradation

Meseta: a new scheduling strategy for speculative parallelization of randomized incremental algorithms

In this work the authors addressed the problem of scheduling loops with dependencies in the context of speculative parallelization. It is shown that scheduling alternatives are highly influenced by the dependence violation pattern presented in the code. The analysis was centered in those algorithms where dependencies are less likely to appear as the execution proceeds, like incremental randomized algorithms. These algorithms are, in general, hard to parallelize by hand, and represent a challenge for any automatic parallelization scheme. The analysis led to the development of Meseta, a new scheduling strategy that takes into account the probability of a dependence violation to determine the number of iterations being scheduled. Meseta is compared, among others, with fixed-size chunking (FSC), the only scheduling alternative used so far in the context of speculative parallelization. The experimental results showed a 3% to 22% speedup improvement over FSC for the same incremental randomized algorithm.

Bichromatic 2-center of pairs of points

We study a class of geometric optimization problems closely related to the 2-center problem: Given a set S of n pairs of points in the plane, for every pair, we want to assign red color to a point of the pair and blue color to the other point in order to optimize the radii of the minimum enclosing ball of the red points and the minimum enclosing ball of the blue points. In particular, we consider the problems of minimizing the maximum and minimizing the sum of the two radii of the minimum enclosing balls. For each case, minmax and minsum, we consider distances measured in the L 2 and in the L ∞ metrics.