Showing papers by "Hans-Peter Lenhof published in 1994"

Using persistent data structures for adding range restrictions to searching problems

Abstract: Nous nous interessons a la question de l'ajout de restrictions de domaine aux problemes de recherche decomposables. D'abord, nous donnons une technique generale qui rend partiellement persistante une structure de donnees arbitraire. Ensuite, nous donnons une technique generale qui transforme une structure de donnees partiellement persistante resolvant un probleme de recherche decomposable, en une structure pour le meme probleme mais soumis a des contraintes supplementaires. L'application de cette technique generale a des problemes specifiques de recherche, fournit des structures de donnees efficaces, particulierement dans le cas ou plus d'une seule restriction de domaine est ajoutee, l'une d'entre elles ayant au moins une constante

An animation of a fixed-radius all-nearest-neighbors algorithm

Abstract: This video shows an animation of an algorithm due to the authors [2] for solving the fixed-radius all-nearest-neighbors problem. In this problem, we are given a set S of n points and a real number 6, and we have to report all pairs of points that are at distance at most 6. The algorithm works in two stages. In the first stage, a grid is computed. Instead of a standard grid, we use a so-called degraded grid that is easier to construct by means of a simple sweep algorithm. This degraded grid consists of boxes with sides of length at least 8. If a box contains points of S, then its sides are of length exactly 8. In the second stage, this grid is used for the actual enumeration. For each non-empty box, it suffices to compare each of its points with all points in the same box or in one of the neighboring boxes. Although the algorithm may compare many pairs having distance more than 6, it can be shown that the total number of pairs considered is proportional to the number of pairs that are at most 6 apart. As a result, the total running time of the algorithm is proportional to n log n plus the number of pairs that are at distance at most 6. As an application, we give an animation of the algorithm of Heiden at al. [1] for triangulating the contact surface of a molecule. In a first step, points on this surface are computed. Given these points,