Fast delaunay point location with search structures
نویسندگان
چکیده
We study the expected time behaviour of the Jumpand-walk paradigm when the set of sites is controlled by a binary search tree or a well-balanced 2-d tree. Throughout the paper, we shall assume that we are given a Delaunay triangulation on N sites uniformly distributed in the unit 2-dimensional square, [0; 1]. We are requested to locate a query point q, which will be assumed to be bounded away from the boundary of the Delaunay triangulation, as the expected analysis of the general case calls for more powerful tools (to be published in a future paper).
منابع مشابه
Expected time analysis for Delaunay point location
Abstract. We consider point location in Delaunay triangulations with the aid of simple data structures. In particular, we analyze methods in which a simple data structure is used to first locate a point close to the query point. For points uniformly distributed on the unit square, we show that the expected point location complexities are Θ( √ n) for the Green-Sibson rectilinear search, Θ(n) for...
متن کاملUsing bistellar flips for rotations in point location structures
Point location in dynamic Delaunay triangulations is a problem that as yet has no elegant solution. Current approaches either only give guarantees against a weakened adversary, or require superlinear space. In this paper we propose that we should seek intuition from balanced binary search trees, where rotations are used to maintain a shallow worst-case depth. We describe a (well-known) data str...
متن کاملCan Nearest Neighbor Searching Be Simple and Always Fast?
Nearest Neighbor Searching, i.e. determining from a set S of n sites in the plane the one that is closest to a given query point q, is a classical problem in computational geometry. Fast theoretical solutions are known, e.g. point location in the Voronoi Diagram of S, or specialized structures such as so-called Delaunay hierarchies. However, practitioners tend to deem these solutions as too com...
متن کاملOn the stabbing number of a random Delaunay triangulation
We consider a Delaunay triangulation defined on n points distributed independently and uniformly on a planar compact convex set of positive volume. Let the stabbing number be the maximal number of intersections between a line and edges of the triangulation. We show that the stabbing number Sn is Θ( √ n) in the mean, and provide tail bounds for P{Sn ≥ t √ n}. Applications to planar point locatio...
متن کاملThe Delaunay Hierarchy
We propose a new data structure to compute the Delaunay triangulation of a set of points in the plane. It combines good worst case complexity, fast behavior on real data, small memory occupation and the possibility of fully dynamic insertions and deletions. The location structure is organized into several levels. The lowest level just consists of the triangulation, then each level contains the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999