Lecture 19 : Well Separated Pair Decomposition
نویسندگان
چکیده
Let P be a set of n points in R d. For any parameter s ≥ 1, A, B ⊆ P are said to be s-separated or well separated if A and B can be enclosed by congruent d-spheres S A and S B of radius r such that the minimum distance between S A and S B is at least sr. There is a stronger notion of well-separated point sets. For any parameter s ≥ 1, A, B ⊆ P are said to be s-separated if the bounding boxes of A and B can be enclosed by congruent d-spheres S A and S B of radius r such that the minimum distance between S A and S B is at least sr. Let A and B be s-separated point sets and let p, p ∈ A and q, q ∈ B. Since both p and p are enclosed by a 19-1
منابع مشابه
INDEX TERMS: none.
Well-separated pair decomposition, introduced by Callahan and Kosaraju [3], has found numerous applications in solving proximity problems for points in the Euclidean space. A pair of point sets (A, B) is c-well-separated if the distance between A,B is at least c times the diameters of both A and B. A well-separated pair decomposition of a point set consists of a set of well-separated pairs that...
متن کاملOptimal Parallel All-Nearest-Neighbors Using the Well-Separated Pair Decomposition (Preliminary Version)
We present an optimal parallel algorithm to construct the well-separated pair decomposition of a point set P in < d. We show how this leads to a deterministic optimal O(logn) time parallel algorithm for nding the k-nearest-neighbors of each point in P, where k is a constant. We discuss several additional applications of the well-separated pair decomposition for which we can derive faster parall...
متن کاملOptimal Parallel All-Nearest-Neighbors Using the Well-Separated Pair Decomposition
W e present an optimal parallel algorithm t o construct the well-separated pair decomposition of a point set P in Zd. W e show how this leads to a deterministic opt imal O(1ogn) t ime parallel algorithm for finding the k nearest neighbors of each point in P, where k is a constant. W e discuss several additional applications of the well-separated pair decomposition for which we can derive fas t ...
متن کاملBibliography of Literature
[3] P. B. Callahan, " Optimal parallel all-nearest-neighbors using the well-separated pair decomposition, " in
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 2007