文章基本信息

标题：An Efficient Sum Query Algorithm for Distance-based Locally Dominating Functions
本地全文：下载
作者：Ziyun Huang ; Jinhui Xu
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：92
页码：47:1-47:13
DOI：10.4230/LIPIcs.ISAAC.2017.47
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：In this paper, we consider the following sum query problem: Given a point set P in R^d, and a distance-based function f(p,q) (i.e. a function of the distance between p and q) satisfying some general properties, the goal is to develop a data structure and a query algorithm for efficiently computing a (1+epsilon)-approximate solution to the sum sum_{p in P} f(p,q) for any query point q in R^d and any small constant epsilon>0. Existing techniques for this problem are mainly based on some core-set techniques which often have difficulties to deal with functions with local domination property. Based on several new insights to this problem, we develop in this paper a novel technique to overcome these encountered difficulties. Our algorithm is capable of answering queries with high success probability in time no more than ~O_{epsilon,d}(n^{0.5 + c}), and the underlying data structure can be constructed in ~O_{epsilon,d}(n^{1+c}) time for any c>0, where the hidden constant has only polynomial dependence on 1/epsilon and d. Our technique is simple and can be easily implemented for practical purpose.
关键词：Sum Query; Distance-based Function; Local Domination; High Dimen- sions; Data Structure