An Efficient Sum Query Algorithm for Distance-Based Locally Dominating Functions

Ziyun Huang, Jinhui Xu

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we consider the following sum query problem: Given a point set P in Rd, 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 + ϵ) -approximate solution to the sum ∑ pPf(p, q) for any query point q∈ Rd and any small constant ϵ> 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~ ϵ,d(n0.5+c) , and the underlying data structure can be constructed in O~ ϵ,d(n1+c) time for any c> 0 , where the hidden constant has only polynomial dependence on 1 / ϵ and d. Our technique is simple and can be easily implemented for practical purpose.

Original languageEnglish (US)
Pages (from-to)2415-2431
Number of pages17
JournalAlgorithmica
Volume82
Issue number9
DOIs
StatePublished - Sep 1 2020

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

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