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

Authors Ziyun Huang, Jinhui Xu

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Keywords
  • Sum Query
  • Distance-based Function
  • Local Domination
  • High Dimen- sions
  • Data Structure

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Abstract

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.

Cite As Get BibTex

Ziyun Huang and Jinhui Xu. An Efficient Sum Query Algorithm for Distance-based Locally Dominating Functions. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 47:1-47:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.ISAAC.2017.47

Author Details

Ziyun Huang
Jinhui Xu

References

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