An efficient sum query algorithm for distance-based locally dominating functions

Ziyun Huang, Jinhui Xu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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)-Approximate solution to the sum P p2P f(p, q) for any query point q 2 Rd and any small constant 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 Od(n0.5+c), and the underlying data structure can be constructed in d(n1+c) time for any c > 0, where the hidden constant has only polynomial dependence on and d. Our technique is simple and can be easily implemented for practical purpose.

Original languageEnglish (US)
Title of host publication28th International Symposium on Algorithms and Computation, ISAAC 2017
EditorsTakeshi Tokuyama, Yoshio Okamoto
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770545
DOIs
StatePublished - Dec 1 2017
Event28th International Symposium on Algorithms and Computation, ISAAC 2017 - Phuket, Thailand
Duration: Dec 9 2017Dec 22 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume92
ISSN (Print)1868-8969

Conference

Conference28th International Symposium on Algorithms and Computation, ISAAC 2017
CountryThailand
CityPhuket
Period12/9/1712/22/17

Fingerprint

Data structures
Polynomials

All Science Journal Classification (ASJC) codes

  • Software

Cite this

Huang, Z., & Xu, J. (2017). An efficient sum query algorithm for distance-based locally dominating functions. In T. Tokuyama, & Y. Okamoto (Eds.), 28th International Symposium on Algorithms and Computation, ISAAC 2017 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 92). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ISAAC.2017.47
Huang, Ziyun ; Xu, Jinhui. / An efficient sum query algorithm for distance-based locally dominating functions. 28th International Symposium on Algorithms and Computation, ISAAC 2017. editor / Takeshi Tokuyama ; Yoshio Okamoto. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2017. (Leibniz International Proceedings in Informatics, LIPIcs).
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Huang, Z & Xu, J 2017, An efficient sum query algorithm for distance-based locally dominating functions. in T Tokuyama & Y Okamoto (eds), 28th International Symposium on Algorithms and Computation, ISAAC 2017. Leibniz International Proceedings in Informatics, LIPIcs, vol. 92, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 28th International Symposium on Algorithms and Computation, ISAAC 2017, Phuket, Thailand, 12/9/17. https://doi.org/10.4230/LIPIcs.ISAAC.2017.47

An efficient sum query algorithm for distance-based locally dominating functions. / Huang, Ziyun; Xu, Jinhui.

28th International Symposium on Algorithms and Computation, ISAAC 2017. ed. / Takeshi Tokuyama; Yoshio Okamoto. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2017. (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 92).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Huang Z, Xu J. An efficient sum query algorithm for distance-based locally dominating functions. In Tokuyama T, Okamoto Y, editors, 28th International Symposium on Algorithms and Computation, ISAAC 2017. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2017. (Leibniz International Proceedings in Informatics, LIPIcs). https://doi.org/10.4230/LIPIcs.ISAAC.2017.47