### 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 language | English (US) |
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Title of host publication | 28th International Symposium on Algorithms and Computation, ISAAC 2017 |

Editors | Takeshi Tokuyama, Yoshio Okamoto |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959770545 |

DOIs | |

State | Published - Dec 1 2017 |

Event | 28th International Symposium on Algorithms and Computation, ISAAC 2017 - Phuket, Thailand Duration: Dec 9 2017 → Dec 22 2017 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 92 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 28th International Symposium on Algorithms and Computation, ISAAC 2017 |
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Country | Thailand |

City | Phuket |

Period | 12/9/17 → 12/22/17 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software

### Cite this

*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

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - An efficient sum query algorithm for distance-based locally dominating functions

AU - Huang, Ziyun

AU - Xu, Jinhui

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85038595613&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038595613&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ISAAC.2017.47

DO - 10.4230/LIPIcs.ISAAC.2017.47

M3 - Conference contribution

AN - SCOPUS:85038595613

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 28th International Symposium on Algorithms and Computation, ISAAC 2017

A2 - Tokuyama, Takeshi

A2 - Okamoto, Yoshio

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

ER -