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An Efficient Sum Query Algorithm for Distance-based Locally Dominating Functions Huang, Ziyun Xu, Jinhui Sum Query Distance-based Function Local Domination High Dimen- sions Data Structure 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ziyun Huang and Jinhui Xu 2017 Is Part Of LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2017.47 urn:nbn:de:0030-drops-82483 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.47 eng https://creativecommons.org/licenses/by/3.0/legalcode