Group Nearest Neighbor Queries in the L1 Plane

  • Hee-Kap Ahn
  • Sang Won Bae
  • Wanbin Son
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7876)

Abstract

Let P be a set of n points in the plane. The k-nearest neighbor (k-NN) query problem is to preprocess P into a data structure that quickly reports k closest points in P for a query point q. This paper addresses a generalization of the k-NN query problem to a query set Q of points, namely, the group nearest neighbor problem, in the L 1 plane. More precisely, a query is assigned with a set Q of at most m points and a positive integer k with k ≤ n, and the distance between a point p and a query set Q is determined as the sum of L 1 distances from p to all q ∈ Q. The maximum number m of query points Q is assumed to be known in advance and to be at most n; that is, m ≤ n. In this paper, we propose two methods, one based on the range tree and the other based on the segment dragging query, obtaining the following complexity bounds: (1) a group k-NN query can be handled in O(m 2logn + k(loglogn + logm)) time after preprocessing P in O(m 2 n log2 n) time and space, or (2) a query can be handled in O(m 2logn + (k + m)log2 n) time after preprocessing P in O(m 2 nlogn) time using O(m 2 n) space. We also show that our approach can be applied to the group k-farthest neighbor query problem.

Keywords

Query Point Query Time Point Event Neighbor Query Neighbor Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hee-Kap Ahn
    • 1
  • Sang Won Bae
    • 2
  • Wanbin Son
    • 1
  1. 1.Department of Computer Science and EngineeringPOSTECHPohangRepublic of Korea
  2. 2.Department of Computer ScienceKyonggi UniversitySuwonRepublic of Korea

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