b-3 - Reverse kNN Search in Arbitrary Dimensionality Yufei...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Reverse k NN Search in Arbitrary Dimensionality Yufei Tao § Dimitris Papadias Xiang Lian § Department of Computer Science City University of Hong Kong Tat Chee Avenue, Hong Kong taoyf@cs.cityu.edu.hk Department of Computer Science Hong Kong University of Science and Technology Clear Water Bay, Hong Kong { dimitris, xlian } @cs.ust.hk Abstract Given a point q , a reverse k nearest neighbor (R k NN) query retrieves all the data points that have q as one of their k nearest neighbors. Existing methods for processing such queries have at least one of the following deficiencies: (i) they do not support arbitrary values of k (ii) they cannot deal efficiently with database updates, (iii) they are applicable only to 2D data (but not to higher dimensionality), and (iv) they retrieve only approximate results. Motivated by these shortcomings, we develop algorithms for exact processing of R k NN with arbitrary values of k on dynamic multidimensional datasets. Our methods utilize a conventional data-partitioning index on the dataset and do not require any pre-computation. In addition to their flexibility, we experimentally verify that the proposed algorithms outperform the existing ones even in their restricted focus. 1. INTRODUCTION Given a multi-dimensional dataset P and a point q , a reverse nearest neighbor (RNN) query retrieves all the points p P that have q as their nearest neighbor. Formally, RNN( q ) = { p P | ¬∃ p' P such that dist ( p , p' ) < dist ( p , q )}, where dist is a distance metric (in this paper we assume Euclidean distance). Although the problem was proposed recently [KM00], it has already received considerable attention due to its importance in several applications involving decision support, resource allocation, profile-based marketing, etc. Other versions of the problem include (i) continuous RNN [BJKS02], where P contains linearly moving objects with fixed velocities, and the goal is to retrieve all RNNs of q for a future interval; (ii) bichromatic RNN [SRAA01] where, given a set Q of queries, the goal is to find the objects p P that are closer to some q Q than any other point of Q ; (iii) stream RNN [KMS02], where data arrive in the form of streams, and the goal is to report aggregate results over the RNNs of a set of query points. This paper focuses on conventional (i.e., monochromatic ) reverse nearest neighbor queries. In addition to single RNN search, we deal with reverse k nearest neighbor (R k NN) queries, which retrieve all the points p P that have q as one of their k nearest neighbors. Specifically, R k NN( q ) = { p P | dist ( p , q ) dist ( p , p k ), where p k is the k -th farthest NN of p }. Figure 1.1 shows four 2D points, where each point p is associated with a circle covering its two nearest neighbors For example, the two NNs of p 4 ( p 2 , p 3 ) are in the circle centered at p 4 .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 12

b-3 - Reverse kNN Search in Arbitrary Dimensionality Yufei...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online