Continuous Group Nearest Group Search over Streaming Data

Abstract

Group nearest group query(GNG for short) is an important variant of NN search. Let $\mathcal {D}$ be the $d-$multi-dimensional object set, $GQ\langle k, Q\rangle$ be a GNG with Q containing a set of d-multi-dimensional query points. The target of GNG is to select k object points $O_Q$ from $\mathcal {D}$ such that the total distance between these query points and their NNs in $O_Q$ is minimal. In this paper, we study GNG in a very dynamical data environment, i.e., continuous GNG query(CGNG for short) over sliding window, which has many applications. To the best of our knowledge, it is the first time to study the problem of CGNG over sliding window.

In this paper, we propose a novel framework named KMPT(short for K-Means Partition Tree-based framework) for supporting CGNG. The key behind KMPT is to partition query points into a group of k subsets, generate a group of k virtual points based on objects in these subsets, and reduce the CGNG problem to continuous NN search over data stream. In order to efficiently support continuous NN search, we first partition objects in the window into a group of sub-windows based on their arrived order. We then form a group of quad-tree based indexes to maintain objects’ position information in each partition, form an R-tree based index to evaluate which objects have a chance to become query result objects in the near future, and finally achieve to goal of using a small number of objects to support query processing. The comprehensive experiments on both real and synthetic data sets demonstrate the superiority in both efficiency and quality.