The Moving Diversified Nearest Neighbor Query

Abstract

As a major type of continuous spatial queries, the moving <inline-formula><tex-math notation="LaTeX">$k$ </tex-math></inline-formula> nearest neighbor ( <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> NN) query has been studied extensively. However, most existing studies have focused on only the query efficiency. In this paper, we consider further the usability of the query results, in particular the diversification of the returned data points. We thereby formulate a new type of query named the <i>moving <inline-formula><tex-math notation="LaTeX">$k$ </tex-math><alternatives><inline-graphic xlink:href="gu-ieq4-2593464.gif" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink"/></alternatives></inline-formula> diversified nearest neighbor query (M<inline-formula><tex-math notation="LaTeX">$k$</tex-math><alternatives> <inline-graphic xlink:href="gu-ieq5-2593464.gif" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink"/></alternatives></inline-formula>DNN)</i> . This type of query continuously reports the <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> diversified nearest neighbors while the query object is moving. Here, the degree of diversity of the <inline-formula><tex-math notation="LaTeX"> $k$</tex-math> </inline-formula> NN set is defined on the distance between the objects in the <inline-formula> <tex-math notation="LaTeX">$k$</tex-math></inline-formula> NN set. Computing the <inline-formula><tex-math notation="LaTeX">$k$ </tex-math></inline-formula> diversified nearest neighbors is an NP-hard problem. We propose an algorithm to maintain incrementally the <inline-formula> <tex-math notation="LaTeX">$k$</tex-math></inline-formula> diversified nearest neighbors to reduce the query processing costs. We further propose two approximate algorithms to obtain even higher query efficiency with precision bounds. We verify the effectiveness and efficiency of the proposed algorithms both theoretically and empirically. The results confirm the superiority of the proposed algorithms over the baseline algorithm.