Evaluating Top-N queries in n-dimensional normed spaces

Abstract

For the problem of processing top-N queries, the threshold algorithm (TA) is an important method in many scenarios. The model of top-N queries with TA has three characteristics: (1) the ranking function is monotone, (2) the query point is fixed, and (3) TA scans the sorted index lists unidirectionally. In many database applications, however, there are opportunities for evaluating top-N queries with arbitrary query points and generic (not necessarily monotone) ranking functions. In this paper, we propose an approach for evaluating top-N queries in n-dimensional normed spaces. Given a query point Q = (q1,…, qn) in the real vector space ℜn and a generic norm distance d as ranking function, our method employs the norm equivalence theorem in Functional Analysis so that the candidate tuples of top-N query Q with d can be obtained using the Maximum distance d∞. This method projects each qi on its corresponding axis and constructs an interval centered at qi, and then enlarges each interval bidirectionally until the n-dimensional hyperrectangle contains enough candidate tuples so that the top-N tuples are retrieved according to the given norm distance d. Extensive experiments are conducted to measure the performance of our approach for both low-dimensional and high-dimensional data.