Indexing Reverse Top-k Queries

TL;DR

This paper introduces a novel indexing method for reverse top-k queries in two dimensions, using k-polygons derived from line arrangements to enable fast, space-efficient query responses with guaranteed worst-case performance.

Contribution

The paper proposes a new index structure based on k-polygons for reverse top-k queries, providing guaranteed logarithmic query time and practical efficiency.

Findings

Index structure achieves logarithmic worst-case query cost.

K-polygon representation is space-efficient, involving a small data subset.

Experimental results show practical speed advantages over existing methods.

Abstract

We consider the recently introduced monochromatic reverse top-k queries which ask for, given a new tuple q and a dataset D, all possible top-k queries on D union {q} for which q is in the result. Towards this problem, we focus on designing indexes in two dimensions for repeated (or batch) querying, a novel but practical consideration. We present the insight that by representing the dataset as an arrangement of lines, a critical k-polygon can be identified and used exclusively to respond to reverse top-k queries. We construct an index based on this observation which has guaranteed worst-case query cost that is logarithmic in the size of the k-polygon. We implement our work and compare it to related approaches, demonstrating that our index is fast in practice. Furthermore, we demonstrate through our experiments that a k-polygon is comprised of a small proportion of the original data, so our index structure consumes little disk space.