Continuous $k$-Regret Minimization Queries: A Dynamic Coreset Approach

Abstract

Finding a small set of representative tuples from a large database is an important functionality for supporting multi-criteria decision-making. In this paper, we study the k-regret minimization query to fulfill this task. Specifically, a k-regret minimization query returns a set R of tuples with a pre-defined size r from a database D such that the maximum k-regret ratio, which captures how well the top-ranked tuple in R represents the top-k tuples in D for any possible utility function, is minimized. Although there have been many methods proposed for k-regret minimization query processing, most of them are designed for static databases, i.e., without tuple insertions and deletions. The only known algorithm to process continuous k-regret minimization queries (CkRMQ) in dynamic databases suffers from large maximum k-regret ratios and high time complexity. We propose a novel dynamic coreset-based approach, called \textsc{DynCore}, for C <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$k$</tex></formula> RMQ processing. It can achieve the same upper bound on the maximum k-regret ratio as the best-known static algorithm. Meanwhile, its time complexity is sublinear to the database size, which is significantly lower than that of the existing dynamic algorithm.