A Fully Dynamic Algorithm for k-Regret Minimizing Sets

TL;DR

This paper introduces the first fully dynamic algorithm for the $k$-regret minimizing set problem, enabling efficient updates in large databases with provable guarantees, significantly outperforming static methods.

Contribution

It presents a novel fully dynamic algorithm for $k$-regret minimizing sets that efficiently handles database updates with theoretical guarantees.

Findings

Runs up to four orders of magnitude faster than existing methods

Maintains nearly equal result quality to static algorithms

Demonstrates effectiveness on real-world and synthetic datasets

Abstract

Selecting a small set of representatives from a large database is important in many applications such as multi-criteria decision making, web search, and recommendation. The $k$-regret minimizing set ($k$-RMS) problem was recently proposed for representative tuple discovery. Specifically, for a large database $P$ of tuples with multiple numerical attributes, the $k$-RMS problem returns a size-$r$ subset $Q$ of $P$ such that, for any possible ranking function, the score of the top-ranked tuple in $Q$ is not much worse than the score of the $k$\textsuperscript{th}-ranked tuple in $P$. Although the $k$-RMS problem has been extensively studied in the literature, existing methods are designed for the static setting and cannot maintain the result efficiently when the database is updated. To address this issue, we propose the first fully-dynamic algorithm for the $k$-RMS problem that can efficiently provide the up-to-date result w.r.t.~any insertion and deletion in the database with a provable guarantee. Experimental results on several real-world and synthetic datasets demonstrate that our algorithm runs up to four orders of magnitude faster than existing $k$-RMS algorithms while returning results of nearly equal quality.