Efficient Processing of k-regret Minimization Queries with Theoretical Guarantees

TL;DR

This paper introduces a theoretically grounded, efficient approach for k-regret minimization queries that balances result quality and computational cost, supported by sampling techniques and extensive experiments.

Contribution

It provides the first theoretical analysis of greedy algorithms for k-regret minimization and proposes a sampling-based method to improve efficiency.

Findings

Theoretical approximation ratio bounds for greedy algorithms.

A sampling method that reduces query processing time.

Empirical validation showing improved efficiency and effectiveness.

Abstract

Assisting end users to identify desired results from a large dataset is an important problem for multi-criteria decision making. To address this problem, top-k and skyline queries have been widely adopted, but they both have inherent drawbacks, i.e., the user either has to provide a specific utility function or faces many results. The k-regret minimization query is proposed, which integrates the merits of top-k and skyline queries. Due to the NP-hardness of the problem, the k-regret minimization query is time consuming and the greedy framework is widely adopted. However, formal theoretical analysis of the greedy approaches for the quality of the returned results is still lacking. In this paper, we first fill this gap by conducting a nontrivial theoretical analysis of the approximation ratio of the returned results. To speed up query processing, a sampling-based method, StocPreGreed,, is developed to reduce the evaluation cost. In addition, a theoretical analysis of the required sample size is conducted to bound the quality of the returned results. Finally, comprehensive experiments are conducted on both real and synthetic datasets to demonstrate the efficiency and effectiveness of the proposed methods.