Faster Algorithms for k -Regret Minimizing Sets via Monotonicity and Sampling

Regret-based queries are a complement of top-k and skyline queries when users cannot specify accurate utility functions while must output a controllable size of the query results. Various regret-based queries are proposed in last decade for multi-criteria decision making. The k-regret minimizing set (k-RMS) query which returns r points from the dataset and minimizes the maximum k-regret ratio has been extensively studied. However, existing state-of-art algorithms to find k-regret minimizing sets are very time-consuming and unapplicable. In this paper, we propose a faster algorithm SAMPGREED for k-RMS queries by utilizing the monotonicity of the regret ratio function with sampling techniques. We provide the theoretical analysis of our SAMPGREED algorithm and experiments on synthetic and real datasets verify our proposed algorithm is superior to existing state-of-art approaches.