A Fully Dynamic Algorithm for k-Regret Minimizing Sets

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 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 tuple 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 providing results of nearly equal quality.Peer reviewe

Algorithms for Average Regret Minimization

In this paper, we study a problem from the realm of multicriteria decision making in which the goal is to select from a given set S of d-dimensional objects a minimum sized subset S0 with bounded regret. Thereby, regret measures the unhappiness of users which would like to select their favorite object from set S but now can only select their favorite object from the subset S0. Previous work focused on bounding the maximum regret which is determined by the most unhappy user. We propose to consider the average regret instead which is determined by the sum of (un)happiness of all possible users. We show that this regret measure comes with desirable properties as supermodularity which allows to construct approximation algorithms. Furthermore, we introduce the regret minimizing permutation problem and discuss extensions of our algorithms to the recently proposed k-regret measure. Our theoretical results are accompanied with experiments on a variety of inputs with d up to 7

Algorithms for Average Regret Minimization

In this paper, we study a problem from the realm of multi-criteria decision making in which the goal is to select from a given set S of d-dimensional objects a minimum sized subset S' with bounded regret. Thereby, regret measures the unhappiness of users which would like to select their favorite object from set S but now can only select their favorite object from the subset S'. Previous work focused on bounding the maximum regret which is determined by the most unhappy user. We propose to consider the average regret instead which is determined by the sum of (un)happiness of all possible users. We show that this regret measure comes with desirable properties as supermodularity which allows to construct approximation algorithms. Furthermore, we introduce the regret minimizing permutation problem and discuss extensions of our algorithms to the recently proposed k-regret measure. Our theoretical results are accompanied with experiments on a variety of inputs with d up to 7