Minimizing Average Regret Ratio in Database

We propose "average regret ratio" as a metric to measure users' satisfaction after a user sees k selected points of a database, instead of all of the points in the database. We introduce the average regret ratio as another means of multi-criteria decision making. Unlike the original k-regret operator that uses the maximum regret ratio, the average regret ratio takes into account the satisfaction of a general user. While assuming the existence of some utility functions for the users, in contrast to the top-k query, it does not require a user to input his or her utility function but instead depends on the probability distribution of the utility functions. We prove that the average regret ratio is a supermodular function and provide a polynomial-time approximation algorithm to find the average regret ratio minimizing set for a database.