Finding Average Regret Ratio Minimizing Set in Database

Selecting a certain number of data points (or records) from a database which "best" satisfy users' expectations is a very prevalent problem with many applications. One application is a hotel booking website showing a certain number of hotels on a single page. However, this problem is very challenging since the selected points should "collectively" satisfy the expectation of all users. Showing a certain number of data points to a single user could decrease the satisfaction of a user because the user may not be able to see his/her favorite point which could be found in the original database. In this paper, we would like to find a set of k points such that on average, the satisfaction (ratio) of a user is maximized. This problem takes into account the probability distribution of the users and considers the satisfaction (ratio) of all users, which is more reasonable in practice, compared with the existing studies that only consider the worst-case satisfaction (ratio) of the users, which may not reflect the whole population and is not useful in some applications. Motivated by this, in this paper, we propose algorithms for this problem. Finally, we conducted experiments to show the effectiveness and the efficiency of the algorithms.