  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.
