Before revision:  Following the convention in many data mining and machine learning applications such as data summarization, recommender systems, and social network analysis , the problem is formulated as maximizing a monotone submodular function subject to a cardinality constraint -- i.e., the size of the selected subset is restricted to be smaller than or equal to an input integer k.
After revision:  In many data mining and machine learning applications such as data summarization, recommender systems, and social network analysis , the problem is formulated as maximizing a monotone submodular function subject to a cardinality constraint -- i.e., the size of the selected subset is restricted to be smaller than or equal to an input integer k.