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:  Following the convention in many data mining and machine learning applications such as data summarization, recommender systems, and social network analysis and recommender systems, this problem can be 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.