For instance, C i (S) could be query-dependent in how it measures how much query-dependent information in i is covered by S. Also, the coefficient α could be query and sentence dependent, where it takes larger value when a sentence is more relevant to query (i.e., a larger value of α means later truncation, and therefore more possible coverage).
although the authors may not have noticed, their objective functions are also submodular, adding more evidence suggesting that submodularity is natural for summarization tasks.