We discuss text summarization in terms of maximum coverage problem and its variant. To solve the optimization problem, we applied some decoding algorithms including the ones never used in this summarization formulation, such as a greedy algorithm with performance guarantee, a randomized algorithm, and a branch-and-bound method. We conduct comparative experiments. On the basis of the experimental results, we also augment the summarization model so that it takes into account the relevance to the document cluster. Through experiments, we showed that the augmented model is at least comparable to the best-performing method of DUC'04.