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Submitted by Assigned_Reviewer_1 Q1 The paper proposes a modified version of the epsilon greedy algorithm for finding approximate solution to the generalized problem of submodular cover on the integer lattice. It is shown that the proposed algorithm provides a bicriteria approximation guarantee while having a running time which is polynomial in the input size. The paper is among a class of resent papers that have been working on accelerating and hence scaling up the optimization methods to be practical for large modern data sets (as is commonly seen in machine learning tasks). Q2 Overall, I think the paper is well-written and through and does a good job of providing theoretical guarantees for the proposed algorithms for submodular maximization over an integer lattice. The proposed problem has real world applications and the quality of the solution is shown through experiments on real and artificial datasets. Submitted by Assigned_Reviewer_2 Q1 PAPER SUMMARY The paper proposes a generalization of submodular cover to integer lattices.