Optimization Algorithms

A.1 Proof of Monotonicity and Submodularity In Equation (3a), we stated the objective of the knapsack cover to be Remark 1. f+M is monotonically increasing. A.2 Knapsack Cover To find a solution to problem 3, we use the greedy algorithm proposed by Badanidiyuru and Vondrák [2], which deals with submodular maximization subject to a system of lknapsack constraints and with pmatroid constraints. We present an adapted version of the algorithm in Algorithm 2 where l = 1. Theparameter allows us to 16 trade-off solution time and solution quality. In this work, we set = 0.2.