In MDS, typical constraints are upper bounds in the number of sentences or words, corresponding to cardinality (|S| ≤ m) or knapsack constraints ( s∈S |words(s)| ≤ m) for some upper bound m. When optimizing a submodular monotone function under such constraints, GREEDY has a performance guarantee of ≈ 0.63 and ≈ 0.39 respectively (Calinescu et al., 2011;Lin and Bilmes, 2011).
for cardinality constraints, the output is at least 0.63 as good as the optimal solution in terms of objective function value.