An optimal approximation for submodular maximization under a matroid constraint in the adaptive complexity model
Eric Balkanski, Aviad Rubinstein, Yaron Singer · 2019
In this paper we study submodular maximization under a matroid constraint in the adaptive complexity model. This model was recently introduced in the context of submodular optimization to quantify the information theoretic complexity of black-box optimization in a parallel computation model. Informally, the adaptivity of an algorithm is the number of sequential rounds it makes when each round can execute polynomially-many function evaluations in parallel. Since submodular optimization is regularly applied on large datasets we seek algorithms with low adaptivity to enable speedups via parallelization. Consequently, a recent line of work has been devoted to designing constant factor approximation algorithms for maximizing submodular functions under various constraints in the adaptive complexity model.