Centralized submodular optimization

Abstract

Submodularity enables efficient approximation of otherwise intractable set optimization problems using simply greedy or local search heuristics, making submodularity a valuable tool in a variety of applications. This chapter gives an overview of submodular optimization algorithms, with emphasis on centralized algorithms for maximizing submodular functions subject to different types of constraints. Applications of submodularity are presented, followed by the standard greedy algorithm for cardinality-constrained submodular maximization. Techniques for robust submodular maximization and submodular maximization under a matroid constraint are discussed. Online submodular maximization, in which the objective function varies over time, is introduced.