Unconstrained submodular maximization with constant adaptive complexity

In this paper, we consider the unconstrained submodular maximization problem. We propose the first algorithm for this problem that achieves a tight (1/2−ε)-approximation guarantee using Õ(ε −1 ) adaptive rounds and a linear number of function evaluations. No previously known algorithm for this problem achieves an approximation ratio better than 1/3 using less than Ω( n ) rounds of adaptivity, where n is the size of the ground set. Moreover, our algorithm easily extends to the maximization of a non-negative continuous DR-submodular function subject to a box constraint, and achieves a tight (1/2−ε)-approximation guarantee for this problem while keeping the same adaptive and query complexities.

Authors

• Lin Chen 0003
• Moran Feldman
• Amin Karbasi

Keywords

• low adaptive complexity
• parallel computation
• submodular maximization