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.
|Title of host publication||STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing|
|Editors||Moses Charikar, Edith Cohen|
|Publisher||Association for Computing Machinery|
|Number of pages||12|
|State||Published - 23 Jun 2019|
|Event||51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 - Phoenix, United States|
Duration: 23 Jun 2019 → 26 Jun 2019
|Name||Proceedings of the Annual ACM Symposium on Theory of Computing|
|Conference||51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019|
|Period||23/06/19 → 26/06/19|
Bibliographical noteFunding Information:
Lin Chen was supported by Google PhD Fellowship, Moran Feldman was supported in part by ISF grant 1357/16, and Amin Karbasi was supported by AFOSR YIP award (FA9550-18-1-0160).
- Low adaptive complexity
- Parallel computation
- Submodular maximization