TY - GEN
T1 - Unconstrained submodular maximization with constant adaptive complexity
AU - Chen, Lin
AU - Feldman, Moran
AU - Karbasi, Amin
N1 - Publisher Copyright: © 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM.
PY - 2019/6/23
Y1 - 2019/6/23
N2 - 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.
AB - 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.
KW - Low adaptive complexity
KW - Parallel computation
KW - Submodular maximization
UR - http://www.scopus.com/inward/record.url?scp=85068755100&partnerID=8YFLogxK
U2 - https://doi.org/10.1145/3313276.3316327
DO - https://doi.org/10.1145/3313276.3316327
M3 - Conference contribution
T3 - Proceedings of the Annual ACM Symposium on Theory of Computing
SP - 102
EP - 113
BT - STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
A2 - Charikar, Moses
A2 - Cohen, Edith
T2 - 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019
Y2 - 23 June 2019 through 26 June 2019
ER -