Unconstrained submodular maximization with constant adaptive complexity

Lin Chen; Moran Feldman; Amin Karbasi

doi:10.1145/3313276.3316327

Unconstrained submodular maximization with constant adaptive complexity

Lin Chen, Moran Feldman, Amin Karbasi

Computer Science discipline

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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.

Original language	English
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
Pages	102-113
Number of pages	12
ISBN (Electronic)	9781450367059
DOIs	https://doi.org/10.1145/3313276.3316327
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

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)	0737-8017

Conference

Conference	51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019
Country/Territory	United States
City	Phoenix
Period	23/06/19 → 26/06/19

Bibliographical note

Publisher Copyright:
© 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM.

Keywords

Low adaptive complexity
Parallel computation
Submodular maximization

Access to Document

10.1145/3313276.3316327

Cite this

Chen, L., Feldman, M., & Karbasi, A. (2019). Unconstrained submodular maximization with constant adaptive complexity. In M. Charikar, & E. Cohen (Eds.), STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing (pp. 102-113). (Proceedings of the Annual ACM Symposium on Theory of Computing). Association for Computing Machinery. https://doi.org/10.1145/3313276.3316327

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Chen, L, Feldman, M & Karbasi, A 2019, Unconstrained submodular maximization with constant adaptive complexity. in M Charikar & E Cohen (eds), STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, pp. 102-113, 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019, Phoenix, United States, 23/06/19. https://doi.org/10.1145/3313276.3316327

Unconstrained submodular maximization with constant adaptive complexity. / Chen, Lin; Feldman, Moran; Karbasi, Amin.
STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing. ed. / Moses Charikar; Edith Cohen. Association for Computing Machinery, 2019. p. 102-113 (Proceedings of the Annual ACM Symposium on Theory of Computing).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Chen L, Feldman M, Karbasi A. Unconstrained submodular maximization with constant adaptive complexity. In Charikar M, Cohen E, editors, STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing. Association for Computing Machinery. 2019. p. 102-113. (Proceedings of the Annual ACM Symposium on Theory of Computing). doi: 10.1145/3313276.3316327

Unconstrained submodular maximization with constant adaptive complexity

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