Unconstrained submodular maximization with constant adaptive complexity

Lin Chen; Moran Feldman; Amin Karbasi

doi:https://doi.org/10.1145/3313276.3316327

Unconstrained submodular maximization with constant adaptive complexity

Lin Chen, Moran Feldman, Amin Karbasi

Open University of Israel

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
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

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

Keywords

Low adaptive complexity
Parallel computation
Submodular maximization

All Science Journal Classification (ASJC) codes

Software

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https://doi.org/10.1145/3313276.3316327

Cite this

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title = "Unconstrained submodular maximization with constant adaptive complexity",

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 {\~O}(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.",

keywords = "Low adaptive complexity, Parallel computation, Submodular maximization",

author = "Lin Chen and Moran Feldman and Amin Karbasi",

note = "Publisher Copyright: {\textcopyright} 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM.; 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 ; Conference date: 23-06-2019 Through 26-06-2019",

year = "2019",

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doi = "https://doi.org/10.1145/3313276.3316327",

language = "English",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

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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, 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. 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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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.

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ER -

Unconstrained submodular maximization with constant adaptive complexity

Abstract

Publication series

Conference

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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