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 |
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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 | |
State | Published - 23 Jun 2019 |
Externally published | Yes |
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 |
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ISSN (Print) | 0737-8017 |
Conference
Conference | 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 |
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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
ASJC Scopus subject areas
- Software