Abstract
We study the problem of maximizing a monotone submodular function subject to a matroid constraint and present a deterministic algorithm that achieves (1/2+ϵ)-approximation for the problem (for some ϵ ≥ 8 10-4). This algorithm is the first deterministic algorithm known to improve over the 1/2-approximation ratio of the classical greedy algorithm proved by Nemhauser, Wolsey, and Fisher in 1978.
| Original language | English |
|---|---|
| Pages (from-to) | 945-967 |
| Number of pages | 23 |
| Journal | SIAM Journal on Computing |
| Volume | 52 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2023 |
| Externally published | Yes |
Bibliographical note
Funding Information:*Received by the editors April 8, 2019; accepted for publication (in revised form) April 18, 2023; published electronically July 27, 2023. An earlier version of this work appeared in Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), SIAM, 2019, pp. 241--254. https://doi.org/10.1137/19M125515X Funding: The work of the first author was supported by ISF grant 2233/19 and US-Israel BSF grant 2018352. The work of the second and third authors was supported in part by ISF grant 1357/16. \dagger Statistics and Operations Research Department, Tel Aviv University, Tel Aviv, Israel (niv.buchbinder@gmail.com). \ddagger Department of Mathematics and Computer Science, The Open University of Israel, Raanana, Israel. Current address: Department of Computer Science, University of Haifa, Haifa, Israel (moranfe@cs.haifa.ac.il). \S Department of Mathematics and Computer Science, The Open University of Israel, Raanana, Israel. Current address: Department of Computer Science and Automation, Indian Institute of Science, Bengaluru, India (mohitgarg@iisc.ac.in). 945
Publisher Copyright:
© 2023 Niv Buchbinder.
Keywords
- deterministic algorithms
- matroid
- submodular optimization
ASJC Scopus subject areas
- Computer Science (all)
- Mathematics (all)