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.
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*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 (email@example.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 (firstname.lastname@example.org). \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 (email@example.com). 945
© 2023 Niv Buchbinder.
- deterministic algorithms
- submodular optimization