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Lower Bound on the Greedy Approximation Ratio for Adaptive Submodular Cover (2405.14995v1)
Published 23 May 2024 in cs.DS, cs.AI, and cs.LG
Abstract: We show that the greedy algorithm for adaptive-submodular cover has approximation ratio at least 1.3*(1+ln Q). Moreover, the instance demonstrating this gap has Q=1. So, it invalidates a prior result in the paper ``Adaptive Submodularity: A New Approach to Active Learning and Stochastic Optimization'' by Golovin-Krause, that claimed a (1+ln Q)2 approximation ratio for the same algorithm.
- Minimum cost adaptive submodular cover. CoRR, abs/2208.08351, 2022.
- Vasek Chvátal. A greedy heuristic for the set-covering problem. Math. Oper. Res., 4(3):233–235, 1979.
- Analytical approach to parallel repetition. In ACM Symposium on Theory of Computing, pages 624–633, 2014.
- Adaptivity in adaptive submodularity. In Proceedings of 34th Conference on Learning Theory, volume 134, pages 1823–1846. PMLR, 2021.
- D. Golovin and A. Krause. Adaptive submodularity: Theory and applications in active learning and stochastic optimization. J. Artif. Intell. Res. (JAIR), 42:427–486, 2011.
- Adaptive submodularity: A new approach to active learning and stochastic optimization. CoRR, abs/1003.3967, 2017.
- A tight bound for stochastic submodular cover. J. Artif. Intell. Res., 71:347–370, 2021.
- Minimum latency submodular cover. ACM Trans. Algorithms, 13(1):13:1–13:28, 2016.
- Comments on the proof of adaptive stochastic set cover based on adaptive submodularity and its implications for the group identification problem in “group-based active query selection for rapid diagnosis in time-critical situations”. IEEE Transactions on Information Theory, 63(11):7612–7614, 2017.
- L.A. Wolsey. An analysis of the greedy algorithm for the submodular set covering problem. Combinatorica, 2(4):385–393, 1982.