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- W3212775003 abstract "For the problem of maximizing a monotone, submodular function with respect to a cardinality constraint $k$ on a ground set of size $n$, we provide an algorithm that achieves the state-of-the-art in both its empirical performance and its theoretical properties, in terms of adaptive complexity, query complexity, and approximation ratio; that is, it obtains, with high probability, query complexity of $O(n)$ in expectation, adaptivity of $O(log(n))$, and approximation ratio of nearly $1-1/e$. The main algorithm is assembled from two components which may be of independent interest. The first component of our algorithm, LINEARSEQ, is useful as a preprocessing algorithm to improve the query complexity of many algorithms. Moreover, a variant of LINEARSEQ is shown to have adaptive complexity of $O( log (n / k) )$ which is smaller than that of any previous algorithm in the literature. The second component is a parallelizable thresholding procedure THRESHOLDSEQ for adding elements with gain above a constant threshold. Finally, we demonstrate that our main algorithm empirically outperforms, in terms of runtime, adaptive rounds, total queries, and objective values, the previous state-of-the-art algorithm FAST in a comprehensive evaluation with six submodular objective functions." @default.
- W3212775003 created "2021-11-22" @default.
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- W3212775003 date "2021-12-06" @default.
- W3212775003 modified "2023-09-24" @default.
- W3212775003 title "Best of Both Worlds: Practical and Theoretically Optimal Submodular Maximization in Parallel" @default.
- W3212775003 hasPublicationYear "2021" @default.
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