Unconstrained Submodular Maximization with Constant Adaptive Complexity
STOC '19: 51st Annual ACM SIGACT Symposium on the Theory of Computing Phoenix AZ USA June, 2019(2018)
摘要
In this paper, we consider the unconstrained submodular maximization problem. We propose the first algorithm for this problem that achieves a tight $(1/2-\varepsilon)$-approximation guarantee using $\tilde{O}(\varepsilon^{-1})$ 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 $\Omega(n)$ 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 $(1/2-\varepsilon)$-approximation guarantee for this problem while keeping the same adaptive and query complexities.
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关键词
submodular maximization,low adaptive complexity,parallel computation
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