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Guided Combinatorial Algorithms for Submodular Maximization
May 9, 2024, 4:42 a.m. | Yixin Chen, Ankur Nath, Chunli Peng, Alan Kuhnle
cs.LG updates on arXiv.org arxiv.org
Abstract: For constrained, not necessarily monotone submodular maximization, guiding the measured continuous greedy algorithm with a local search algorithm currently obtains the state-of-the-art approximation factor of 0.401 \citep{buchbinder2023constrained}. These algorithms rely upon the multilinear extension and the Lovasz extension of a submodular set function. However, the state-of-the-art approximation factor of combinatorial algorithms has remained $1/e \approx 0.367$ \citep{buchbinder2014submodular}. In this work, we develop combinatorial analogues of the guided measured continuous greedy algorithm and obtain approximation ratio …
abstract algorithm algorithms approximation art arxiv continuous cs.dm cs.ds cs.lg extension function however search set state type
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