Deletion Robust Non-Monotone Submodular Maximization over Matroids
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Maximizing a submodular function is a fundamental task in machine learning and in this paper we study the deletion robust version of the problem under the classic matroids constraint. Here the goal is to extract a small size summary of the dataset that contains a high value independent set even after an adversary deleted some elements. We present constant-factor approximation algorithms, whose space complexity depends on the rank k of the matroid and the number d of deleted elements. In the centralized setting we present a (4.597+O(ε))-approximation algorithm with summary size O( k+d/ε^2logk/ε) that is improved to a (3.582+O(ε))-approximation with O(k + d/ε^2logk/ε) summary size when the objective is monotone. In the streaming setting we provide a (9.435 + O(ε))-approximation algorithm with summary size and memory O(k + d/ε^2logk/ε); the approximation factor is then improved to (5.582+O(ε)) in the monotone case.
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