Deletion Robust Non-Monotone Submodular Maximization over Matroids

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(varepsilon))-approximation algorithm with summary size O( frack+dvarepsilon2log frackvarepsilon) that is improved to a (3.582+O(varepsilon))-approximation with O(k + fracdvarepsilon2log frackvarepsilon) summary size when the objective is monotone. In the streaming setting we provide a (9.435 + O(varepsilon))-approximation algorithm with summary size and memory O(k + fracdvarepsilon2log frackvarepsilon); the approximation factor is then improved to (5.582+O(varepsilon)) in the monotone case.