Deletion Robust Non-Monotone Submodular Maximization over Matroids

• URL: http://arxiv.org/abs/2208.07582v1
• Date: Tue, 16 Aug 2022 07:51:58 GMT
• Title: Deletion Robust Non-Monotone Submodular Maximization over Matroids
• Abstract summary: We study the deletion robust version of the problem under the classic matroids constraint. We present constant-factor approximation algorithms, whose space complexity depends on the rank $k$ of the matroid. In the streaming setting we provide a $(9.435 + O(varepsilon))$-approximation algorithm with summary size and memory.
• Score: 27.83996903538686
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $O( \frac{k+d}{\varepsilon^2}\log \frac{k}{\varepsilon})$ that is improved to a $(3.582+O(\varepsilon))$-approximation with $O(k + \frac{d}{\varepsilon^2}\log \frac{k}{\varepsilon})$ 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 $O(k + \frac{d}{\varepsilon^2}\log \frac{k}{\varepsilon})$; the approximation factor is then improved to $(5.582+O(\varepsilon))$ in the monotone case.

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