2022/08/16 by Paul Dütting, Dütting, Paul, Federico Fusco +7
Computer Science · #Complexity and Algorithms in Graphs #Cryptography and Data Security #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Privacy-Preserving Technologies in Data
paper · pdf · doi:10.48550/arxiv.2208.07582
openalex publication_date 2022/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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)/(ε2)log (k)/(ε)) that is improved to a (3.582+O(ε))-approximation with O(k + (d)/(ε2)log (k)/(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)/(ε2)log (k)/(ε)); the approximation factor is then improved to (5.582+O(ε)) in the monotone case.