Approximation Algorithms for Size-Constrained Non-Monotone Submodular Maximization in Deterministic Linear Time - Chen, Yixin; Kuhnle, Alan (arXiv.org, 2023)
In this work, we study the problem of finding the maximum value of a non-negative submodular function subject to a limit on the number of items selected, a ubiquitous problem that appears in many applications, such as data summarization and nonlinear regression. We provide the first deterministic, linear-time approximation algorithms for this problem that do not assume the objective is monotone. We present three deterministic, linear-time algorithms: a single-pass streaming algorithm with a ratio of \(23.313 + ε\), which is the first linear-time streaming algorithm; a simpler deterministic linear-time algorithm with a ratio of \(11.657\); and a \((4 + O(ε ))\)-approximation algorithm. Finally, we present a deterministic algorithm that obtains ratio of \(e + ε\) in \(O_{ε}(n \log(n))\) time, close to the best known expected ratio of \(e - 0.121\) in polynomial time.