Papers › Practical $0.385$-Approximation for Submodular Maximization Subject to a Cardinality Constraint
Practical $0.385$-Approximation for Submodular Maximization Subject to a Cardinality Constraint
Murad Tukan, Loay Mualem, Moran Feldman
Non-monotone constrained submodular maximization plays a crucial role in various machine learning applications. However, existing algorithms often struggle with a trade-off between approximation guarantees and practical efficiency. The current state-of-the-art is a recent $0.401$-approximation algorithm, but its computational complexity makes it highly impractical. The best practical algorithms for the problem only guarantee 1/e-approximation. In this work, we present a novel algorithm for submodular maximization subject to a cardinality constraint that combines a guarantee of $0.385$-approximation with a low and practical query complexity of O(n+k²). Furthermore, we evaluate the empirical performance of our algorithm in experiments based on various machine learning applications, including Movie Recommendation, Image Summarization, and more. These experiments demonstrate the efficacy of our approach.
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