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arXiv · 2405.12252

Enhanced Deterministic Approximation Algorithm for Non-monotone Submodular Maximization under Knapsack Constraint with Linear Query Complexity

Canh V. Pham
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Abstract

In this work, we consider the Submodular Maximization under Knapsack (SMK) constraint problem over the ground set of size $n$. The problem recently attracted a lot of attention due to its applications in various domains of combination optimization, artificial intelligence, and machine learning. We improve the approximation factor of the fastest deterministic algorithm from $6+\epsilon$ to $5+\epsilon$ while keeping the best query complexity of $O(n)$, where $\epsilon >0$ is a constant parameter. Our technique is based on optimizing the performance of two components: the threshold greedy subroutine and the building of two disjoint sets as candidate solutions. Besides, by carefully analyzing the cost of candidate solutions, we obtain a tighter approximation factor.

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Canh V. Pham. 2024-05-20. Enhanced Deterministic Approximation Algorithm for Non-monotone Submodular Maximization under Knapsack Constraint with Linear Query Complexity. https://arxiv.org/abs/2405.12252

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