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

• URL: http://arxiv.org/abs/2405.12252v1
• Date: Mon, 20 May 2024 02:24:58 GMT
• Title: Enhanced Deterministic Approximation Algorithm for Non-monotone Submodular Maximization under Knapsack Constraint with Linear Query Complexity
• Authors: Canh V. Pham,
• Abstract summary: We improve the approximation factor of the fastest deterministic algorithm from $6+epsilon$ to $5+epsilon$. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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