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Enhanced deterministic approximation algorithm for non-monotone submodular maximization under knapsack constraint with linear query complexity

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  • Canh V. Pham

    (Phenikaa University)

Abstract

In this work, we consider the Submodular Maximization under Knapsack ( $$\textsf{SMK}$$ 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 combinatorial optimization, artificial intelligence, and machine learning. We improve the approximation factor of the fastest deterministic algorithm from $$6+\epsilon $$ 6 + ϵ to $$5+\epsilon $$ 5 + ϵ while keeping the best query complexity of O(n), where $$\epsilon >0$$ ϵ > 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.

Suggested Citation

  • Canh V. Pham, 2025. "Enhanced deterministic approximation algorithm for non-monotone submodular maximization under knapsack constraint with linear query complexity," Journal of Combinatorial Optimization, Springer, vol. 49(1), pages 1-14, January.
    • Handle: RePEc:spr:jcomop:v:49:y:2025:i:1:d:10.1007_s10878-024-01232-9
    DOI: 10.1007/s10878-024-01232-9
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    References listed on IDEAS

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    1. Niv Buchbinder & Moran Feldman, 2019. "Constrained Submodular Maximization via a Nonsymmetric Technique," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 988-1005, August.
    2. WOLSEY, Laurence A., 1982. "Maximising real-valued submodular functions: primal and dual heuristics for location problems," LIDAM Reprints CORE 486, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Laurence A. Wolsey, 1982. "Maximising Real-Valued Submodular Functions: Primal and Dual Heuristics for Location Problems," Mathematics of Operations Research, INFORMS, vol. 7(3), pages 410-425, August.
    4. Ariel Kulik & Hadas Shachnai & Tami Tamir, 2013. "Approximations for Monotone and Nonmonotone Submodular Maximization with Knapsack Constraints," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 729-739, November.
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