A note on fast deterministic algorithms for non-monotone submodular maximization under a knapsack constraint

We present a refined analysis of a variant of the algorithm in the literature for solving the knapsack-constrained submodular maximization problem. By deriving a strong approximation bound for this variant, we reduce the size of the sets requiring enumeration, from two to one, to ensure the final al...

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Bibliographic Details
Published in:Operations research letters Vol. 61; p. 107295
Main Author: Lu, Cheng
Format: Journal Article
Language:English
Published: Elsevier B.V 01.07.2025
Subjects:
Approximation algorithm
Greedy algorithm
Knapsack constraint
Submodular maximization
Greedy algorithm
Submodular maximization
Approximation algorithm
Knapsack constraint
ISSN:0167-6377
Online Access:Get full text
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Summary:We present a refined analysis of a variant of the algorithm in the literature for solving the knapsack-constrained submodular maximization problem. By deriving a strong approximation bound for this variant, we reduce the size of the sets requiring enumeration, from two to one, to ensure the final algorithm achieves 1/4-approximation. As a result, we obtain the fastest deterministic algorithm so far which achieves an approximation ratio of 1/4 for the problem.
ISSN:0167-6377
DOI:10.1016/j.orl.2025.107295