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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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
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Abstract 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.
AbstractList 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.
ArticleNumber 107295
Author Lu, Cheng
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Cites_doi 10.1137/090750020
10.1016/S0167-6377(03)00062-2
10.1007/s00453-022-01071-2
10.1613/jair.1.13472
10.1016/S0020-0190(99)00031-9
10.1016/j.orl.2021.04.006
10.1145/3447383
10.1287/moor.2013.0592
10.1016/j.tcs.2023.114293
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Keywords Greedy algorithm
Submodular maximization
Approximation algorithm
Knapsack constraint
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References Badanidiyuru, Vondrák (br0050) 2014
Kulik, Shachnai, Tamir (br0070) 2013; 38
Kulik, Schwartz, Shachnai (br0040) 2021; 49
Gupta, Roth, Schoenebeck, Talwar (br0110) 2010
Amanatidis, Fusco, Lazos, Leonardi, Reiffenhäuser (br0090) 2022; 74
Sun, Zhang, Zhang, Zhang (br0130) 2024
Khuller, Moss, Naor (br0010) 1999; 70
Sviridenko (br0020) 2004; 32
Feldman, Nutov, Shoham (br0030) 2023; 85
Pham (br0120) 2024
Lee, Mirrokni, Nagarajan, Sviridenko (br0060) 2010; 23
Pham, Tran, Ha, Thai (br0100) 2023
Buchbinder, Feldman (br0080) 2023
Han, Cui, Zhu, Zhang, Wu, Yin, Xu, Tang, Huang (br0140) 2021; 5
Kulik (10.1016/j.orl.2025.107295_br0040) 2021; 49
Kulik (10.1016/j.orl.2025.107295_br0070) 2013; 38
Badanidiyuru (10.1016/j.orl.2025.107295_br0050) 2014
Pham (10.1016/j.orl.2025.107295_br0100) 2023
Amanatidis (10.1016/j.orl.2025.107295_br0090) 2022; 74
Sviridenko (10.1016/j.orl.2025.107295_br0020) 2004; 32
Gupta (10.1016/j.orl.2025.107295_br0110) 2010
Feldman (10.1016/j.orl.2025.107295_br0030) 2023; 85
Pham (10.1016/j.orl.2025.107295_br0120)
Sun (10.1016/j.orl.2025.107295_br0130) 2024
Khuller (10.1016/j.orl.2025.107295_br0010) 1999; 70
Lee (10.1016/j.orl.2025.107295_br0060) 2010; 23
Buchbinder (10.1016/j.orl.2025.107295_br0080)
Han (10.1016/j.orl.2025.107295_br0140) 2021; 5
References_xml – start-page: 4127
  year: 2023
  end-page: 4135
  ident: br0100
  article-title: Linear query approximation algorithms for non-monotone submodular maximization under knapsack constraint
  publication-title: Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence (IJCAI)
– volume: 23
  start-page: 2053
  year: 2010
  end-page: 2078
  ident: br0060
  article-title: Maximizing nonmonotone submodular functions under matroid or knapsack constraints
  publication-title: SIAM J. Discrete Math.
– volume: 5
  start-page: 1
  year: 2021
  end-page: 31
  ident: br0140
  article-title: Approximation algorithms for submodular data summarization with a knapsack constraint
  publication-title: Proc. ACM Meas. Anal. Comput. Syst.
– start-page: 246
  year: 2010
  end-page: 257
  ident: br0110
  article-title: Constrained non-monotone submodular maximization: offline and secretary algorithms
  publication-title: Proceedings of the 6th International Conference on Internet and Network Economics (WINE)
– start-page: 1497
  year: 2014
  end-page: 1514
  ident: br0050
  article-title: Fast algorithms for maximizing submodular functions
  publication-title: Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)
– year: 2024
  ident: br0130
  article-title: Improved deterministic algorithms for non-monotone submodular maximization
  publication-title: Theor. Comput. Sci.
– volume: 74
  start-page: 661
  year: 2022
  end-page: 690
  ident: br0090
  article-title: Fast adaptive non-monotone submodular maximization subject to a knapsack constraint
  publication-title: J. Artif. Intell. Res.
– volume: 32
  start-page: 41
  year: 2004
  end-page: 43
  ident: br0020
  article-title: A note on maximizing a submodular set function subject to a knapsack constraint
  publication-title: Oper. Res. Lett.
– year: 2024
  ident: br0120
  article-title: Enhanced deterministic approximation algorithm for non-monotone submodular maximization under knapsack constraint with linear query complexity
– volume: 85
  start-page: 1332
  year: 2023
  end-page: 1371
  ident: br0030
  article-title: Practical budgeted submodular maximization
  publication-title: Algorithmica
– year: 2023
  ident: br0080
  article-title: Constrained submodular maximization via new bounds for DR-submodular functions
– volume: 49
  start-page: 507
  year: 2021
  end-page: 514
  ident: br0040
  article-title: A refined analysis of submodular greedy
  publication-title: Oper. Res. Lett.
– volume: 70
  start-page: 39
  year: 1999
  end-page: 45
  ident: br0010
  article-title: The budgeted maximum coverage problem
  publication-title: Inf. Process. Lett.
– volume: 38
  start-page: 729
  year: 2013
  end-page: 739
  ident: br0070
  article-title: Approximations for monotone and nonmonotone submodular maximization with knapsack constraints
  publication-title: Math. Oper. Res.
– volume: 23
  start-page: 2053
  year: 2010
  ident: 10.1016/j.orl.2025.107295_br0060
  article-title: Maximizing nonmonotone submodular functions under matroid or knapsack constraints
  publication-title: SIAM J. Discrete Math.
  doi: 10.1137/090750020
– volume: 32
  start-page: 41
  year: 2004
  ident: 10.1016/j.orl.2025.107295_br0020
  article-title: A note on maximizing a submodular set function subject to a knapsack constraint
  publication-title: Oper. Res. Lett.
  doi: 10.1016/S0167-6377(03)00062-2
– volume: 85
  start-page: 1332
  year: 2023
  ident: 10.1016/j.orl.2025.107295_br0030
  article-title: Practical budgeted submodular maximization
  publication-title: Algorithmica
  doi: 10.1007/s00453-022-01071-2
– volume: 74
  start-page: 661
  year: 2022
  ident: 10.1016/j.orl.2025.107295_br0090
  article-title: Fast adaptive non-monotone submodular maximization subject to a knapsack constraint
  publication-title: J. Artif. Intell. Res.
  doi: 10.1613/jair.1.13472
– volume: 70
  start-page: 39
  year: 1999
  ident: 10.1016/j.orl.2025.107295_br0010
  article-title: The budgeted maximum coverage problem
  publication-title: Inf. Process. Lett.
  doi: 10.1016/S0020-0190(99)00031-9
– start-page: 4127
  year: 2023
  ident: 10.1016/j.orl.2025.107295_br0100
  article-title: Linear query approximation algorithms for non-monotone submodular maximization under knapsack constraint
– volume: 49
  start-page: 507
  year: 2021
  ident: 10.1016/j.orl.2025.107295_br0040
  article-title: A refined analysis of submodular greedy
  publication-title: Oper. Res. Lett.
  doi: 10.1016/j.orl.2021.04.006
– volume: 5
  start-page: 1
  year: 2021
  ident: 10.1016/j.orl.2025.107295_br0140
  article-title: Approximation algorithms for submodular data summarization with a knapsack constraint
  publication-title: Proc. ACM Meas. Anal. Comput. Syst.
  doi: 10.1145/3447383
– volume: 38
  start-page: 729
  year: 2013
  ident: 10.1016/j.orl.2025.107295_br0070
  article-title: Approximations for monotone and nonmonotone submodular maximization with knapsack constraints
  publication-title: Math. Oper. Res.
  doi: 10.1287/moor.2013.0592
– ident: 10.1016/j.orl.2025.107295_br0080
– ident: 10.1016/j.orl.2025.107295_br0120
– start-page: 246
  year: 2010
  ident: 10.1016/j.orl.2025.107295_br0110
  article-title: Constrained non-monotone submodular maximization: offline and secretary algorithms
– start-page: 1497
  year: 2014
  ident: 10.1016/j.orl.2025.107295_br0050
  article-title: Fast algorithms for maximizing submodular functions
– year: 2024
  ident: 10.1016/j.orl.2025.107295_br0130
  article-title: Improved deterministic algorithms for non-monotone submodular maximization
  publication-title: Theor. Comput. Sci.
  doi: 10.1016/j.tcs.2023.114293
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SubjectTerms Approximation algorithm
Greedy algorithm
Knapsack constraint
Submodular maximization
Title A note on fast deterministic algorithms for non-monotone submodular maximization under a knapsack constraint
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