[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Log in

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

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

In this work, we consider the Submodular Maximization under Knapsack (\(\textsf{SMK}\)) 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 \(6+\epsilon \) 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Algorithm 1

Similar content being viewed by others

Data availability

There is no data included in this research.

References

  • Amanatidis G, Fusco F, Lazos P, Leonardi S, Marchetti-Spaccamela A, Reiffenhäuser R (2021) Submodular maximization subject to a knapsack constraint: Combinatorial algorithms with near-optimal adaptive complexity. In: International conference on machine learning, proceedings of machine learning research, 139:231–242

  • Amanatidis G, Fusco F, Lazos P, Leonardi S, Reiffenhäuser R (2020) Fast adaptive non-monotone submodular maximization subject to a knapsack constraint. In: Annual conference on neural information processing systems

  • Badanidiyuru A, Vondrák J (2014) Fast algorithms for maximizing submodular functions. In: Annual ACM-SIAM symposium on discrete algorithms, pp. 1497–1514. https://doi.org/10.1137/1.9781611973402.110

  • Buchbinder N, Feldman M (2019) Constrained submodular maximization via a nonsymmetric technique. Math Oper Res 44(3):988–1005

    Article  MathSciNet  Google Scholar 

  • Chekuri C, Vondrák J, Zenklusen R (2014) Submodular function maximization via the multilinear relaxation and contention resolution schemes. SIAM J Comput 43(6):1831–1879

    Article  MathSciNet  Google Scholar 

  • Chen Y, Kuhnle A (2023) Approximation algorithms for size-constrained non-monotone submodular maximization in deterministic linear time. In: A.K. Singh, Y. Sun, L. Akoglu, D. Gunopulos, X. Yan, R. Kumar, F. Ozcan, J. Ye (eds.) Proceedings of the 29th ACM SIGKDD conference on knowledge discovery and data mining, KDD 2023, Long Beach, CA, USA, August 6-10, 2023, pp. 250–261. ACM

  • Cui S, Han K, Tang J, Huang H, Li X, Li Z (2021) Streaming algorithms for constrained submodular maximization. Proc ACM Meas Anal Comput Syst 6(3):54:1-54:32

    Google Scholar 

  • Ene A, Nguyen HL (2019) A nearly-linear time algorithm for submodular maximization with a knapsack constraint. Int Colloq Autom Lang Programm 132:53:1-53:12

    MathSciNet  Google Scholar 

  • Feldman M, Naor J, Schwartz R (2011) A unified continuous greedy algorithm for submodular maximization. In: Annual symposium on foundations of computer science, pp. 570–579

  • Gupta A, Roth A, Schoenebeck G, Talwar K (2010) Constrained non-monotone submodular maximization: offline and secretary algorithms. In: International workshop on internet and network economics

  • Ha DTK, Pham CV, Tran TD (2024) Improved approximation algorithms for k-submodular maximization under a knapsack constraint. Comput Oper Res 161:106452. https://doi.org/10.1016/j.cor.2023.106452

    Article  MathSciNet  Google Scholar 

  • Han K, Cui S, Zhu T, Zhang E, Wu B, Yin Z, Xu T, Tang S, Huang H (2021) Approximation algorithms for submodular data summarization with a knapsack constraint. Proc ACM Meas Anal Comput Syst 5(1):05:1-05:31

    Article  Google Scholar 

  • Kuhnle A (2019) Interlaced greedy algorithm for maximization of submodular functions in nearly linear time. In: Neural information processing systems, pp. 2371–2381

  • Kulik A, Shachnai H, Tamir T (2013) Approximations for monotone and nonmonotone submodular maximization with knapsack constraints. Math Oper Res 38(4):729–739

    Article  MathSciNet  Google Scholar 

  • Lee J, Mirrokni VS, Nagarajan V, Sviridenko M (2010) Maximizing nonmonotone submodular functions under matroid or knapsack constraints. SIAM J Discret Math 23(4):2053–2078

    Article  MathSciNet  Google Scholar 

  • Lee J, Mirrokni VS, Nagarajan V, Sviridenko M (2010) Maximizing nonmonotone submodular functions under matroid or knapsack constraints. SIAM J Discret Math 23(4):2053–2078

    Article  MathSciNet  Google Scholar 

  • Leskovec J, Krause A, Guestrin C, Faloutsos C, VanBriesen JM, Glance NS (2007) Cost-effective outbreak detection in networks. In: Proc. of the 13th ACM SIGKDD Conf., 2007, pp. 420–429

  • Li W (2018) Nearly linear time algorithms and lower bound for submodular maximization. preprint, arXiv:1804.08178

  • Li W, Feldman M, Kazemi E, Karbasi A (2022) Submodular maximization in clean linear time. In: Advances in neural information processing systems, pp. 7887–7897

  • Mirzasoleiman B, Badanidiyuru A, Karbasi A (2016) Fast constrained submodular maximization: Personalized data summarization. In: International conference on machine learning, JMLR Workshop and Conf. Proc., vol. 48, pp. 1358–1367

  • Mirzasoleiman B, Karbasi A, Badanidiyuru A, Krause A (2015) Distributed submodular cover: Succinctly summarizing massive data. In: Proc. of the 28th NeurIPS 2015, pp. 2881–2889

  • Nutov Z, Shoham E (2020) Practical budgeted submodular maximization. CoRR abs/2007.04937. arxiv:2007.04937

  • Pham CV, Tran TD, Ha DTK, Thai MT (2023) Linear query approximation algorithms for non-monotone submodular maximization under knapsack constraint. In: Proceedings of the thirty-second international joint conference on artificial intelligence, IJCAI 2023, 19th-25th August 2023, Macao, SAR, China, pp. 4127–4135. ijcai.org

  • Pham CV, Vu QC, Ha DK, Nguyen TT (2021) Streaming algorithms for budgeted k-submodular maximization problem. In: Computational data and social networks—10th international conference, CSoNet 2021, Virtual Event, November 15-17, 2021, Proceedings, Lecture Notes in Computer Science, vol. 13116, pp. 27–38. Springer

  • Sun X, Zhang J, Zhang S, Zhang Z (2024) Improved deterministic algorithms for non-monotone submodular maximization. Theor Comput Sci 984:114293

    Article  MathSciNet  Google Scholar 

  • Sviridenko M (2004) A note on maximizing a submodular set function subject to a knapsack constraint. Oper Res Lett 32(1):41–43

    Article  MathSciNet  Google Scholar 

  • Wolsey LA (1982) Maximising real-valued submodular functions: primal and dual heuristics for location problems. Math Oper Res 7(3):410–425

    Article  MathSciNet  Google Scholar 

  • Yaroslavtsev G, Zhou S, Avdiukhin D (2020) "bring your own greedy"+max: Near-optimal 1/2-approximations for submodular knapsack. In: The international conference on artificial intelligence and statistics. 108:3263–3274

Download references

Funding

The is no funding for this study.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Canh V. Pham.

Ethics declarations

Conflict of interest

All authors declare that have no conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pham, C.V. Enhanced deterministic approximation algorithm for non-monotone submodular maximization under knapsack constraint with linear query complexity. J Comb Optim 49, 2 (2025). https://doi.org/10.1007/s10878-024-01232-9

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10878-024-01232-9

Keywords

Navigation