Semi-Streaming Algorithms for Submodular Function Maximization Under b-Matching Constraint

Authors Chien-Chung Huang, François Sellier

Thumbnail PDF


  • Filesize: 0.69 MB
  • 18 pages

Document Identifiers

Author Details

Chien-Chung Huang
  • CNRS, DI ENS, École normale supérieure, Université PSL, France
François Sellier
  • École polytechnique, Institut Polytechnique de Paris, France


The authors thank David Wajc and the anonymous reviewers for their helpful comments.

Cite AsGet BibTex

Chien-Chung Huang and François Sellier. Semi-Streaming Algorithms for Submodular Function Maximization Under b-Matching Constraint. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We consider the problem of maximizing a submodular function under the b-matching constraint, in the semi-streaming model. Our main results can be summarized as follows. - When the function is linear, i.e. for the maximum weight b-matching problem, we obtain a 2+ε approximation. This improves the previous best bound of 3+ε [Roie Levin and David Wajc, 2021]. - When the function is a non-negative monotone submodular function, we obtain a 3 + 2 √2 ≈ 5.828 approximation. This matches the currently best ratio [Roie Levin and David Wajc, 2021]. - When the function is a non-negative non-monotone submodular function, we obtain a 4 + 2 √3 ≈ 7.464 approximation. This ratio is also achieved in [Roie Levin and David Wajc, 2021], but only under the simple matching constraint, while we can deal with the more general b-matching constraint. We also consider a generalized problem, where a k-uniform hypergraph is given with an extra matroid constraint imposed on the edges, with the same goal of finding a b-matching that maximizes a submodular function. We extend our technique to this case to obtain an algorithm with an approximation of 8/3k+O(1). Our algorithms build on the ideas of the recent works of Levin and Wajc [Roie Levin and David Wajc, 2021] and of Garg, Jordan, and Svensson [Paritosh Garg et al., 2021]. Our main technical innovation is to introduce a data structure and associate it with each vertex and the matroid, to record the extra information of the stored edges. After the streaming phase, these data structures guide the greedy algorithm to make better choices.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
  • Theory of computation → Approximation algorithms analysis
  • Maximum Weight Matching
  • Submodular Function Maximization
  • Streaming
  • Matroid


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Niv Buchbinder, Moran Feldman, Joseph Naor, and Roy Schwartz. Submodular maximization with cardinality constraints. In Proc . 25th SODA, pages 1433-1452, 2014. Google Scholar
  2. Amit Chakrabarti and Sagar Kale. Submodular maximization meets streaming: matchings, matroids, and more. Math. Program., 154(1-2):225-247, 2015. Google Scholar
  3. Chandra Chekuri, Shalmoli Gupta, and Kent Quanrud. Streaming algorithms for submodular function maximization. In Proc . 42nd ICALP, pages 318-330, 2015. Google Scholar
  4. Michael Crouch and D.M. Stubbs. Improved streaming algorithms for weighted matching, via unweighted matching. Leibniz International Proceedings in Informatics, LIPIcs, 28:96-104, September 2014. URL:
  5. Leah Epstein, Asaf Levin, Julián Mestre, and Danny Segev. Improved approximation guarantees for weighted matching in the semi-streaming model. SIAM Journal on Discrete Mathematics, 25, July 2009. URL:
  6. Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. On graph problems in a semi-streaming model. Theoretical Computer Science, 348:207-216, December 2005. URL:
  7. Moran Feldman, Amin Karbasi, and Ehsan Kazemi. Do less, get more: Streaming submodular maximization with subsampling. In NeurIPS, pages 730-740, 2018. Google Scholar
  8. Moran Feldman, Joseph (Seffi) Naor, Roy Schwartz, and Justin Ward. Improved approximations for k-exchange systems. In Proc . 19th ESA, pages 784-798, 2011. URL:
  9. Paritosh Garg, Linus Jordan, and Ola Svensson. Semi-streaming algorithms for submodular matroid intersection. In IPCO, 2021. Google Scholar
  10. Mohsen Ghaffari and David Wajc. Space-optimal semi-streaming for (2+ε)-approximate matching, 2019. Google Scholar
  11. Roie Levin and David Wajc, 2021. private communication. Google Scholar
  12. Roie Levin and David Wajc. Streaming submodular matching meets the primal-dual method. In SODA, pages 1914-1933, 2021. Google Scholar
  13. Andrew McGregor. Finding graph matchings in data streams. In Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. APPROX 2005, RANDOM 2005., pages 170-181, 2005. URL:
  14. S. Muthukrishnan. Data Streams: Algorithms and Applications. Now Foundations and Trends, 2005. URL:
  15. Ami Paz and Gregory Schwartzman. A (2 + ε)-approximation for maximum weight matching in the semi-streaming model. In Proceedings of the 2017 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 2153-2161, 2017. URL:
  16. Alexander Schrijver. Combinatorial Optimization: Polyhedra and Efficiency. Springer, 2003. Google Scholar
  17. Mariano Zelke. Weighted matching in the semi-streaming model. Algorithmica, 62:1-20, February 2008. URL:
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail