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Semi-Streaming Algorithms for Hypergraph Matching

Authors Henrik Reinstädtler , S M Ferdous , Alex Pothen , Bora Uçar , Christian Schulz

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ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Hypergraphs
Keywords
  • hypergraph
  • matching
  • semi-streaming

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Abstract

We propose two one-pass streaming algorithms for the NP-hard hypergraph matching problem. The first algorithm stores a small subset of potential matching edges in a stack using dual variables to select edges. It has an approximation guarantee of 1/(d(1+ε)) and requires 𝒪((n/ε)log²n) bits of memory, where n is the number of vertices in the hypergraph, d is the maximum number of vertices in a hyperedge, and ε > 0 is a parameter to be chosen. The second algorithm computes, stores, and updates a single matching as the edges stream, with an approximation ratio dependent on a parameter α. Its best approximation guarantee is 1/((2d-1) + 2 √{d(d-1)}), and it requires only 𝒪(n) memory.
We have implemented both algorithms and compared them with respect to solution quality, memory consumption, and running times on two diverse sets of hypergraphs with a non-streaming greedy and a naive streaming algorithm. Our results show that the streaming algorithms achieve much better solution quality than naive algorithms when facing adverse orderings. Furthermore, these algorithms reduce the memory required by a factor of 13 in the geometric mean on our test problems, and also outperform the offline Greedy algorithm in running time.

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Henrik Reinstädtler, S M Ferdous, Alex Pothen, Bora Uçar, and Christian Schulz. Semi-Streaming Algorithms for Hypergraph Matching. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 79:1-79:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.79

Author Details

Henrik Reinstädtler
  • Heidelberg University, Germany
S M Ferdous
  • Pacific Northwest National Laboratory, Richland, WA, USA
Alex Pothen
  • Purdue University, West Lafayette, IN, USA
Bora Uçar
  • CNRS and LIP, ENS de Lyon, France
  • UMR5668 (CNRS, ENS de Lyon, Inria, UCBL1), France
Christian Schulz
  • Heidelberg University, Germany

Funding

We acknowledge support by DFG grant SCHU 2567/8-1. Moreover, we like to acknowledge Dagstuhl Seminar 24201 on discrete algorithms on modern and emerging compute infrastructure. Alex Pothen’s research was supported by the U.S. Department of Energy grant SC-0022260. S M Ferdous’s research was supported by the Laboratory Directed Research and Development Program at PNNL.

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References

  1. Mokhtar S Bazaraa, John J Jarvis, and Hanif D Sherali. Linear Programming and Network Flows. John Wiley & Sons, 2011. Google Scholar
  2. Anton Belov, Daniel Diepold, Marijn Heule, and Matti Järvisalo. The SAT competition 2014. http://www.satcompetition.org/2014/index.shtml, 2014.
  3. Austin R. Benson, Rediet Abebe, Michael T. Schaub, Ali Jadbabaie, and Jon M. Kleinberg. Simplicial closure and higher-order link prediction. Proc. Natl. Acad. Sci. USA, 115(48):E11221-E11230, 2018. URL: https://doi.org/10.1073/pnas.1800683115.
  4. Piotr Berman. A d/2 approximation for maximum weight independent set in d-claw free graphs. In Magnús M. Halldórsson, editor, Algorithm Theory - SWAT 2000, 7th Scandinavian Workshop on Algorithm Theory, Bergen, Norway, July 5-7, 2000, Proceedings, volume 1851 of Lecture Notes in Computer Science, pages 214-219, Berlin, Heidelberg, 2000. Springer. URL: https://doi.org/10.1007/3-540-44985-X_19.
  5. B. Besser and M. Poloczek. Greedy matching: Guarantees and limitations. Algorithmica, 77:201-234, 2017. URL: https://doi.org/10.1007/S00453-015-0062-2.
  6. Marcel Birn, Vitaly Osipov, Peter Sanders, Christian Schulz, and Nodari Sitchinava. Efficient parallel and external matching. In Felix Wolf, Bernd Mohr, and Dieter an Mey, editors, Euro-Par 2013 Parallel Processing - 19th International Conference, Aachen, Germany, August 26-30, 2013. Proceedings, volume 8097 of Lecture Notes in Computer Science, pages 659-670. Springer, Springer, 2013. URL: https://doi.org/10.1007/978-3-642-40047-6_66.
  7. Marek Cygan. Improved approximation for 3-dimensional matching via bounded pathwidth local search. In 54th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2013, 26-29 October, 2013, Berkeley, CA, USA, pages 509-518. IEEE, IEEE Computer Society, 2013. URL: https://doi.org/10.1109/FOCS.2013.61.
  8. Timothy A. Davis and Yifan Hu. The university of florida sparse matrix collection. ACM Trans. Math. Softw., 38(1):1:1-1:25, December 2011. URL: https://doi.org/10.1145/2049662.2049663.
  9. Elizabeth D. Dolan and Jorge J. Moré. Benchmarking optimization software with performance profiles. Math. Program., 91(2):201-213, 2002. URL: https://doi.org/10.1007/s101070100263.
  10. Doratha E. Drake and Stefan Hougardy. A simple approximation algorithm for the weighted matching problem. Inf. Process. Lett., 85(4):211-213, 2003. URL: https://doi.org/10.1016/S0020-0190(02)00393-9.
  11. Fanny Dufossé, Kamer Kaya, Ioannis Panagiotas, and Bora Uçar. Effective heuristics for matchings in hypergraphs. In Ilias S. Kotsireas, Panos M. Pardalos, Konstantinos E. Parsopoulos, Dimitris Souravlias, and Arsenis Tsokas, editors, Analysis of Experimental Algorithms - Special Event, SEA² 2019, Kalamata, Greece, June 24-29, 2019, Revised Selected Papers, volume 11544 of Lecture Notes in Computer Science, pages 248-264. Springer, Springer, 2019. URL: https://doi.org/10.1007/978-3-030-34029-2_17.
  12. Jack Edmonds. Paths, trees, and flowers. Canadian Journal of Mathematics, 17:449-467, 1965. URL: https://doi.org/10.4153/CJM-1965-045-4.
  13. Jason Evans. jemalloc. http://jemalloc.net/, 2006-. Accessed: 2025-04-15.
  14. Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. On graph problems in a semi-streaming model. Departmental Papers (CIS), page 236, 2005. URL: https://doi.org/10.1016/j.tcs.2005.09.013.
  15. S. M. Ferdous, Alex Pothen, and Mahantesh Halappanavar. Streaming matching and edge cover in practice. In Leo Liberti, editor, 22nd International Symposium on Experimental Algorithms, SEA 2024, July 23-26, 2024, Vienna, Austria, volume 301 of LIPIcs, pages 12:1-12:22, Dagstuhl, Germany, 2024. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.SEA.2024.12.
  16. S. M. Ferdous, Bhargav Samineni, Alex Pothen, Mahantesh Halappanavar, and Bala Krishnamoorthy. Semi-streaming algorithms for weighted k-disjoint matchings. In Timothy M. Chan, Johannes Fischer, John Iacono, and Grzegorz Herman, editors, 32nd Annual European Symposium on Algorithms, ESA 2024, September 2-4, 2024, Royal Holloway, London, United Kingdom, volume 308 of LIPIcs, pages 53:1-53:19, Dagstuhl, Germany, 2024. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.ESA.2024.53.
  17. Aurélien Froger, Olivier Guyon, and Eric Pinson. A set packing approach for scheduling passenger train drivers: the French experience. In RailTokyo2015, 2015. Google Scholar
  18. Mohsen Ghaffari and David Wajc. Simplified and space-optimal semi-streaming (2+epsilon)-approximate matching. In Jeremy T. Fineman and Michael Mitzenmacher, editors, 2nd Symposium on Simplicity in Algorithms, SOSA 2019, January 8-9, 2019, San Diego, CA, USA, volume 69 of OASIcs, pages 13:1-13:8, Dagstuhl, Germany, 2019. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/OASIcs.SOSA.2019.13.
  19. Google Cloud Platform. Bigquery public datasets. https://cloud.google.com/bigquery/public-data. Accessed: 2025-04-19.
  20. Lars Gottesbüren, Tobias Heuer, Nikolai Maas, Peter Sanders, and Sebastian Schlag. Scalable high-quality hypergraph partitioning. CoRR, abs/2303.17679, 2023. URL: https://doi.org/10.48550/arXiv.2303.17679.
  21. Georg Gottlob and Gianluigi Greco. Decomposing combinatorial auctions and set packing problems. J. ACM, 60(4):24:1-24:39, 2013. URL: https://doi.org/10.1145/2508028.2505987.
  22. Ernestine Großmann, Felix Joos, Henrik Reinstädtler, and Christian Schulz. Engineering hypergraph b-matching algorithms. arXiv preprint arXiv:2408.06924, 2024. URL: https://doi.org/10.48550/arXiv.2408.06924.
  23. Oussama Hanguir and Clifford Stein. Distributed algorithms for matching in hypergraphs. In Christos Kaklamanis and Asaf Levin, editors, Approximation and Online Algorithms - 18th International Workshop, WAOA 2020, Virtual Event, September 9-10, 2020, Revised Selected Papers, volume 12806 of Lecture Notes in Computer Science, pages 30-46. Springer, Springer, 2020. URL: https://doi.org/10.1007/978-3-030-80879-2_3.
  24. Elad Hazan, Shmuel Safra, and Oded Schwartz. On the complexity of approximating k-set packing. Comput. Complex., 15(1):20-39, 2006. URL: https://doi.org/10.1007/s00037-006-0205-6.
  25. Chien-Chung Huang and François Sellier. Semi-streaming algorithms for submodular function maximization under b-matching constraint. In Mary Wootters and Laura Sanità, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2021, August 16-18, 2021, University of Washington, Seattle, Washington, USA (Virtual Conference), volume 207 of LIPIcs, pages 14:1-14:18, Dagstuhl, Germany, 2021. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.14.
  26. Cor A. J. Hurkens and Alexander Schrijver. On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems. SIAM J. Discret. Math., 2(1):68-72, 1989. URL: https://doi.org/10.1137/0402008.
  27. Richard M. Karp. Reducibility among combinatorial problems. In Michael Jünger, Thomas M. Liebling, Denis Naddef, George L. Nemhauser, William R. Pulleyblank, Gerhard Reinelt, Giovanni Rinaldi, and Laurence A. Wolsey, editors, 50 Years of Integer Programming 1958-2008 - From the Early Years to the State-of-the-Art, pages 219-241. Springer, 2010. URL: https://doi.org/10.1007/978-3-540-68279-0_8.
  28. B. Korte and D. Hausmann. An analysis of the greedy algorithm for independence systems. Annals of Discrete Mathematics, 2:65-74, 1978. Google Scholar
  29. Fredrik Manne and Mahantesh Halappanavar. New effective multithreaded matching algorithms. In 2014 IEEE 28th International Parallel and Distributed Processing Symposium, pages 519-528. IEEE Computer Society, 2014. URL: https://doi.org/10.1109/IPDPS.2014.61.
  30. Jens Maue and Peter Sanders. Engineering algorithms for approximate weighted matching. In Camil Demetrescu, editor, Experimental Algorithms, 6th International Workshop, WEA 2007, Rome, Italy, June 6-8, 2007, Proceedings, volume 4525 of Lecture Notes in Computer Science, pages 242-255. Springer, Springer, 2007. URL: https://doi.org/10.1007/978-3-540-72845-0_19.
  31. Andrew McGregor. Finding graph matchings in data streams. In Chandra Chekuri, Klaus Jansen, José D. P. Rolim, and Luca Trevisan, editors, Approximation, Randomization and Combinatorial Optimization, Algorithms and Techniques, 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and 9th InternationalWorkshop on Randomization and Computation, RANDOM 2005, Berkeley, CA, USA, August 22-24, 2005, Proceedings, volume 3624 of Lecture Notes in Computer Science, pages 170-181. Springer, Springer, 2005. URL: https://doi.org/10.1007/11538462_15.
  32. Meike Neuwohner. Passing the limits of pure local search for weighted k-set packing. In Nikhil Bansal and Viswanath Nagarajan, editors, Proceedings of the 2023 ACM-SIAM Symposium on Discrete Algorithms, SODA 2023, Florence, Italy, January 22-25, 2023, pages 1090-1137. SIAM, SIAM, 2023. URL: https://doi.org/10.1137/1.9781611977554.ch41.
  33. Ami Paz and Gregory Schwartzman. A (2+ε)-approximation for maximum weight matching in the semi-streaming model. ACM Trans. Algorithms, 15(2):18:1-18:15, December 2019. URL: https://doi.org/10.1145/3274668.
  34. Seth Pettie and Peter Sanders. A simpler linear time 2/3-ε approximation for maximum weight matching. Information Processing Letters, 91(6):271-276, 2004. URL: https://doi.org/10.1016/j.ipl.2004.05.007.
  35. Alex Pothen, SM Ferdous, and Fredrik Manne. Approximation algorithms in combinatorial scientific computing. Acta Numerica, 28:541-633, 2019. URL: https://doi.org/10.1017/S0962492919000035.
  36. Robert Preis. Linear time 1/2-approximation algorithm for maximum weighted matching in general graphs. In Christoph Meinel and Sophie Tison, editors, STACS 99, 16th Annual Symposium on Theoretical Aspects of Computer Science, Trier, Germany, March 4-6, 1999, Proceedings, volume 1563 of Lecture Notes in Computer Science, pages 259-269. Springer, Springer, 1999. URL: https://doi.org/10.1007/3-540-49116-3_24.
  37. Henrik Reinstädtler, S M Ferdous, Alex Pothen, Bora Uçar, and Christian Schulz. HeiHGM/Streaming. Software, DFG-SCHU 2567/8-1, (visited on 2025-09-05). URL: https://github.com/HeiHGM/Streaming
    Software Heritage Logo archived version
    full metadata available at: https://doi.org/10.4230/artifacts.24674
  38. Henrik Reinstädtler, S M Ferdous, Alex Pothen, Bora Uçar, and Christian Schulz. Semi-streaming algorithms for hypergraph matching, 2025. URL: https://doi.org/10.48550/arXiv.2502.13636.
  39. StackExchange. Stackexchange data explorer. https://data.stackexchange.com/. Accessed: 2025-04-19.
  40. Thorben Tröbst and Rajan Udwani. Almost tight bounds for online hypergraph matching. arXiv preprint arXiv:2402.08775, 2024. URL: https://doi.org/10.1016/j.orl.2024.107143.
  41. Natarajan Viswanathan, Charles J. Alpert, Cliff C. N. Sze, Zhuo Li, and Yaoguang Wei. The DAC 2012 routability-driven placement contest and benchmark suite. In Patrick Groeneveld, Donatella Sciuto, and Soha Hassoun, editors, The 49th Annual Design Automation Conference 2012, DAC '12, San Francisco, CA, USA, June 3-7, 2012, DAC '12, pages 774-782, New York, NY, USA, 2012. ACM. URL: https://doi.org/10.1145/2228360.2228500.
  42. David P. Williamson and David B. Shmoys. The Design of Approximation Algorithms. Cambridge University Press, 2011. URL: http://www.cambridge.org/de/knowledge/isbn/item5759340/?site_locale=de_DE.
  43. Laurence A Wolsey. Integer Programming. John Wiley & Sons, 2020. Google Scholar
  44. Stephen J. Wright. Primal-Dual Interior-Point Methods. SIAM, 1997. URL: https://doi.org/10.1137/1.9781611971453.
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