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Semi-Streaming Algorithms for Weighted k-Disjoint Matchings

Authors S M Ferdous , Bhargav Samineni , Alex Pothen , Mahantesh Halappanavar , Bala Krishnamoorthy

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LIPIcs.ESA.2024.53.pdf
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ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Graph algorithms analysis
  • Mathematics of computing → Matchings and factors
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Matchings
  • Semi-Streaming Algorithms
  • Approximation Algorithms

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Abstract

We design and implement two single-pass semi-streaming algorithms for the maximum weight k-disjoint matching (k-DM) problem. Given an integer k, the k-DM problem is to find k pairwise edge-disjoint matchings such that the sum of the weights of the matchings is maximized. For k ≥ 2, this problem is NP-hard. Our first algorithm is based on the primal-dual framework of a linear programming relaxation of the problem and is 1/(3+ε)-approximate. We also develop an approximation preserving reduction from k-DM to the maximum weight b-matching problem. Leveraging this reduction and an existing semi-streaming b-matching algorithm, we design a (1/(2+ε))(1 - 1/(k+1))-approximate semi-streaming algorithm for k-DM. For any constant ε > 0, both of these algorithms require O(nk log_{1+ε}² n) bits of space. To the best of our knowledge, this is the first study of semi-streaming algorithms for the k-DM problem.
We compare our two algorithms to state-of-the-art offline algorithms on 95 real-world and synthetic test problems, including thirteen graphs generated from data center network traces. On these instances, our streaming algorithms used significantly less memory (ranging from 6× to 512× less) and were faster in runtime than the offline algorithms. Our solutions were often within 5% of the best weights from the offline algorithms. We highlight that the existing offline algorithms run out of 1 TB memory for most of the large instances (> 1 billion edges), whereas our streaming algorithms can solve these problems using only 100 GB memory for k = 8.

Cite As Get BibTex

S M Ferdous, Bhargav Samineni, Alex Pothen, Mahantesh Halappanavar, and Bala Krishnamoorthy. Semi-Streaming Algorithms for Weighted k-Disjoint Matchings. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 53:1-53:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ESA.2024.53

Author Details

S M Ferdous
  • Pacific Northwest National Laboratory, Richland, WA, USA
Bhargav Samineni
  • The University of Texas at Austin, TX, USA
Alex Pothen
  • Purdue University, West Lafayette, IN, USA
Mahantesh Halappanavar
  • Pacific Northwest National Laboratory, Richland, WA, USA
Bala Krishnamoorthy
  • Washington State University Vancouver, WA, USA

Funding

  • Ferdous, S M: Laboratory Directed Research and Development Program at PNNL.
  • Samineni, Bhargav: U.S. DOE Science Undergraduate Laboratory Internships (SULI) program.
  • Pothen, Alex: U.S. Department of Energy SC-0022260.
  • Halappanavar, Mahantesh: U.S. Department of Energy 17-SC-20-SC (ECP ExaGraph) at PNNL.

Supplementary Materials

References

  1. Mohammad Alizadeh, Shuang Yang, Milad Sharif, Sachin Katti, Nick McKeown, Balaji Prabhakar, and Scott Shenker. pfabric: Minimal near-optimal datacenter transport. ACM SIGCOMM Computer Communication Review, 43(4):435-446, 2013. Google Scholar
  2. Chen Avin, Manya Ghobadi, Chen Griner, and Stefan Schmid. On the complexity of traffic traces and implications. Proceedings of the ACM on Measurement and Analysis of Computing Systems, 4(1):1-29, 2020. Google Scholar
  3. Hitesh Ballani, Paolo Costa, Raphael Behrendt, Daniel Cletheroe, Istvan Haller, Krzysztof Jozwik, Fotini Karinou, Sophie Lange, Kai Shi, Benn Thomsen, and Hugh Williams. Sirius: A flat datacenter network with nanosecond optical switching. In Proc. of the 2020 Conference of the ACM Special Interest Group on Data Communication (SIGCOMM 2020), pages 782-797, 2020. URL: https://doi.org/10.1145/3387514.3406221.
  4. Marcin Bienkowski, David Fuchssteiner, Jan Marcinkowski, and Stefan Schmid. Online dynamic b-matching: With applications to reconfigurable datacenter networks. SIGMETRICS Performance Evaluation Review, 48(3):99-108, 2021. URL: https://doi.org/10.1145/3453953.3453976.
  5. Marcin Bienkowski, David Fuchssteiner, and Stefan Schmid. Online b-matchings for reconfigurable datacenters: The power of randomization. arXiv preprint arXiv:2209.01863, 2022. URL: https://doi.org/10.48550/arXiv.2209.0186.
  6. Deepayan Chakrabarti, Yiping Zhan, and Christos Faloutsos. R-MAT: A recursive model for graph mining. In Proc. of the 2004 SIAM International Conference on Data Mining (SDM 2004), pages 442-446, 2004. URL: https://doi.org/10.1137/1.9781611972740.43.
  7. Ernest J. Cockayne, Bert L. Hartnell, and Stephen T. Hedetniemi. A linear algorithm for disjoint matchings in trees. Discrete Mathematics, 21(2):129-136, 1978. URL: https://doi.org/10.1016/0012-365X(78)90085-7.
  8. Michael S. Crouch and Daniel M. Stubbs. Improved streaming algorithms for weighted matching, via unweighted matching. In Proc. of the 17th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2014), pages 96-104, 2014. URL: https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2014.96.
  9. Timothy A. Davis and Yifan Hu. The University of Florida Sparse Matrix Collection. ACM Transactions on Mathematical Software, 38(1), 2011. URL: https://doi.org/10.1145/2049662.2049663.
  10. Jack Edmonds. Paths, trees, and flowers. Canadian Journal of Mathematics, 17:449-467, 1965. URL: https://doi.org/10.4153/CJM-1965-045-4.
  11. Antoine El-Hayek, Kathrin Hanauer, and Monika Henzinger. On b-matching and fully-dynamic maximum k-edge coloring, 2023. URL: https://doi.org/10.48550/arXiv.2310.01149.
  12. 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(3):1251-1265, 2011. URL: https://doi.org/10.1137/100801901.
  13. Lene M. Favrholdt and Morten N. Nielsen. On-line edge-coloring with a fixed number of colors. Algorithmica, 35:176-191, 2003. URL: https://doi.org/10.1007/s00453-002-0992-3.
  14. Uriel Feige, Eran Ofek, and Udi Wieder. Approximating maximum edge coloring in multigraphs. In Proc. of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2002), pages 108-121, 2002. URL: https://doi.org/10.1007/3-540-45753-4_11.
  15. Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. On graph problems in a semi-streaming model. Theoretical Computer Science, 348(2-3):207-216, 2005. URL: https://doi.org/10.1016/j.tcs.2005.09.013.
  16. SM Ferdous, Alex Pothen, and Mahantesh Halappanavar. Streaming matching and edge cover in practice. In Leo Liberti, editor, Proceedings of the 22nd International Symposium on Experimental Algorithms (SEA 2024), LIPIcs, volume 301, 2024. Google Scholar
  17. Buddhima Gamlath, Sagar Kale, Slobodan Mitrovic, and Ola Svensson. Weighted matchings via unweighted augmentations. In Proc. of the 2019 ACM Symposium on Principles of Distributed Computing (PODC 2019), pages 491-500, 2019. URL: https://doi.org/10.1145/3293611.3331603.
  18. Mohsen Ghaffari and David Wajc. Simplified and space-optimal semi-streaming (2+ε)-approximate matching. In Proc. of the 2nd Symposium on Simplicity in Algorithms (SOSA 2019), pages 13:1-13:8, 2019. URL: https://doi.org/10.4230/OASIcs.SOSA.2019.13.
  19. Kathrin Hanauer, Monika Henzinger, Lara Ost, and Stefan Schmid. Dynamic demand-aware link scheduling for reconfigurable datacenters. In Proc. of the 42nd IEEE Conference on Computer Communications (INFOCOM 2023), 2023. URL: https://doi.org/10.48550/arXiv.2301.05751.
  20. Kathrin Hanauer, Monika Henzinger, Stefan Schmid, and Jonathan Trummer. DJ-Match/DJ-Match: Version 1.0.0, January 2022. URL: https://doi.org/10.5281/zenodo.5851268.
  21. Kathrin Hanauer, Monika Henzinger, Stefan Schmid, and Jonathan Trummer. Fast and heavy disjoint weighted matchings for demand-aware datacenter topologies. In Proc. of the 41st IEEE Conference on Computer Communications (INFOCOM 2022), pages 1649-1658, 2022. URL: https://doi.org/10.1109/INFOCOM48880.2022.9796921.
  22. Ian Holyer. The NP-Completeness of edge-coloring. SIAM Journal on Computing, 10(4):718-720, 1981. URL: https://doi.org/10.1137/0210055.
  23. Chien-Chung Huang and François Sellier. Semi-streaming algorithms for submodular function maximization under b-matching constraint. In Proc. of the 24th International Conference on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2021), pages 14:1-14:18, 2021. URL: https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.14.
  24. Marcin Kamiński and Łukasz Kowalik. Beyond the Vizing’s bound for at most seven colors. SIAM Journal on Discrete Mathematics, 28(3):1334-1362, 2014. URL: https://doi.org/10.1137/120899765.
  25. Michael Kapralov. Space lower bounds for approximating maximum matching in the edge arrival model. In Proc. of the 32nd ACM-SIAM Symposium on Discrete Algorithms (SODA 2021), pages 1874-1893, 2021. URL: https://doi.org/10.1137/1.9781611976465.112.
  26. Arif Khan, Krzysztof Choromanski, Alex Pothen, S. M. Ferdous, Mahantesh Halappanavar, and Antonino Tumeo. Adaptive anonymization of data using b-edge cover. In Proc. of the 2018 International Conference for High Performance Computing, Networking, Storage, and Analysis (SC 2018), pages 59:1-59:11, 2018. URL: https://doi.org/10.1109/SC.2018.00062.
  27. Roie Levin and David Wajc. Streaming submodular matching meets the primal-dual method. In Proc. of the 32nd ACM-SIAM Symposium on Discrete Algorithms (SODA 2021), pages 1914-1933, 2021. URL: https://doi.org/10.1137/1.9781611976465.114.
  28. Fredrik Manne and Mahantesh Halappanavar. New effective multithreaded matching algorithms. In Proc. of the 2014 IEEE 28th International Parallel and Distributed Processing Symposium (IPDPS 2014), pages 519-528, 2014. URL: https://doi.org/10.1109/IPDPS.2014.61.
  29. Jens Maue and Peter Sanders. Engineering algorithms for approximate weighted matching. In Proc. of the 6th International Conference on Experimental Algorithms (WEA 2007), pages 242-255, 2007. URL: https://doi.org/10.1007/978-3-540-72845-0_19.
  30. Andrew McGregor. Finding graph matchings in data streams. In Proc. of the 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2005), pages 170-181, 2005. URL: https://doi.org/10.1007/11538462_15.
  31. William M. Mellette, Rob McGuinness, Arjun Roy, Alex Forencich, George Papen, Alex C. Snoeren, and George Porter. Rotornet: A scalable, low-complexity, optical datacenter network. In Proc. of the 2017 Conference of the ACM Special Interest Group on Data Communication (SIGCOMM 2017), pages 267-280, 2017. URL: https://doi.org/10.1145/3098822.3098838.
  32. Jayadev Misra and David Gries. A constructive proof of Vizing’s Theorem. Information Processing Letters, 41(3):131-133, 1992. URL: https://doi.org/10.1016/0020-0190(92)90041-S.
  33. S. Muthukrishnan. Data streams: Algorithms and applications. Foundations and Trends in Theoretical Computer Science, 1(2):117-236, 2005. URL: https://doi.org/10.1561/0400000002.
  34. Ami Paz and Gregory Schwartzman. A (2+ε)-approximation for maximum weight matching in the semi-streaming model. ACM Transactions on Algorithms, 15(2):18:1-18:15, 2019. URL: https://doi.org/10.1145/3274668.
  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. Arjun Roy, Hongyi Zeng, Jasmeet Bagga, George Porter, and Alex C Snoeren. Inside the social network’s (datacenter) network. In Proceedings of the 2015 ACM Conference on Special Interest Group on Data Communication, pages 123-137, 2015. Google Scholar
  37. Vadim G. Vizing. The chromatic class of a multigraph. Cybernetics, 1(3):32-41, 1965. URL: https://doi.org/10.1007/BF01885700.
  38. Mariano Zelke. Weighted matching in the semi-streaming model. Algorithmica, 62(1-2):1-20, 2012. URL: https://doi.org/10.1007/s00453-010-9438-5.
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