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3.415-Approximation for Coflow Scheduling via Iterated Rounding

Authors Lars Rohwedder , Leander Schnaars

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ACM Subject Classification
  • Theory of computation → Scheduling algorithms
Keywords
  • Coflow Scheduling
  • Approximation Algorithms
  • Iterated Rounding

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Abstract

We provide an algorithm giving a 140/41 (< 3.415)-approximation for Coflow Scheduling and a 4.36-approximation for Coflow Scheduling with release dates. This improves upon the best known 4- and respectively 5-approximations and addresses an open question posed by Agarwal, Rajakrishnan, Narayan, Agarwal, Shmoys, and Vahdat [Agarwal et al., 2018], Fukunaga [Fukunaga, 2022], and others. We additionally show that in an asymptotic setting, the algorithm achieves a (2+ε)-approximation, which is essentially optimal under ℙ ≠ NP. The improvements are achieved using a novel edge allocation scheme using iterated LP rounding together with a framework which enables establishing strong bounds for combinations of several edge allocation algorithms.

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Lars Rohwedder and Leander Schnaars. 3.415-Approximation for Coflow Scheduling via Iterated Rounding. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 128:1-128:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.128

Author Details

Lars Rohwedder
  • University of Southern Denmark, Odense, Denmark
Leander Schnaars
  • Technical University of Munich, Germany

Funding

  • Rohwedder, Lars: Supported by Dutch Research Council (NWO) project "The Twilight Zone of Efficiency: Optimality of Quasi-Polynomial Time Algorithms" [grant number OCEN.W.21.268].
  • Schnaars, Leander: Supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - GRK 2201/2 - Projektnummer 277991500.

References

  1. Saksham Agarwal, Shijin Rajakrishnan, Akshay Narayan, Rachit Agarwal, David Shmoys, and Amin Vahdat. Sincronia: near-optimal network design for coflows. In Proceedings of SIGCOMM, pages 16-29. ACM, 2018. URL: https://doi.org/10.1145/3230543.3230569.
  2. Saba Ahmadi, Samir Khuller, Manish Purohit, and Sheng Yang. On Scheduling Coflows. In Proceedings of IPCO, volume 10328, pages 13-24. Springer International Publishing, 2017. URL: https://doi.org/10.1007/978-3-319-59250-3_2.
  3. Nikhil Bansal. New Developments in Iterated Rounding. In Proceedings of FSTTCS, volume 29 of LIPIcs, pages 1-10, Dagstuhl, Germany, 2014. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.FSTTCS.2014.1.
  4. József Beck and Tibor Fiala. “integer-making” theorems. Discrete Applied Mathematics, 3(1):1-8, 1981. URL: https://doi.org/10.1016/0166-218x(81)90022-6.
  5. Maurizio Bonuccelli, Inder Gopal, and Chak-Kuen Wong. Incremental time-slot assignment in SS/TDMA satellite systems. IEEE Transactions on Communications, 39(7):1147-1156, 1991. URL: https://doi.org/10.1109/26.87220.
  6. Mosharaf Chowdhury, Yuan Zhong, and Ion Stoica. Efficient coflow scheduling with Varys. In Proceedings of SIGCOMM, pages 443-454. ACM, 2014. URL: https://doi.org/10.1145/2619239.2626315.
  7. Jeffrey Dean and Sanjay Ghemawat. Mapreduce: simplified data processing on large clusters. Communications of the ACM, 51(1):107-113, 2008. URL: https://doi.org/10.1145/1327452.1327492.
  8. Alexander Eckl, Luisa Peter, Maximilian Schiffer, and Susanne Albers. Minimization of Weighted Completion Times in Path-based Coflow Scheduling. arXiv:1911.13085 [cs], 2020. URL: https://doi.org/10.48550/arXiv.1911.13085.
  9. Takuro Fukunaga. Integrality Gap of Time-Indexed Linear Programming Relaxation for Coflow Scheduling. In Proceedings of APPROX/RANDOM, volume 245 of LIPIcs, pages 36:1-36:13, Dagstuhl, Germany, 2022. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2022.36.
  10. Naveen Garg, Amit Kumar, and Vinayaka Pandit. Order Scheduling Models: Hardness and Algorithms. In Proceedings of FSTTCS, volume 4855, pages 96-107. Springer Berlin Heidelberg, 2007. URL: https://doi.org/10.1007/978-3-540-77050-3_8.
  11. Runxin Guo, Yi Zhao, Quan Zou, Xiaodong Fang, and Shaoliang Peng. Bioinformatics applications on apache spark. GigaScience, 2018. URL: https://doi.org/10.1093/gigascience/giy098.
  12. Anand Gupta, Hardeo Kumar Thakur, Ritvik Shrivastava, Pulkit Kumar, and Sreyashi Nag. A big data analysis framework using apache spark and deep learning. In Proceedings of ICDMW, pages 9-16. IEEE, 2017. URL: https://doi.org/10.1109/icdmw.2017.9.
  13. Pankaj Gupta. Scheduling in input queued switches: A survey. Technical document, Stanford University, 1996. Google Scholar
  14. Sungjin Im, Benjamin Moseley, Kirk Pruhs, and Manish Purohit. Matroid Coflow Scheduling. In Proceedings of ICALP, volume 132 of LIPIcs, pages 145:1-145:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL: https://doi.org/10.4230/LIPIcs.ICALP.2019.145.
  15. Sungjin Im and Manish Purohit. A tight approximation for co-flow scheduling for minimizing total weighted completion time, 2018. URL: https://arxiv.org/abs/1707.04331.
  16. Hamidreza Jahanjou, Erez Kantor, and Rajmohan Rajaraman. Asymptotically Optimal Approximation Algorithms for Coflow Scheduling. In Proceedings of SPAA. ACM, 2017. URL: https://doi.org/10.1145/3087556.3087567.
  17. Samir Khuller, Jingling Li, Pascal Sturmfels, Kevin Sun, and Prayaag Venkat. Select and permute: An improved online framework for scheduling to minimize weighted completion time. Theoretical Computer Science, 795:420-431, 2019. URL: https://doi.org/10.1016/j.tcs.2019.07.026.
  18. Dénes König. Über graphen und ihre anwendung auf determinantentheorie und mengenlehre. Mathematische Annalen, 77:453-465, 1916. URL: https://doi.org/10.1007/BF01456961.
  19. Joseph Y.-T. Leung, Haibing Li, and Michael Pinedo. Scheduling orders for multiple product types to minimize total weighted completion time. Discrete Applied Mathematics, 155(8):945-970, 2007. URL: https://doi.org/10.1016/j.dam.2006.09.012.
  20. Monaldo Mastrolilli, Maurice Queyranne, Andreas S. Schulz, Ola Svensson, and Nelson A. Uhan. Minimizing the sum of weighted completion times in a concurrent open shop. Operations Research Letters, 38(5):390-395, 2010. URL: https://doi.org/10.1016/j.orl.2010.04.011.
  21. Ali Mostafaeipour, Amir Jahangard Rafsanjani, Mohammad Ahmadi, and Joshuva Arockia Dhanraj. Investigating the performance of hadoop and spark platforms on machine learning algorithms. The Journal of Supercomputing, 77(2):1273-1300, 2020. URL: https://doi.org/10.1007/s11227-020-03328-5.
  22. Zhen Qiu, Cliff Stein, and Yuan Zhong. Minimizing the total weighted completion time of coflows in datacenter networks. In Proceedings of SPAA, pages 294-303. ACM, 2015. URL: https://doi.org/10.1145/2755573.2755592.
  23. Sushant Sachdeva and Rishi Saket. Optimal inapproximability for scheduling problems via structural hardness for hypergraph vertex cover. In 2013 IEEE Conference on Computational Complexity, pages 219-229. IEEE, 2013. URL: https://doi.org/10.1109/ccc.2013.30.
  24. Alexander Schrijver. Theory of linear and integer programming. John Wiley & Sons, Inc., USA, 1986. Google Scholar
  25. Konstantin Shvachko, Hairong Kuang, Sanjay Radia, and Robert Chansler. The hadoop distributed file system. In Proceedings of IEEE MSST, pages 1-10, 2010. URL: https://doi.org/10.1109/MSST.2010.5496972.
  26. Éva Tardos. A strongly polynomial algorithm to solve combinatorial linear programs. Operations Research, 34(2):250-256, 1986. URL: https://doi.org/10.1287/opre.34.2.250.
  27. Matei Zaharia, Mosharaf Chowdhury, Michael J. Franklin, Scott Shenker, and Ion Stoica. Spark: cluster computing with working sets. In Proceedings of the 2nd USENIX Conference on Hot Topics in Cloud Computing, page 10, USA, 2010. USENIX Association. URL: https://www.usenix.org/conference/hotcloud-10/spark-cluster-computing-working-sets.
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