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Integrality Gap of Time-Indexed Linear Programming Relaxation for Coflow Scheduling

Author Takuro Fukunaga

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Author Details

Takuro Fukunaga
  • Faculty of Science and Engineering, Chuo University, Tokyo, Japan

Funding

  • Fukunaga, Takuro: JSPS KAKENHI Grant Numbers JP20H05965, JP21K11759, and JP21H03397, Japan.

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Takuro Fukunaga. Integrality Gap of Time-Indexed Linear Programming Relaxation for Coflow Scheduling. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 36:1-36:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2022.36

Abstract

Coflow is a set of related parallel data flows in a network. The goal of the coflow scheduling is to process all the demands of the given coflows while minimizing the weighted completion time. It is known that the coflow scheduling problem admits several polynomial-time 5-approximation algorithms that compute solutions by rounding linear programming (LP) relaxations of the problem. In this paper, we investigate the time-indexed LP relaxation for coflow scheduling. We show that the integrality gap of the time-indexed LP relaxation is at most 4. We also show that yet another polynomial-time 5-approximation algorithm can be obtained by rounding the solutions to the time-indexed LP relaxation.

Subject Classification

ACM Subject Classification
  • Theory of computation → Scheduling algorithms
Keywords
  • coflow scheduling
  • hypergraph matching
  • approximation algorithm

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References

  1. Ron Aharoni and Penny Haxell. Hall’s theorem for hypergraphs. Journal of Graph Theory, 35(2):83-88, 2000. Google Scholar
  2. Saba Ahmadi, Samir Khuller, Manish Purohit, and Sheng Yang. On scheduling coflows. Algorithmica, 82(12):3604-3629, 2020. Google Scholar
  3. Chidambaram Annamalai. Finding perfect matchings in bipartite hypergraphs. Combinatorica, 38(6):1285-1307, 2018. Google Scholar
  4. Chidambaram Annamalai, Christos Kalaitzis, and Ola Svensson. Combinatorial algorithm for restricted max-min fair allocation. ACM Transactions on Algorithms, 13(3):37:1-37:28, 2017. Google Scholar
  5. Arash Asadpour, Uriel Feige, and Amin Saberi. Santa Claus meets hypergraph matchings. ACM Transactions on Algorithms, 8(3):24:1-24:9, 2012. Google Scholar
  6. Mosharaf Chowdhury, Samir Khuller, Manish Purohit, Sheng Yang, and Jie You. Near optimal coflow scheduling in networks. In Christian Scheideler and Petra Berenbrink, editors, The 31st ACM on Symposium on Parallelism in Algorithms and Architectures, SPAA 2019, Phoenix, AZ, USA, June 22-24, 2019, pages 123-134. ACM, 2019. Google Scholar
  7. Mosharaf Chowdhury and Ion Stoica. Coflow: a networking abstraction for cluster applications. In Srikanth Kandula, Jitendra Padhye, Emin Gün Sirer, and Ramesh Govindan, editors, 11th ACM Workshop on Hot Topics in Networks, HotNets-XI, Redmond, WA, USA - October 29 - 30, 2012, pages 31-36. ACM, 2012. Google Scholar
  8. Mosharaf Chowdhury and Ion Stoica. Efficient coflow scheduling without prior knowledge. In Steve Uhlig, Olaf Maennel, Brad Karp, and Jitendra Padhye, editors, Proceedings of the 2015 ACM Conference on Special Interest Group on Data Communication, SIGCOMM 2015, London, United Kingdom, August 17-21, 2015, pages 393-406. ACM, 2015. Google Scholar
  9. Mosharaf Chowdhury, Yuan Zhong, and Ion Stoica. Efficient coflow scheduling with Varys. In Fabián E. Bustamante, Y. Charlie Hu, Arvind Krishnamurthy, and Sylvia Ratnasamy, editors, ACM SIGCOMM 2014 Conference, SIGCOMM'14, Chicago, IL, USA, August 17-22, 2014, pages 443-454. ACM, 2014. Google Scholar
  10. Alessandra Graf and Penny Haxell. Finding independent transversals efficiently. Combinatorics, Probability & Computing, 29(5):780-806, 2020. Google Scholar
  11. Penny E. Haxell. A condition for matchability in hypergraphs. Graphs and Combinatorics, 11(3):245-248, 1995. Google Scholar
  12. Sungjin Im and Shi Li. Better unrelated machine scheduling for weighted completion time via random offsets from non-uniform distributions. In Irit Dinur, editor, IEEE 57th Annual Symposium on Foundations of Computer Science, FOCS 2016, 9-11 October 2016, Hyatt Regency, New Brunswick, New Jersey, USA, pages 138-147. IEEE Computer Society, 2016. Google Scholar
  13. Sungjin Im, Benjamin Moseley, Kirk Pruhs, and Manish Purohit. Matroid coflow scheduling. In Christel Baier, Ioannis Chatzigiannakis, Paola Flocchini, and Stefano Leonardi, editors, 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019, July 9-12, 2019, Patras, Greece, volume 132 of LIPIcs, pages 145:1-145:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. Google Scholar
  14. Hamidreza Jahanjou, Erez Kantor, and Rajmohan Rajaraman. Asymptotically optimal approximation algorithms for coflow scheduling. In Christian Scheideler and Mohammad Taghi Hajiaghayi, editors, Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2017, Washington DC, USA, July 24-26, 2017, pages 45-54. ACM, 2017. Google Scholar
  15. Richard M. Karp. Reducibility among combinatorial problems. In Raymond E. Miller and James W. Thatcher, editors, Proceedings of a symposium on the Complexity of Computer Computations, held March 20-22, 1972, at the IBM Thomas J. Watson Research Center, Yorktown Heights, New York, USA, The IBM Research Symposia Series, pages 85-103. Plenum Press, New York, 1972. Google Scholar
  16. Sushant Sachdeva and Rishi Saket. Optimal inapproximability for scheduling problems via structural hardness for hypergraph vertex cover. In Proceedings of the 28th Conference on Computational Complexity, CCC 2013, K.lo Alto, California, USA, 5-7 June, 2013, pages 219-229. IEEE Computer Society, 2013. Google Scholar
  17. Mehrnoosh Shafiee and Javad Ghaderi. An improved bound for minimizing the total weighted completion time of coflows in datacenters. IEEE/ACM Transactions on Networking, 26(4):1674-1687, 2018. Google Scholar
  18. Yue Zeng, Baoliu Ye, Bin Tang, Songtao Guo, and Zhihao Qu. Scheduling coflows of multi-stage jobs under network resource constraints. Computer Networks, 184:107686, 2021. Google Scholar
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