Advertisement

On Scheduling Coflows

(Extended Abstract)
  • Saba Ahmadi
  • Samir Khuller
  • Manish Purohit
  • Sheng YangEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10328)

Abstract

Applications designed for data-parallel computation frameworks such as MapReduce usually alternate between computation and communication stages. Coflow scheduling is a recent popular networking abstraction introduced to capture such application-level communication patterns in datacenters. In this framework, a datacenter is modeled as a single non-blocking switch with m input ports and m output ports. A coflow j is a collection of flow demands \(\{d^j_{io}\}_{i \in m, o \in m}\) that is said to be complete once all of its requisite flows have been scheduled.

We consider the offline coflow scheduling problem with and without release times to minimize the total weighted completion time. Coflow scheduling generalizes the well studied concurrent open shop scheduling problem and is thus NP-hard. Qiu, Stein and Zhong [15] obtain the first constant approximation algorithms for this problem via LP rounding and give a deterministic \(\frac{67}{3}\)-approximation and a randomized \((9 + \frac{16\sqrt{2}}{3}) \approx 16.54\)-approximation algorithm. In this paper, we give a combinatorial algorithm that yields a deterministic 5-approximation algorithm with release times, and a deterministic 4-approximation for the case without release time.

Keywords

Coflow scheduling Concurrent open shop 

References

  1. 1.
  2. 2.
  3. 3.
    Bansal, N., Khot, S.: Inapproximability of hypergraph vertex cover and applications to scheduling problems. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6198, pp. 250–261. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-14165-2_22 CrossRefGoogle Scholar
  4. 4.
    Chen, Z.-L., Hall, N.G.: Supply chain scheduling: conflict and cooperation in assembly systems. Oper. Res. 55(6), 1072–1089 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Chowdhury, M., Stoica, I. Coflow: a networking abstraction for cluster applications. In: ACM Workshop on Hot Topics in Networks, pp. 31–36. ACM (2012)Google Scholar
  6. 6.
    Chowdhury, M., Stoica, I.: Efficient coflow scheduling without prior knowledge. In: SIGCOMM, pp. 393–406. ACM (2015)Google Scholar
  7. 7.
    Chowdhury, M., Zhong, Y., Stoica, I.: Efficient coflow scheduling with varys. In: SIGCOMM, SIGCOMM 2014, pp. 443–454. ACM, New York (2014)Google Scholar
  8. 8.
    Davis, J.M., Gandhi, R., Kothari, V.H.: Combinatorial algorithms for minimizing the weighted sum of completion times on a single machine. Oper. Res. Lett. 41(2), 121–125 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Dean, J., Ghemawat, S.: Mapreduce: simplified data processing on large clusters. Commun. ACM 51(1), 107–113 (2008)CrossRefGoogle Scholar
  10. 10.
    Garg, N., Kumar, A., Pandit, V.: Order scheduling models: hardness and algorithms. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 96–107. Springer, Heidelberg (2007). doi: 10.1007/978-3-540-77050-3_8 CrossRefGoogle Scholar
  11. 11.
    Khuller, S., Li, J., Sturmfels, P., Sun, K., Venkat, P.: Select, permute: an improved online framework for scheduling to minimize weighted completion time (2016) (Submitted)Google Scholar
  12. 12.
    Leung, J.Y.-T., Li, H., Pinedo, M.: Scheduling orders for multiple product types to minimize total weighted completion time. Discrete Appl. Math. 155(8), 945–970 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Luo, S., Yu, H., Zhao, Y., Wang, S., Yu, S., Li, L.: Towards practical, near-optimal coflow scheduling for data center networks. IEEE Trans. Parallel Distrib. Syst. PP(99), 1 (2016)Google Scholar
  14. 14.
    Mastrolilli, M., Queyranne, M., Schulz, A.S., Svensson, O., Uhan, N.A.: Minimizing the sum of weighted completion times in a concurrent open shop. Oper. Res. Lett. 38(5), 390–395 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Qiu, Z., Stein, C., Zhong, Y.: Minimizing the total weighted completion time of coflows in datacenter networks. In: SPAA 2015, pp. 294–303. ACM, New York (2015)Google Scholar
  16. 16.
    Queyranne, M.: Structure of a simple scheduling polyhedron. Math. Program. 58(1–3), 263–285 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Sachdeva, S., Saket, R.: Optimal inapproximability for scheduling problems via structural hardness for hypergraph vertex cover. In: IEEE Conference on Computational Complexity, pp. 219–229. IEEE (2013)Google Scholar
  18. 18.
    Wang, G., Cheng, T.E.: Customer order scheduling to minimize total weighted completion time. Omega 35(5), 623–626 (2007)CrossRefGoogle Scholar
  19. 19.
    Zaharia, M., Chowdhury, M., Franklin, M.J., Shenker, S., Stoica, I.: Spark: cluster computing with working sets. HotCloud 10, 10 (2010)Google Scholar
  20. 20.
    Zhao, Y., Chen, K., Bai, W., Yu, M., Tian, C., Geng, Y., Zhang, Y., Li, D., Wang, S. Rapier: integrating routing and scheduling for coflow-aware data center networks. In: INFOCOM, pp. 424–432. IEEE (2015)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Saba Ahmadi
    • 1
  • Samir Khuller
    • 1
  • Manish Purohit
    • 2
  • Sheng Yang
    • 1
    Email author
  1. 1.University of MarylandCollege ParkUSA
  2. 2.GoogleMountain ViewUSA

Personalised recommendations