Abstract
We consider the online scheduling problem in a CPU-GPU cluster. In this problem there are two sets of processors, the CPU processors and GPU processors. Each job has two distinct processing times, one for the CPU processor and the other for the GPU processor. Once a job is released, a decision should be made immediately about which processor it should be assigned to. The goal is to minimize the makespan, i.e., the largest completion time among all the processors. Such a problem could be seen as an intermediate model between the scheduling problem on identical machines and unrelated machines. We provide a 3.85-competitive online algorithm for this problem and show that no online algorithm exists with competitive ratio strictly less than 2. We also consider two special cases of this problem, the balanced case where the number of CPU processors equals to that of GPU processors, and the one-sided case where there is only one CPU or GPU processor. We provide a \((1+\sqrt{3})\)-competitive algorithm for the balanced case, and a 3-competitive algorithm for the one-sided case.
Research was supported by in part by NSFC(11071215,11271325).
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References
Aspnes, J., Azar, Y., Fiat, A., Plotkin, S., Waarts, O.: On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the ACM 44(3), 486–504 (1997)
Azar, Y., Naor, J.S., Rom, R.: The competitiveness of on-line assignments. In: Proc. 3rd Symp. on Discrete Algorithms (SODA), pp. 203–210 (1992)
Berman, P., Charikar, M., Karpinski, M.: On-line load balancing for related machines. Journal of Algorithms 35, 108–121 (2000)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press (1998)
Cheng, T., Ng, C., Kotov, V.: A new algorithm for online uniform-machine scheduling to minimize the makespan. Information Processing Letters 99(3), 102–105 (2006)
Cho, Y., Sahni, S.: Bounds for list schedules on uniform processors. SIAM Journal on Computing 9(1), 91–103 (1980)
Ebenlendr, T., Sgall, J.: A lower bound on deterministic online algorithms for scheduling on related machines without preemption. In: Solis-Oba, R., Persiano, G. (eds.) WAOA 2011. LNCS, vol. 7164, pp. 102–108. Springer, Heidelberg (2012)
Graham, R.: Bounds for certain multiprocessing anomalies. Bell System Technical J. 45, 1563–1581 (1966)
Grigoriev, A., Sviridenko, M., Uetz, M.: Machine scheduling with resource dependent processing times. Mathematical Programming 110(1), 209–228 (2007)
Hochbaum, D., Shmoys, D.: A polynomial approximation scheme for scheduling on uniform processors: Using the dual approximation approach. SIAM Journal on Computing 17(3), 539–551 (1988)
Jansen, K., Porkolab, L.: Improved approximation schemes for scheduling unrelated parallel machines. In: Proceedings of the 31st Annual ACM Symposium on Theory of Computing (STOC), pp. 408–417 (1999)
Kellerer, H., Strusevich, V.: Scheduling parallel dedicated machines with the speeding-up resource. Naval Research Logistics 55(5), 377–389 (2008)
Kokash, N.: An efficient heuristic for online scheduling in a system with one fast machine. M.S. thesis, Belorussian State University (2004)
Lenstra, J., Shmoys, D., Tardos, E.: Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programing 46(1), 259–271 (1990)
Li, R., Shi, L.: An on-line algorithm for some uniform processor scheduling. SIAM Journal on Computing 27(2), 414–422 (1998)
Luk, C., Hong, S., Kim, H.: Qilin: exploiting parallelism on heterogeneous multiprocessors with adaptive mapping. In: Proceedings of the 42nd Annual IEEE/ACM International Symposium on Microarchitecture (MICRO), pp. 45–55 (2009)
Verner, U., Schuster, A., Silberstein, M.: Processing data streams with hard real-time constraints on heterogeneous systems. In: Proceedings of the International Conference on Supercomputing (ICS), pp. 120–129 (2011)
Xu, H., Chen, L., Ye, D., Zhang, G.: Scheduling on two identical machines with a speed-up resource. Information Processing Letters 111, 831–835 (2011)
Yang, C., Wang, F., Du, Y., Chen, J., Liu, J., Yi, H., Lu, K.: Adaptive optimization for petascale heterogeneous cpu/gpu computing. In: Proceedings of the IEEE International Conference on Cluster Computing (CLUSTER), pp. 19–28 (2010)
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Chen, L., Ye, D., Zhang, G. (2013). Online Scheduling on a CPU-GPU Cluster. In: Chan, TH.H., Lau, L.C., Trevisan, L. (eds) Theory and Applications of Models of Computation. TAMC 2013. Lecture Notes in Computer Science, vol 7876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38236-9_1
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DOI: https://doi.org/10.1007/978-3-642-38236-9_1
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