Online Scheduling on a CPU-GPU Cluster

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.

[1]  Jirí Sgall,et al.  A Lower Bound on Deterministic Online Algorithms for Scheduling on Related Machines Without Preemption , 2011, Theory of Computing Systems.

[2]  Amos Fiat,et al.  On-line routing of virtual circuits with applications to load balancing and machine scheduling , 1997, JACM.

[3]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[4]  Assaf Schuster,et al.  Processing data streams with hard real-time constraints on heterogeneous systems , 2011, ICS '11.

[5]  Sartaj Sahni,et al.  Bounds for List Schedules on Uniform Processors , 1980, SIAM J. Comput..

[6]  Marek Karpinski,et al.  On-Line Load Balancing for Related Machines , 1997, J. Algorithms.

[7]  Klaus Jansen,et al.  Improved approximation schemes for scheduling unrelated parallel machines , 1999, STOC '99.

[8]  T. C. Edwin Cheng,et al.  A new algorithm for online uniform-machine scheduling to minimize the makespan , 2006, Inf. Process. Lett..

[9]  Jan Karel Lenstra,et al.  Approximation algorithms for scheduling unrelated parallel machines , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[10]  Hyesoon Kim,et al.  Qilin: Exploiting parallelism on heterogeneous multiprocessors with adaptive mapping , 2009, 2009 42nd Annual IEEE/ACM International Symposium on Microarchitecture (MICRO).

[11]  Hans Kellerer,et al.  Scheduling parallel dedicated machines with the speeding‐up resource , 2003 .

[12]  Lin Chen,et al.  Scheduling on two identical machines with a speed-up resource , 2011, Inf. Process. Lett..

[13]  Ronald L. Graham,et al.  Bounds for certain multiprocessing anomalies , 1966 .

[15]  Oscar H. Ibarra,et al.  Bounds for LPT Schedules on Uniform Processors , 1977, SIAM J. Comput..

[16]  David B. Shmoys,et al.  A Polynomial Approximation Scheme for Scheduling on Uniform Processors: Using the Dual Approximation Approach , 1988, SIAM J. Comput..

[17]  Alexander Grigoriev,et al.  Machine scheduling with resource dependent processing times , 2007, Math. Program..

[18]  Rongheng Li,et al.  An On-Line Algorithm for Some Uniform Processor Scheduling , 1995, SIAM J. Comput..

[19]  Yossi Azar,et al.  The competitiveness of on-line assignments , 1992, SODA '92.

[20]  Kai Lu,et al.  Adaptive Optimization for Petascale Heterogeneous CPU/GPU Computing , 2010, 2010 IEEE International Conference on Cluster Computing.