Scheduling Independent Jobs on Partitionable Hypercubes

We consider the problem of scheduling k independent jobs on an n-dimensional hypercube system to minimize finishing time, where each job Ji is associated with a dimension di and a processing time ti, meaning that Ji requires a di-dimensional subcube for ti units of time. This problem is NP-hard if no preemption is allowed. We propose a simple heuristic called LDLPT (largest dimension longest processing time) and analyze its worst-case performance; the ratio of the heuristic to the optimal finishing time does not exceed 2 − 12n−1.

[1]  Ten-Hwang Lai,et al.  Preemptive Scheduling of Independent Jobs on a Hypercube , 1988, Inf. Process. Lett..

[2]  John C. Peterson,et al.  The Mark III Hypercube-Ensemble Concurrent Computer , 1985, International Conference on Parallel Processing.

[3]  John P. Hayes,et al.  Architecture of a Hypercube Supercomputer , 1986, ICPP.

[4]  Yahui Zhu,et al.  An O(n log n) Feasibility Algorithm for Preemptive Scheduling of n Independent Jobs on a Hypercube , 1990, Inf. Process. Lett..

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

[6]  Ronald L. Graham,et al.  Bounds on Multiprocessing Timing Anomalies , 1969, SIAM Journal of Applied Mathematics.

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

[8]  Jeffrey D. Ullman,et al.  NP-Complete Scheduling Problems , 1975, J. Comput. Syst. Sci..

[9]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[10]  Ming-Syan Chen,et al.  Processor Allocation in an N-Cube Multiprocessor Using Gray Codes , 1987, IEEE Transactions on Computers.

[11]  Chita R. Das,et al.  A Processor Allocation Scheme for Hypercube Computers , 1989, ICPP.

[12]  Ten-Hwang Lai,et al.  Constructing Parallel Paths Betweesn Two Subcubes , 1992, IEEE Trans. Computers.

[13]  J. P. Hayes,et al.  On allocating subcubes in a hypercube multiprocessor , 1988, C3P.

[14]  Kam-Hoi Cheng,et al.  Job Scheduling in Partitionable Mesh Connected Systems , 1989, ICPP.

[15]  Ming-Syan Chen,et al.  Subcube Allocation and Task Migration in Hypercube Multiprocessors , 1990, IEEE Trans. Computers.