Optimal Time-Critical Scheduling via Resource Augmentation

AbstractWe consider two fundamental problems in dynamic scheduling: scheduling to meet deadlines in a preemptive multiprocessor setting, and scheduling to provide good response time in a number of scheduling environments. When viewed from the perspective of traditional worst-case analysis, no good on-line algorithms exist for these problems, and for some variants no good off-line algorithms exist unless P = NP .We study these problems using a relaxed notion of competitive analysis, introduced by Kalyanasundaram and Pruhs, in which the on-line algorithm is allowed more resources than the optimal off-line algorithm to which it is compared. Using this approach, we establish that several well-known on-line algorithms, that have poor performance from an absolute worst-case perspective, are optimal for the problems in question when allowed moderately more resources. For optimization of average flow time, these are the first results of any sort, for any NP -hard version of the problem, that indicate that it might be possible to design good approximation algorithms.

[1]  Aloysius K. Mok,et al.  Multiprocessor On-Line Scheduling of Hard-Real-Time Tasks , 1989, IEEE Trans. Software Eng..

[2]  Evripidis Bampis,et al.  Approximation schemes for minimizing average weighted completion time with release dates , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[3]  Eugene L. Lawler,et al.  Preemptive scheduling of uniform machines subject to release dates : (preprint) , 1979 .

[4]  Jeff Edmonds,et al.  Scheduling in the dark , 1999, STOC '99.

[5]  David B. Shmoys,et al.  Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms , 1997, Math. Oper. Res..

[6]  Michel X. Goemans,et al.  A Supermodular Relaxation for Scheduling with Release Dates , 1996, IPCO.

[7]  Michael A. Bender,et al.  Flow and stretch metrics for scheduling continuous job streams , 1998, SODA '98.

[8]  Bala Kalyanasundaram,et al.  Maximizing Job Completions Online , 1998, ESA.

[9]  David B. Shmoys,et al.  Scheduling to minimize average completion time: off-line and on-line algorithms , 1996, SODA '96.

[10]  Cynthia A. Phillips,et al.  Scheduling Jobs that Arrive Over Time (Extended Abstract) , 1995, WADS.

[11]  Michel X. Goemans,et al.  Improved approximation algorthims for scheduling with release dates , 1997, SODA '97.

[12]  V. Rich.  Personal communication , 1989, Nature.

[13]  Han Hoogeveen,et al.  Optimal On-Line Algorithms for Single-Machine Scheduling , 1996, IPCO.

[14]  Tak Wah Lam,et al.  Trade-offs between speed and processor in hard-deadline scheduling , 1999, SODA '99.

[15]  Bala Kalyanasundaram,et al.  Eliminating migration in multi-processor scheduling , 1999, SODA '99.

[16]  Cynthia A. Phillips,et al.  Minimizing average completion time in the presence of release dates , 1998, Math. Program..

[17]  Rajeev Motwani,et al.  Non-clairvoyant scheduling , 1994, SODA '93.

[18]  Sanjoy K. Baruah,et al.  Scheduling for Overload in Real-Time Systems , 1997, IEEE Trans. Computers.

[19]  Michael H. Goldwasser.  Patience is a Virtue: The Effect of Slack on Competitiveness for Admission Control , 1999, SODA '99.

[20]  Cynthia A. Phillips,et al.  Improved Scheduling Algorithms for Minsum Criteria , 1996, ICALP.

[21]  David P. Williamson,et al.  Scheduling Parallel Machines On-Line , 1995, SIAM J. Comput..

[22]  Sartaj Sahni,et al.  Nearly On Line Scheduling of a Uniform Processor System with Release Times , 1979, SIAM J. Comput..

[23]  Stefano Leonardi,et al.  Approximating total flow time on parallel machines , 1997, STOC '97.

[24]  Dennis Shasha,et al.  MOCA: A Multiprocessor On-Line Competitive Algorithm for Real-Time System Scheduling , 1994, Theor. Comput. Sci..

[25]  Gerhard J. Woeginger,et al.  Approximability and Nonapproximability Results for Minimizing Total Flow Time on a Single Machine , 1999, SIAM J. Comput..

[26]  Dan Gusfield,et al.  Bounds for Naive Multiple Machine Scheduling with Release Times and Deadlines , 1984, J. Algorithms.

[27]  Michael L. Dertouzos,et al.  Control Robotics: The Procedural Control of Physical Processes , 1974, IFIP Congress.

[28]  David B. Shmoys,et al.  Improved approximation algorithms for minsum criteria , 1996 .