Non-Clairvoyant Scheduling for Mean Slowdown

We consider the problem of scheduling jobs online non-clairvoyantly, that is, when the job sizes are not known. Our focus is on minimizing mean slowdown, deened as the ratio of response time to the size of the job. We rst show that no (deterministic or randomized) algorithm can achieve a competitive ratio of (n), where n is the number of jobs. Resource augmentation is the concept of allowing the online algorithm a speed-up to make up for its non-clairvoyance, since the competitive ratio is obtained by comparing against an optimal ooine, clairvoyant algorithm. We show that our lower bound continues to hold even with resource augmentation. Finally, we consider the case when the ratio of job sizes (denoted B) is bounded. In this case, we show that any non-clairvoyant algorithm needs at least (log B) speed up to be constant competitive. We provide an algorithm which is O(log 2 B) competitive when the speed up is O(logB). In the special case when all the jobs arrive at the same time we provide an algorithm which is constant competitive and uses a O(logB) speed up.

[1]  David J. DeWitt,et al.  Dynamic Memory Allocation for Multiple-Query Workloads , 1993, VLDB.

[2]  S HochbaDorit.  Approximation Algorithms for NP-Hard Problems , 1997 .

[3]  Bala Kalyanasundaram,et al.  Speed is as powerful as clairvoyance , 2000, JACM.

[4]  D. Atkin.  OR scheduling algorithms. , 2000, Anesthesiology.

[5]  Eugene L. Lawler,et al.  Sequencing and scheduling: algorithms and complexity , 1989 .

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

[7]  Sanjeev Khanna,et al.  Algorithms for minimizing weighted flow time , 2001, STOC '01.

[8]  Andrew Chi-Chih Yao,et al.  Probabilistic computations: Toward a unified measure of complexity , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[9]  Piotr Berman,et al.  Speed is More Powerful than Clairvoyance , 1998, Nord. J. Comput..

[10]  Rajmohan Rajaraman,et al.  Online scheduling to minimize average stretch , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[11]  Mor Harchol-Balter,et al.  On Choosing a Task Assignment Policy for a Distributed Server System , 1998, Computer Performance Evaluation.

[12]  Ray Jain,et al.  The art of computer systems performance analysis - techniques for experimental design, measurement, simulation, and modeling , 1991, Wiley professional computing.

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