Extra unit-speed machines are almost as powerful as speedy machines for flow time scheduling

We study online scheduling of jobs to minimize the flow time and stretch on parallel machines. We consider algorithms that are given extra resources so as to compensate for the lack of future information. Recent results show that a modest increase in machine speed can provide very competitive performance; in particular, using O(1) times faster machines, the algorithm SRPT (shortest remaining processing time) is 1-competitive for both flow time [C. A. Phillips et al., in Proceedings of STOC, ACM, New York, 1997, pp. 140-149] and stretch [W. T. Chan et al., in Proceedings of MFCS, Springer-Verlag, Berlin, 2005, pp. 236-247] and HDF (highest density first) is O(1)-competitive for weighted flow time [L. Becchetti et al., in Proceedings of RANDOM-APPROX, Springer-Verlag, Berlin, 2001, pp. 36-47]. Using extra unit-speed machines instead of faster machines to achieve competitive performance is more challenging, as a faster machine can speed up a job but extra unit-speed machines cannot. This paper gives a nontrivial relationship between the extra-speed and extra-machine analyses. It shows that competitive results via faster machines can be transformed to similar results via extra machines, hence giving the first algorithms that, using O(1) times unit-speed machines, are 1-competitive for flow time and stretch and O(1)-competitive for weighted flow time. © 2008 Society for Industrial and Applied Mathematics.published_or_final_versio

New resource augmentation analysis of the total stretch of SRPT and SJF in multiprocessor scheduling

LNCS v. 3618 entitled: Mathematical Foundations of Computer Science 2005: 30th International Symposium, MFCS 2005, Gdansk, Poland, August29-September 2. 2005, ProceedingsThis paper studies online job scheduling on multiprocessors and, in particular, investigates the algorithms SRPT and SJF for minimizing total stretch, where the stretch of a job is its flow time (response time) divided by its processing time. SRPT is perhaps the most well-studied algorithm for minimizing total flow time or stretch. This paper gives the first resource augmentation analysis of the total stretch of SRPT, showing that it is indeed O(1)-speed 1-competitive. This paper also gives a simple lower bound result that SRPT is not s-speed 1-competitive for any s < 1.5. This paper also makes contribution to the analysis of SJF. Extending the work of [4], we are able to show that SJF is O(1)-speed 1-competitive for minimizing total stretch. More interestingly, we find that the competitiveness of SJF can be reduced arbitrarily by increasing the processor speed (precisely, SJF is O(s)-speed (1/s)-competitive for any s ≥ 1). We conjecture that SRPT also admits a similar result. © Springer-Verlag Berlin Heidelberg 2005.link_to_subscribed_fulltex

New resource augmentation analysis of the total stretch of SRPT and SJF in multiprocessor scheduling

This paper studies online job scheduling on multiprocessors and, in particular, investigates the algorithms Shortest Remaining Processing Time First (SRPT) and Shortest Job First (SJF) for minimizing total stretch, where the stretch of a job is its flow time (response time) divided by its processing time. SRPT is perhaps the most well-studied algorithm for minimizing total flow time or stretch. This paper gives the first resource augmentation analysis of the total stretch of SRPT, showing that it is indeed O (1)-speed 1-competitive. This paper also gives a simple lower bound result showing that SRPT is not s-speed 1-competitive for any s < 1.5. This paper also makes contribution to the analysis of SJF. Extending the work of [L. Becchetti, S. Leonardi, A. Marchetti-Spaccamela, K. Pruhs, Online weighted flow time and deadline scheduling, in: RANDOM-APPROX, 2001, pp. 36-47], we are able to show that SJF is O (1)-speed 1-competitive for minimizing total stretch. More interestingly, we find that the competitiveness of SJF can be reduced arbitrarily by increasing the processor speed (precisely, SJF is O (s)-speed (1 / s)-competitive for any s ≥ 1). We conjecture that SRPT also admits a similar result. © 2006 Elsevier B.V. All rights reserved.link_to_subscribed_fulltex

New Resource Augmentation Analysis of the Total Stretch of SRPT and SJF in Multiprocessor Scheduling

LNCS v. 3618 entitled: Mathematical Foundations of Computer Science 2005: 30th International Symposium, MFCS 2005, Gdansk, Poland, August29-September 2. 2005, ProceedingsThis paper studies online job scheduling on multiprocessors and, in particular, investigates the algorithms SRPT and SJF for minimizing total stretch, where the stretch of a job is its flow time (response time) divided by its processing time. SRPT is perhaps the most well-studied algorithm for minimizing total flow time or stretch. This paper gives the first resource augmentation analysis of the total stretch of SRPT, showing that it is indeed O(1)-speed 1-competitive. This paper also gives a simple lower bound result that SRPT is not s-speed 1-competitive for any s < 1.5. This paper also makes contribution to the analysis of SJF. Extending the work of [4], we are able to show that SJF is O(1)-speed 1-competitive for minimizing total stretch. More interestingly, we find that the competitiveness of SJF can be reduced arbitrarily by increasing the processor speed (precisely, SJF is O(s)-speed (1/s)-competitive for any s ≥ 1). We conjecture that SRPT also admits a similar result. © Springer-Verlag Berlin Heidelberg 2005.link_to_subscribed_fulltex