An overview of some results for reordering buffers Authors Matthias Englert DIMAP and Department of Computer Science University of Warwick Special Issue Paper

First Online: 23 June 2011 DOI :
10.1007/s00450-011-0180-2

Cite this article as: Englert, M. Comput Sci Res Dev (2012) 27: 217. doi:10.1007/s00450-011-0180-2
Abstract Lookahead is a classic concept in the theory of online scheduling. An online algorithm without lookahead has to process tasks as soon as they arrive and without any knowledge about future tasks. With lookahead, this strict assumption is relaxed. There are different variations on the exact type of information provided to the algorithm under lookahead but arguably the most common one is to assume that, at every point in time, the algorithm has knowledge of the attributes of the next k tasks to arrive. This assumption is justified by the fact that, in practice, tasks may not always strictly arrive one-by-one and therefore, a certain number of tasks are always waiting in a queue to be processed.

In recent years, so-called reordering buffers have been studied as a sensible generalization of lookahead. The basic idea is that, in problem settings where the order in which the tasks are processed is not important, we can permit a scheduling algorithm to choose to process any task waiting in the queue. This stands in contrast to lookahead, where the algorithm has knowledge of all the tasks in the queue but still has to process them in the order they arrived. We discuss some of the results for reordering buffers for different scheduling problems.

Keywords Online algorithms Reordering buffers Competitive analysis Survey M. Englert supported by EPSRC grant EP/F043333/1 and DIMAP (the Centre for Discrete Mathematics and its Applications).

References 1.

Albers S (2004) New results on web caching with request reordering. In: Proceedings of the 16th ACM symposium on parallel algorithms and architectures (SPAA), pp 84–92

2.

Alborzi H, Torng E, Uthaisombut P, Wagner S (2001) The

k -client problem. J Algorithms 41(2):115–173

MathSciNet MATH CrossRef 3.

Asahiro Y, Kawahara K, Miyano E (2010) NP-hardness of the sorting buffer problem on the uniform metric. Unpublished manuscript

4.

Aspnes J, Azar Y, Fiat A, Plotkin SA, Waarts O (1997) On-line routing of virtual circuits with applications to load balancing and machine scheduling. J ACM 44(3):486–504

MathSciNet MATH CrossRef 5.

Avigdor-Elgrabli N, Rabani Y (2010) An improved competitive algorithm for reordering buffer management. In: Proceedings of the 21st ACM-SIAM symposium on discrete algorithms (SODA), pp. 13–21

6.

Azar Y, Gamzu I, Rabani Y (October 2008) Personal communication

7.

Azar Y, Naor J, Rom R (1995) The competitiveness of on-line assignments. J Algorithms 18(2):221–237

MathSciNet MATH CrossRef 8.

Berman P, Charikar M, Karpinski M (2000) On-line load balancing for related machines. J Algorithms 35(1):108–121

MathSciNet MATH CrossRef 9.

Chan H-L, Megow N, van Stee R, Sitters R (2010) The sorting buffer problem is NP-hard. CoRR,

arXiv:1009.4355
10.

Chen B, van Vliet A, Woeginger GJ (1995) An optimal algorithm for preemptive on-line scheduling. Oper Res Lett 18(3):127–131

MathSciNet MATH CrossRef 11.

Dósa G, Epstein L (2008) Online scheduling with a buffer on related machines. Journal of Combinatorial Optimization. doi:

10.1007/s10878-008-9200-y
12.

Dósa G, Epstein L (2009) Preemptive online scheduling with reordering. In: Proceedings of the 17th European symposium on algorithms (ESA), pp 456–467

13.

Englert M, Özmen D, Westermann M (2008) The power of reordering for online minimum makespan scheduling. In: Proceedings of the 49th IEEE symposium on foundations of computer science (FOCS), pp 603–612

CrossRef 14.

Englert M, Räcke H, Westermann M (2007) Reordering buffers for general metric spaces. In: Proceedings of the 39th ACM symposium on theory of computing (STOC), pp 556–564

15.

Englert M, Westermann M (2005) Reordering buffer management for non-uniform cost models. In: Proceedings of the 32nd international colloquium on automata, languages and programming (ICALP), pp 627–638

CrossRef 16.

Epstein L, Levin A, van Stee R (2010) Max-min online allocations with a reordering buffer. In: Proceedings of the 37th international colloquium on automata, languages and programming (ICALP), pp 336–347

CrossRef 17.

Fakcharoenphol J, Rao SB, Talwar K (2004) A tight bound on approximating arbitrary metrics by tree metrics. J Comput Syst Sci 69(3):485–497

MathSciNet MATH CrossRef 18.

Feder T, Motwani R, Panigrahy R, Seiden SS, van Stee R, Zhu A (2004) Combining request scheduling with web caching. Theor Comput Sci 324(2–3):201–218

MATH CrossRef 19.

Fleischer R, Wahl M (2000) On-line scheduling revisited. J Sched 3(6):343–353

MathSciNet MATH CrossRef 20.

Gamzu I, Segev D (2007) Improved online algorithms for the sorting buffer problem. In: Proceedings of the 24th symposium on theoretical aspects of computer science (STACS), pp 658–669

21.

Kellerer H, Kotov V, Speranza MG, Tuza Z (1997) Semi on-line algorithms for the partition problem. Oper Res Lett 21(5):235–242

MathSciNet MATH CrossRef 22.

Khandekar R, Pandit V (2006) Online sorting buffers on line. In: Proceedings of the 23rd symposium on theoretical aspects of computer science (STACS), pp 584–595

23.

Li S, Zhou Y, Sun G, Chen F (2007) Study on parallel machine scheduling problem with buffer. In: Proceedings of the 2nd international multi-symposiums on computer and computational sciences, pp 278–273

24.

McNaughton R (1959) Scheduling with deadlines and loss functions. Manag Sci 6(1):1–12

MathSciNet MATH CrossRef 25.

Räcke H, Sohler C, Westermann M (2002) Online scheduling for sorting buffers. In: Proceedings of the 10th European symposium on algorithms (ESA), pp 820–832

26.

Rudin JF III (2001) Improved bound for the online scheduling problem. PhD thesis, University of Texas at Dallas

27.

Sleator D, Tarjan R (1985) Amortized efficiency of list update and paging rules. Commun ACM 28(2):202–208

MathSciNet CrossRef 28.

Zhang G (1997) A simple semi on-line algorithm for

P 2//

C
_{max } with a buffer. Inf Process Lett 61(3):145–148

CrossRef