The Library
Reordering buffers for general metric spaces
Tools
Englert, Matthias, Raecke, Harald and Westermann, Matthias. (2010) Reordering buffers for general metric spaces. Theory of Computing, Vol.6 (No.1). pp. 2746. ISSN 15572862

PDF
WRAP_Englert_Reordering_buffers.pdf  Published Version  Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Available under License Creative Commons Attribution. Download (338Kb) 
Official URL: http://dx.doi.org/10.4086/toc.2010.v006a002
Abstract
In the reordering buffer problem, we are given an input sequence of requests for service each of which corresponds to a point in a metric space. The cost of serving the requests heavily depends on the processing order. When serving a request the cost is equal to the distance, in the metric space, between this request and the previously served request. A reordering buffer with storage capacity k can be used to reorder the input sequence in a restricted fashion so as to construct an output sequence with lower service cost. This simple and universal framework is useful for many applications in computer science and economics, e. g., disk scheduling, rendering in computer graphics, or painting shops in car plants. In this paper, we design online algorithms for the reordering buffer problem where the goal is to minimize the total cost. Our main result is a strategy with a polylogarithmic competitive ratio for general metric spaces. Previous work on the reordering buffer problem only considered very restricted metric spaces. We obtain our result by first developing a deterministic algorithm for weighted trees whose competitive ratio depends on k and the hopdiameter of the tree. Then we show how to improve this competitive ratio to O(log2 k) for metric spaces that correspond to hierarchically wellseparated trees. Combining this result with the results on the probabilistic approximation of arbitrary metrics by tree metrics due to Fakcharoenphol, Rao, and Talwar, we obtain a randomized strategy for general metric spaces that achieves a competitive ratio of O(log2 k · log n) in expectation against an oblivious adversary. Here n denotes the number of distinct points in the metric space. Note that the length of the input sequence can be much larger than n.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software 
Divisions:  Faculty of Science > Computer Science 
Library of Congress Subject Headings (LCSH):  Buffer storage (Computer science)  Mathematical models, Metric spaces 
Journal or Publication Title:  Theory of Computing 
Publisher:  University of Chicago, Department of Computer Science 
ISSN:  15572862 
Date:  2010 
Volume:  Vol.6 
Number:  No.1 
Page Range:  pp. 2746 
Identification Number:  10.4086/toc.2010.v006a002 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
Funder:  Deutsche Forschungsgemeinschaft (DFG), Engineering and Physical Sciences Research Council (EPSRC), University of Warwick. Centre for Discrete Mathematics and Its Applications, Sixth Framework Programme (European Commission) (FP6) 
Grant number:  WE 2842/1 (DFG), EP/F043333/1 (EPSRC), 001907 (FP6) 
References:  [1] AMJAD ABOUD: Correlation clustering with penalties and approximating the recordering buffer management problem. Master’s thesis, The Technion  Israel Institute of Technology, Janurary 2008. [Technion TR archive]. 29 [2] HOUMAN ALBORZI, ERIC TORNG, PATCHRAWAT UTHAISOMBUT, AND STEPHEN WAGNER: The kclient problem. J. Algorithms, 41(2):115–173, 2001. [doi:10.1006/jagm.2001.1182]. 30 [3] NOA AVIGDORELGRABLI AND YUVAL RABANI: An improved competitive algorithm for reordering buffer management. In Proc. 21st ACMSIAM Symp. on Discrete Algorithms (SODA), pp. 13–21. ACM Press, 2010. 29 [4] REUVEN BARYEHUDA AND JONATHAN LASERSON: Exploiting locality: Approximating sorting buffers. In Proc. 3rd Workshop on Approximation and Online Algorithms (WAOA), volume 3879 of Lecture Notes in Computer Science, pp. 69–81. Springer, 2005. [doi:10.1007/11671411 6]. 28, 30 [5] YAIR BARTAL: Probabilistic approximations of metric spaces and its algorithmic applications. In Proc. 37th FOCS, pp. 184–193. IEEE Comp. Soc. Press, 1996. [doi:10.1109/SFCS.1996.548477]. 29, 42 [6] YAIR BARTAL: On approximating arbitrary metrics by tree metrics. In Proc. 30th STOC, pp. 161–168. ACM Press, 1998. [doi:10.1145/276698.276725]. 29 [7] MATTHIAS ENGLERT, DENIZ ¨OZMEN, AND MATTHIAS WESTERMANN: The power of reordering for online minimum makespan scheduling. In Proc. 49th FOCS, pp. 603–612. IEEE Comp. Soc. Press, 2008. [doi:10.1109/FOCS.2008.46]. 30 [8] MATTHIAS ENGLERT, HEIKO R¨O GLIN, AND MATTHIAS WESTERMANN: Evaluation of online strategies for reordering buffers. In Proc. 5th Internat. Workshop on Efficient and Experimental Algorithms (WEA), volume 4007 of Lecture Notes in Computer Science, pp. 183–194. Springer, 2006. [doi:10.1007/11764298 17]. 29 [9] MATTHIAS ENGLERT AND MATTHIAS WESTERMANN: Reordering buffer management for nonuniform cost models. In Proc. 32nd Internat. Colloquium on Automata, Languages and Programming (ICALP), volume 3580 of Lecture Notes in Computer Science, pp. 627–638. Springer, 2005. [doi:10.1007/11523468 51]. 28, 29, 31 [10] JITTAT FAKCHAROENPHOL, SATISH B. RAO, AND KUNAL TALWAR: A tight bound on approximating arbitrary metrics by tree metrics. J. Comput. System Sci., 69(3):485–497, 2004. [doi:10.1016/j.jcss.2004.04.011]. 29, 31 [11] IFTAH GAMZU AND DANNY SEGEV: Improved online algorithms for the sorting buffer problem. In Proc. 24th Symp. on Theoretical Aspects of Computer Science (STACS), volume 4393 of Lecture Notes in Computer Science, pp. 658–669. Springer, 2007. [doi:10.1007/9783540709183 56]. 29, 30 [12] KAI GUTENSCHWAGER, SVEN SPIEKERMANN, AND STEFAN VOSS: A sequential ordering problem in automotive paint shops. Internat. J. Production Research, 42(9):1865–1878, 2004. [doi:10.1080/00207540310001646821]. 29 [13] ROHIT KHANDEKAR AND VINAYAKA PANDIT: Online and offline algorithms for the sorting buffers problem on the line metric. J. Discrete Algorithms, 2008. [doi:10.1016/j.jda.2008.08.002]. 28, 29, 30 [14] JENS S. KOHRT AND KIRK PRUHS: A constant factor approximation algorithm for sorting buffers. In Proc. 6th Latin American Symp. on Theoretical Informatics (LATIN), volume 2976 of Lecture Notes in Computer Science, pp. 193–202. Springer, 2004. [LATIN:fqbc84923gveuhlr]. 28, 30 [15] JENS KROKOWSKI, HARALD R¨ACKE, CHRISTIAN SOHLER, AND MATTHIAS WESTERMANN: Reducing state changes with a pipeline buffer. In Proc. 9th Internat. Fall Workshop Vision, Modeling, and Visualization (VMV), pp. 217–224. Aka GmbH, 2004. 29 [16] HARALD R¨ACKE, CHRISTIAN SOHLER, AND MATTHIAS WESTERMANN: Online scheduling for sorting buffers. In Proc. 10th European Symp. on Algorithms (ESA), volume 2461 of Lecture Notes in Computer Science, pp. 820–832. Springer, 2002. [doi:10.1007/3540457496 71, ESA:mx7mdle1j62b5n3h]. 28, 29 [17] TOBY J. TEOREY AND TAD B. PINKERTON: A comparative analysis of disk scheduling policies. Comm. ACM, 15(3):177–184, 1972. [doi:10.1145/361268.361278]. 28 
URI:  http://wrap.warwick.ac.uk/id/eprint/42236 
Actions (login required)
View Item 