Anna Adamaszek
Artur Czumaj
ABSTRACT
We introduce a buffer scheduling problem for block operation devices in an online setting. We consider a stream of items of different types to be processed by a block device. The block device can process all items of the same type in a single step. To improve the performance of the system a buffer of size k is used to store items in order to reduce the number of operations required. Whenever the buffer becomes full a buffer scheduling strategy has to select one type and then a block operation on all elements with this type that are currently in the buffer is performed. The goal is to design a scheduling strategy that minimizes the number of block operations required. In this paper we consider the online version of this problem, where the buffer scheduling strategy must make decisions without knowing the future items that appear in the input stream. Our main result is the design of an O(log log k)-competitive online randomized buffer scheduling strategy. The bound is asymptotically tight. As a byproduct of our LP-based techniques, we obtain a randomized offline algorithm that approximates the optimal number of block operations to within a constant factor.
Supplemental Material
- Amjad Aboud. Correlation clustering with penalties and approximating the reordering buffer management problem. Master's thesis, Computer Science Department, The Technion | Israel Institute of Technology, 2008.Google Scholar
- Anna Adamaszek, Artur Czumaj, Matthias Englert, and Harald Racke. Almost tight bounds for reordering buffer management. In Proceedings of the 43rd ACM Symposium on Theory of Computing (STOC), pages 607--616, 2011. Google ScholarDigital Library
- Anna Adamaszek, Artur Czumaj, Matthias Englert, and Harald Racke. An O(logk)-competitive algorithm for generalized caching. In Proceedings of the 23rd ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 1681--1689, 2012. Google ScholarDigital Library
- Yuichi Asahiro, Kenichi Kawahara, and Eiji Miyano. NP-hardness of the sorting buffer problem on the uniform metric. Unpublished manuscript, 2010.Google Scholar
- Noa Avigdor-Elgrabli and Yuval Rabani. An improved competitive algorithm for reordering buffer management. In Proceedings of the 21st ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 13--21, 2010. Google ScholarDigital Library
- Noa Avigdor-Elgrabli and Yuval Rabani. A constant factor approximation algorithm for reordering buffer management. arXiv:1202.4504, 2012.Google Scholar
- Nikhil Bansal, Niv Buchbinder, Aleksander Madry, and Joseph Naor. A polylogarithmic-competitive algorithm for the k-server problem. In Proceedings of the 52nd IEEE Symposium on Foundations of Computer Science (FOCS), pages 267--276, 2011. Google ScholarDigital Library
- Nikhil Bansal, Niv Buchbinder, and Joseph Naor. A primal-dual randomized algorithm for weighted paging. In Proceedings of the 48th IEEE Symposium on Foundations of Computer Science (FOCS), pages 507--517, 2007. Google ScholarDigital Library
- Nikhil Bansal, Niv Buchbinder, and Joseph Naor. Ran-domized competitive algorithms for generalized caching. In Proceedings of the 30th ACM Symposium on Theory of Computing (STOC), pages 235--244, 2008. Google ScholarDigital Library
- Reuven Bar-Yehuda and Jonathan Laserson. Exploiting locality: Approximating sorting buffers. In Proceedings of the 3rd Workshop on Approximation and Online Algorithms (WAOA), pages 69--81, 2005. Google ScholarDigital Library
- Dan Blandford and Guy Blelloch. Index compression through document reordering. In Proceedings of the Data Compression Conference (DCC), pages 342--351, 2002. Google ScholarDigital Library
- Niv Buchbinder and Joseph Naor. Online primal-dual algorithms for covering and packing problems. In Proceedings of the 13th European Symposium on Algorithms (ESA), pages 689--701, 2005. Google ScholarDigital Library
- Ho-Leung Chan, Nicole Megow, Rob van Stee, and Rene Sitters. The sorting buffer problem is NP-hard.CoRR, abs/1009.4355, 2010.Google Scholar
- Matthias Englert, Harald Racke, and Matthias Westermann. Reordering buffers for general metric spaces. In Proceedings of the 39th ACM Symposium on Theory of Computing (STOC), pages 556--564, 2007. Google ScholarDigital Library
- Matthias Englert, Heiko Roglin, and Matthias Westermann. Evaluation of online strategies for reordering buffers.ACM Journal of Experimental Algorithmics, 14:3:3.3--3:3.14, 2009. Google ScholarDigital Library
- Matthias Englert and Matthias Westermann. Reordering buffer management for non-uniform cost models. In Proceedings of the 32nd International Colloquium on Automata, Languages and Programming (ICALP), pages 627--638, 2005. Google ScholarDigital Library
- Iftah Gamzu and Danny Segev. Improved online algorithms for the sorting buffer problem. In Proceedings of the 24th Symposium on Theoretical Aspects of Computer Science (STACS), pages 658--669, 2007. Google ScholarDigital Library
- Kai Gutenschwager, Sven Spiekermann, and Stefan Vo. A sequential ordering problem in automotive paint shops. International Journal of Production Research, 42(9):1865--1878, 2004.Google ScholarCross Ref
- Rohit Khandekar and Vinayaka Pandit. Online and offline algorithms for the sorting buffers problem on the line metric. Journal of Discrete Algorithms, 8(1):24--35, 2010. Google ScholarDigital Library
- Jens S. Kohrt and Kirk Pruhs. A constant factor approximation algorithm for sorting buffers. In Proceedings of the 6th Latin American Symposium on Theoretical Informatics (LATIN), pages 193--202, 2004.Google Scholar
- Jens Krokowski, Harald Racke, Christian Sohler, and Matthias Westermann. Reducing state changes with a pipeline buffer. In Proceedings of the 9th International Fall Workshop Vision, Modeling, and Visualization (VMV), pages 217--224, 2004.Google Scholar
- Harald Racke, Christian Sohler, and Matthias Westermann. Online scheduling for sorting buffers. In Proceedings of the 10th European Symposium on Algorithms (ESA), pages 820--832, 2002. Google ScholarDigital Library
Index Terms
- Optimal online buffer scheduling for block devices
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