Abstract
In a systematic erasure code for the correction of two simultaneous erasures, each information symbol must have two associated parity symbols. When implemented in a redundant array of independent disks (RAID), performance requirements on the update penalty necessitate that each information symbol be associated with no more parity symbols than the two required. This leads to a simple graph model of the erasure codes, with parity symbols as vertices and information symbols as edges. Ordering the edges so that no more than f check disks (vertices) appear amongan y set of d consecutive edges is found to optimize access performance of the disk array when d is maximized. These cluttered orderings are examined for the complete graph K n. The maximum number d of edges is determined precisely when f ≤ 5 and when f = n - 1, and bounds are derived in the remainingcases.
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References
Juraj Bosák Decompositions of Graphs. Kluwer Academic Publishers, Dordrecht, 1990.
Yeow MengChee, Charles J. Colbourn and Alan C.H. Ling Asymptotically optimal erasure-resilient codes for large disk arrays. Discrete Applied Mathematics 102 (2000), 3–36.
Peter M. Chen, Edward K. Lee, Garth A. Gibson, Randy H. Katz and David A. Patterson RAID: High-performance, reliable secondary storage. ACM Computing Surveys 26 (1994) 145–185.
Myra B. Cohen Performance analysis of triple erasure codes in large disk arrays. Master’s thesis, University of Vermont, 1999.
M.B. Cohen and C.J. Colbourn Optimal and pessimal orderings of Steiner triple systems in disk arrays. Theoretical Computer Science, to appear.
M.B. Cohen and C.J. Colbourn Steiner triple systems as multiple erasure codes in large disk arrays. Proceedings of IPCCC 2000 (19th IEEE International Conference on Performance, Computing and Communications), 2000, pp. 288–294.
M.B. Cohen and C.J. Colbourn Ladder orderings of pairs and RAID performance. submitted for publication, 2000.
M.B. Cohen and C.J. Colbourn Orderingedg es for double erasure codes. Proceedings of the Symposium on Parallel Algorithms and Architectures, Crete, July 2001, to appear.
Garth A. Gibson Redundant Disk Arrays, Reliable Parallel Secondary Storage. MIT Press, 1992.
Lisa Hellerstein, Garth A. Gibson, Richard M. Karp, Randy H. Katz and David A. Patterson Codingtec hniques for handlingfailures in large disk arrays. Algorithmica 12 (1994) 182–208.
Mark C. Holland On-Line Data Reconstruction In Redundant Disk Arrays. PhD thesis, Carnegie Mellon University, 1994.
Edward K. Lee Software and performance issues in the implementation of a RAID prototype. Technical Report CSD-90-573, University of California at Berkeley, 1990.
Edward K. Lee Performance Modeling and Analysis of Disk Arrays. PhD thesis, University of California at Berkeley, 1993.
Paul Massiglia The RAID Book, A Storage System Technology Handbook, 6th Edition. The RAID Advisory Board, 1997.
Alexander Rosa On certain valuations of the vertices of a graph. Theory of Graphs (Internat. Sympos., Rome, 1966), Gordon and Breach, New York, 1967, pp. 349–355.
K. Salem and H. Garcia-Molina Disk striping. In Proceedings of the 2nd International Conference on Data Engineering, pages 336–342, Washington, D. C., 1986. IEEE.
Daniel Stodolsky, Garth Gibson, and Mark Holland Parity logging: Overcoming the small write problem in redundant disk arrays. Computer Architecture News 21 (1993), 64–75.
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Cohen, M.B., Colbourn, C.J., Froncek, D. (2001). Cluttered Orderings for the Complete Graph. In: Wang, J. (eds) Computing and Combinatorics. COCOON 2001. Lecture Notes in Computer Science, vol 2108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44679-6_48
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DOI: https://doi.org/10.1007/3-540-44679-6_48
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