Schwabe, E.J., and I.M. Sutherland. Improved Parity-Declustered Layouts for Disk Arrays. In Proceedings of the 6th Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 76--84, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....times each point serves as such a representative is to be as equal as possible for all points. Holland and Gibson [139] suggest repeating the blocks of the designs k times, where k is the block size, so that each point in a block can serve as the representative of one copy. Schwabe and Sutherland [142] establish that such replication is not needed, proving via network flow techniques that occurrences of points as representatives can be equalized. Indeed, this result is implied by a stronger result of Levi [140] In the connection with designs, the fourth requirement of Holland and Gibson is ....

....is perhaps the most problematical. We cannot reasonably store the entire disk layout in array format and undertake table lookups whenever a block is to be mapped to a disk location. For this reason, recent work has concentrated on properties of designs that make them quick to generate on the fly [142]. This problem is addressed by Alvarez et al. 136] They also examine disk layouts which permit reconstruction from multiple failures. C. J. Colbourn, J. H. Dinitz, D. R. Stinson Mapping data to memory arises elsewhere in connection with designs, for example in the processing of partial match ....

E. J. Schwabe & I. M. Sutherland, Improved parity-declustered layouts for disk arrays, J. Comput. Syst. Sci., 53 (1996), 328--343. (t; m; s)-Nets and Numerical Integration: 62 C. J. Colbourn, J. H. Dinitz, D. R. Stinson

....during both degraded operation and on line disk reconstruction. These layouts rely on balanced incomplete block designs (BIBDs) 9] which are known to exist for only some array configurations, and may require the storage of tables with O(k Gamma n k Delta ) entries. Schwabe and Sutherland [16] introduced BIBD based layouts for a restricted Technical Report CS98 576, CSE, UCSD, February 1998. 1 subset of the possible configurations, as well as perturbations that yield layouts for other cases with a bounded degradation in performance. Alvarez, Burkhard, and Cristian [2] presented ....

....The functions that map client addresses to array locations are efficiently computable, with low time and space requirements. A layout is ideal if it satisfies all six properties. To the best of our knowledge, no previously published declustered layout is ideal. The BIBD based layouts presented in [11, 16] satisfy the first three properties; and depending on how the client data units are mapped to the stripes, they can be made to satisfy either large write optimization or maximal parallelism, although it was not known how to satisfy both simultaneously. Holland [12] studied the problem of ....

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E. Schwabe and I. Sutherland. Improved parity-declustered layouts for disk arrays. In Proc. of the Symposium on Parallel Algorithms and Architectures, pages 76--84, 1994.

....is obtained. A dispersal factor larger than 1 can be achieved by using data organiza1 2 D 1 D m D m 1 D n D 1 D m D m 1 D n Data Check 1 m m 1 C C C n C . Reconstruction . Figure I. 1: Erasure Correction tions which are based on balanced incomplete block designs [8, 9, 13, 14, 17, 19, 21]. However, such data organizations do not generally allow contiguous reconstruction accesses (see Section I.I) Segmented information dispersal (SID) achieves high dispersal factors while maintaining the contiguity of the reconstruction accesses (provided that the reconstruction proceeds in units ....

....3 P 3 P 3 P 4 P 4 P 4 Table I. 4: A (4; 4; 3; 3; 2) BIBD organizations are based on balanced incomplete block designs (BIBD) The technique was suggested by Muntz and Lui [13] and studied by Holland and Gibson [9] Ng and Mattson [14] and Reddy, Chandy and Banerjee [17] Schwabe and Sutherland [19] studied layouts obtained by relaxing some of the balance constraints. In this section we compare BIBD solutions to SID solutions. A (b; v; s; k; BIBD [8, 14, 21] is a grouping of v different varieties of objects into b blocks such that: 1. each block contains k distinct varieties of objects, ....

Schwabe, E.J., and I.M. Sutherland. Improved Parity-Declustered Layouts for Disk Arrays. In Proc. 6th Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 76--84, 1994.

....increased overheads. When new data is written, its parity has to be computed and stored. When a disk fails, all the other disks have to be read in order to reconstruct its data. Most of the research on RAID involves the reduction of this overhead and its even distribution among the different disks [39, 45, 28, 62, 60]. For example, the RAID 5 scheme improves on the RAID 3 and 4 schemes by distributing the parity information among all the disks, thereby avoiding a bottleneck for parity updates (Fig. 5) In parallel systems, RAID is used in two main ways: hardware RAID boxes attached to I O nodes, or software ....

E. J. Schwabe and I. M. Sutherland, "Improved parity-declustered layouts for disk arrays". In 6th Symp. Parallel Algorithms & Architectures, pp. 76--84, Jun 1994. 34

....designs and any of the alternative layouts. Pessimistically, if a declustered parity group size exceeds about 40 disks, it cannot be guaranteed that a sufficiently small block design exists for all possible values of G; for such a guarantee, Schwabe and Sutherland s approximately balanced designs [Schwabe94], or Merchant and Yu s random permutations layout [Merchant92a] can be used. The primary conditions under which these mechanisms become necessary are when the design mandates both very high failure recovery performance (low declustering ratio) and very low capacity overhead (high G) It s ....

....of i into the unselected set, while still maintaining the ordering property on the selected set. The algorithm occasionally needs to perform a more complex swap on three tuples rather than just two, but never more than three. Figure 3.27 defines the algorithm more precisely. Schwabe and Sutherland [Schwabe94] have also investigated whether or not it is possible to balance parity without duplicating the block design table G times and rotating the parity slot. They proved that parity can be balanced if and only if b is a multiple of v. Note that the expanded design (B ) is simply a new block design with ....

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E. Schwabe and I. Sutherland, personal communications, and "Improved Parity-Declustered Layouts for Disk Arrays," draft submission to the Symposium on Parallel Algorithms and Architectures, 1994.

....been proposed. We note, however, that some authors choose to use the phrase clustering schemes for exactly the same notion. Reddy and Bannerjee [ Holland and Gibson[1] and Ng and Mattson [5] propose data layout schemes based on balanced incomplete block designs (BIBD) Schwabe and Sutherland [7] propose new BIBD contructions as well as approximatelybalanced layouts for parity declustering within disk arrays. Muntz and Liu [3] mention the BIBD approach. However balanced incomplete block designs are not available for all configurations of disk arrays. Merchant and Yu [ as well as Schwarz ....

E. J. Schwabe and I. M. Sutherland. Improved paritydeclustered layouts for disk arrays. In Proceedings of the Symposium on Parallel Algorithms and Architectures, pages 76--84, Cape May, N.J., June 1994.

....drawbacks: they do not exist for every array configuration (thus only certain values of the array parameters can be implemented) and they can require substantial amounts of controller memory for table storage, of the order of several Mbytes. To address the first problem, Schwabe and Sutherland [19] have extended the BIBD generation techniques, and bounded the degradation in uniformity incurred when using approximate block designs. Unlike these approaches, Datum does not place restrictions on the configuration parameters of the array, and does not need to store a block design in memory as ....

E. Schwabe and I. Sutherland. Improved paritydeclustered layouts for disk arrays. In Proc. of the Symposium on Parallel Algorithms and Architectures, pages 76--84, Cape May, N.J., June 1994.

....declustering which decouples the number of units in a parity stripe from the number of disks in the array, and distributes the contents of each parity stripe. Illustrated in Figure 4, their idea has since been extended by mechanisms evaluated by analytical modeling and event driven simulation [Holland92, Merchant92, Schwabe94, Ng92b]. These studies suggest that parity declustering should be able to improve user performance during on line recovery and to dramatically reduce the duration of on line reconstruction. An implementation of parity declustering on C disks differs from an implementation of RAID level 5 on G C disks ....

E. Schwabe and I. Sutherland, "Improved Parity-Declustered Layouts for Disk Arrays," draft submission to the Symposium on Parallel Algorithms and Architectures, 1994.

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Schwabe, E.J., and I.M. Sutherland. Improved Parity-Declustered Layouts for Disk Arrays. In Proceedings of the 6th Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 76--84, 1994.

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E.J. Schwabe and I. M. Sutherland, Improved ParityDeclustered Layouts for Disk Arrays, Journal of Computer and System Sciences, Vol. 53, No. 3, Academic Press, Dec, 1996, Pages 328-343.

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