We present the design and implementation of a parallel out-of-core sorting algorithm, which is based on Leighton's columnsort algorithm. We show how to relax some of the steps of the original columnsort algorithm to permit a faster out-of-core implementation. Our algorithm requires only 4 passes over the data, and a 3-pass implementation is possible. Although there is a limit on the number of records that can be sorted---as a function of the memory used per processor---this upper limit need not be a severe restriction, and it increases superlinearly with the per-processor memory. To the best of our knowledge, our implementation is the first out-of-core multiprocessor sorting algorithm whose output is in the order assumed by the Parallel Disk Model. We define several measures of sorting efficiency and demonstrate that our implementation's sorting efficiency is competitive with that of NOW-Sort, a sorting algorithm developed to sort large amounts of data quickly on a cluster of workstations.

This paper presents asymptotically equal lower and upper bounds for the number of parallel I/O operations required to perform bit-matrix-multiply/complement (BMMC) permutations on the Parallel Disk Model proposed by Vitter and Shriver. A BMMC permutation maps a source index to a target index by an affine transformation over GF(2), where the source and target indices are treated as bit vectors. The class of BMMC permutations includes many common permutations, such as matrix transposition (when dimensions are powers of 2), bit-reversal permutations, vector-reversal permutations, hypercube permutations, matrix reblocking, Gray-code permutations, and inverse Gray-code permutations. The upper bound improves upon the asymptotic bound in the previous best known BMMC algorithm and upon the constant factor in the previous best known bit-permute/complement (BPC) permutation algorithm. The algorithm achieving the upper bound uses basic linear-algebra techniques to factor the characteristic matrix for the BMMC permutation into a product of factors, each of which characterizes a permutation that can be performed in one pass over the data. The factoring uses new subclasses of BMMC permutations: memoryload-dispersal (MLD) permutations and their inverses. These subclasses extend the catalog of one-pass permutations. Although many BMMC permutations of practical interest fall into subclasses that might be explicitly invoked within the source code, this paper shows how to quickly detect whether a given vector of target addresses specifies a BMMC permutation. Thus, one can determine efficiently at run time whether a permutation to be performed is BMMC and then avoid the general-permutation algorithm and save parallel I/Os by using the BMMC permutation algorithm herein.

Article Free Access Share on Asymptotically tight bounds for performing BMMC permutations on parallel disk systems Authors: Thomas H. Cormen View Profile , Leonard F. Wisniewski View Profile Authors Info & Claims SPAA '93: Proceedings of the fifth annual ACM symposium on Parallel Algorithms and ArchitecturesAugust 1993 Pages 130–139https://doi.org/10.1145/165231.165248Published:01 August 1993Publication History 6citation177DownloadsMetricsTotal Citations6Total Downloads177Last 12 Months14Last 6 weeks3 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF