Disk allocation for Cartesian product files on multiple-disk systems

Abstract

Cartesian product files have recently been shown to exhibit attractive properties for partial match queries. This paper considers the file allocation problem for Cartesian product files, which can be stated as follows: Given a k-attribute Cartesian product file and an m-disk system, allocate buckets among the m disks in such a way that, for all possible partial match queries, the concurrency of disk accesses is maximis ed. The Risk Modulo (DM) allocation method is described first, and it is shown to be strict optimal under many conditions commonly occurring in practice, including all possible partial match queries when the number of disks is 2 or 3. It is also shown that although it has good performance, the DM allocation method is not strict optimal for all possible partial match queries when the number of disks is greater than 3. The General Disk Modulo (GDM) allocation method is then described, and a sufficient but not necessary condition for strict optimal&y of the GDM method for all partial match queries and any number of disks is then derived. Simulation studies comparing the DM and random allocation methods in terms of the average number of disk accesses, in response to various classes of partial match queries, show the former to be significantly more effective even when the number of disks is greater than 3, that is, even in cases where the DM method is not strict optimal. The results that have been derived formally and shown by simulation can be used for more effective design of optimal file systems for partial match queries. When considering multiple-disk systems with independent access paths, it is important to ensure that similar records are clustered into the same or similar buckets, while similar buckets should be dispersed uniformly among the disks.

Replicated Parallel I/O without Additional Scheduling Costs

“…it is the maximum number of tiles in Q retrieved from a single disk). These schemes include Disk Modulo DM [6], Fieldwise eXclusive (FX) or [9], the cyclic schemes (including RPHM, GFIB, and EXH) [11], GRS [4], a technique developed by Atallah and Prabhakar [2] which we will call RFX, and several techniques based on discrepancy theory [5,14] (for an introduction to discrepancy theory see [10]). Note that these are just a subset of the declustering techniques that have been developed for this problem.…”

“…A declustering is called strictly optimal if all range queries can be answered optimally, however it was shown in [1] that this is not achievable except in a few limited circumstances. Thus there has been a significant amount of work to develop declustering schemes that have close to optimal performance, a sampling of which are in [2,3,4,5,6,9,11,14].…”

“…In this paper we focus on answering range queries in a multidimensional database (such as a GIS), where each of its dimensions is divided uniformly to obtain tiles which are placed on different disks; there has been a significant amount of research for this problem (a subset of which is [1,2,3,4,5,6,7,8,9,11,12,13,14,15]). A declustering scheme would be optimal if any range query could be answered by doing no more than # of tiles inside the range/# of disks retrievals from any one disk.…”

Analysis and Comparison of Replicated Declustering Schemes

“…Several methods have been proposed for declustering data, including Disk Modulo [12], Field-wise Exclusive OR [29], Hilbert [13], Near-Optimal Declustering [5], General Multidimensional Data Allocation [27], cyclic allocation schemes [36], [37], Golden Ratio Sequences [7], Hierarchical Declustering [6], and Discrepancy Declustering [9]. Using declustering and replication, approaches including Complete Coloring [20] have optimal performance and Square Root Colors Disk Modulo [20] has one more than optimal.…”

“…Given the established bounds on the extra cost and the impossibility result, a large number of declustering techniques have been proposed to achieve performance close to the bounds either on the average case [5], [12], [13], [14], [16], [22], [24], [25], [29], [31], [36], [37] or, in the worst case, [3], [6], [7], [9], [41]. Although initial approaches in the literature were originally for relational databases or Cartesian product files, recent techniques focus more on spatial data declustering.…”