Duality Between Prefetching and Queued Writing with Parallel Disks

Abstract

Parallel disks promise to be a cost effective means for achieving high bandwidth in applications involving massive data sets, but algorithms for parallel disks can be difficult to devise. To combat this problem, we define a useful and natural duality between writing to parallel disks and the seemingly more difficult problem of prefetching. We first explore this duality for applications involving read-once accesses using parallel disks. We get a simple linear time algorithm for computing optimal prefetch schedules and analyze the efficiency of the resulting schedules for randomly placed data and for arbitrary interleaved accesses to striped sequences. Duality also provides an optimal schedule for prefetching plus caching, where blocks can be accessed multiple times. Another application of this duality gives us the first parallel disk sorting algorithms that are provably optimal up to lower-order terms. One of these algorithms is a simple and practical variant of multiway mergesort, addressing a question that had been open for some time.1. Introduction. External memory (EM) algorithms are those for which the problem data set is too large to fit into the high-speed random access memory (RAM) of a computer and therefore must reside on external devices such as disk drives [23]. In order to cope with the high latency of accessing data on disks, efficient EM algorithms exploit locality in their design. In the I/O model, EM algorithms access a large block of B contiguous data elements in one I/O step and perform the necessary algorithmic operations on the elements in the block while in the high-speed memory. The speedup can be significant. However, even with blocked access, a single disk provides much less bandwidth than the internal memory. This problem can be mitigated by using multiple disks in parallel. For each input/output operation, one block is transferred between a fast memory of size M and each of the D disks. The algorithm therefore transfers D blocks at the cost of a single-disk access delay.A simple approach to algorithm design for parallel disks is to employ large logical blocks, or superblocks, of size B · D in the algorithm. This reduces the problem to designing an EM algorithm for one disk with logical block size BD. A superblock is split into D physical blocks-one on each disk. All D physical blocks are accessed *

Slabpose Columnsort: A New Oblivious Algorithm for Out-of-Core Sorting on Distributed-Memory Clusters

“…Greed sort by Nodine and Vitter [31], (l, m)-merge sort by Rajasekaran [34], Sharesort by Aggarwal and Plaxton [1], and Simple Randomized Mergesort by Vitter and Barve [7] are a few examples of merging-based out-of-core sorting algorithms. More recently, there has been some work on efficient prefetching strategies with applications to sorting [23], [24], [39].…”

Optimal Read-Once Parallel Disk Scheduling

“…The latter situation may require evicting a previously fetched block of lower priority that has not yet been serviced. As noted in [9], for practical reasons it may be desirable to avoid fetching a block if it will be evicted before being used. In the batched scheduling situation under consideration, it is straightforward to identify such blocks and avoid unnecessary I/Os.…”

“…Actual I/Os are then initiated using the virtual schedule created. An alternative scheme to avoid these unnecessary I/Os, resulting in a so-called conservative schedule was proposed in [9]. The batched scheduling schemes described above are interesting because of their simplicity.…”

“…Independently, Hutchinson et al [8], [9] explored an elegant and interesting duality between prefetching (reading) and writing in the parallel disk model, and showed how schedules for prefetching in the read-once parallel I/O model can be obtained by first obtaining a schedule for writing all the blocks in the reversed reference string. This approach also leads to a linear-time optimal offline scheduling algorithm for read-once reference strings.…”

Lexicographic QoS scheduling for parallel I/O

“…Previous work on prefetching and caching in parallel I/O systems has dealt with the problem of a single flow; efficient algorithms are now known that maximize disk system throughput for a single flow (see [1,16,[18][19][20] for example). However, the problems of sharing the parallel disks among multiple concurrent flows has not been addressed previously.…”