The power of duality for prefetching and sorting with parallel disks

David A. Hutchinson, Peter Sanders, Jeffrey Scott Vitter
2001 Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures - SPAA '01  
External memory EM algorithms are designed to be efcient when the problem data do not t into the high-speed random access memory RAM of a computer and must instead reside on external devices such as disk drives 7 . Because of the high latency of accessing data on such devices, data are transferred in units of blocks of B contiguous data items, and e cient EM algorithms exploit locality in their design in order to maximize the amount of useful data transferred in each input output I O step. But
more » ... ven with blocked access, a single disk provides much lower bandwidth than the internal memory of a computer. This I O bottleneck can be mitigated by using multiple disks in parallel. In an I O operation, each of D disks simultaneously transfers a block t o or from internal memory. The algorithm thus transfers D blocks at the cost of a single-disk access delay. In this paper we consider parallel disk input and output separately, in particular as the prefetch scheduling problem and the output scheduling problem, respectively. The online queued writing or output scheduling problem takes as input a xed size pool of m empty memory bu ers for storing blocks, and the sequence hw0; w 1 ; : : : ; w L , 1 i of block write requests as they are issued. Each write request is labeled with the disk it will use. The output is an optimal output schedule: an ordered sequence of parallel output steps, of minimal length for the given bu er pool capacity. The o ine prefetch scheduling problem takes as input a xed size pool of m empty memory bu ers for storing blocks, and the sequence hr0; r 1 ; : : : ; r L , 1 i of distinct block read requests that will be issued. Each read request is labeled with the disk it will use. The output is an optimal prefetch schedule: an ordered sequence of parallel input steps that allows the requested blocks to be delivered in the required order and is of minimal length for the given bu er pool capacity. The central theme in this paper is the newly discovered duality b e t w een these two problems. We illustrate how applications in one domain can be analyzed via duality with applications in the other domain.
doi:10.1145/378580.378760 dblp:conf/spaa/HutchinsonSV01 fatcat:o2eh7rc6e5acdfvszgkcnqzrry