By Jeffrey Scott Vitter
Information units in huge functions are usually too sizeable to slot thoroughly contained in the computer's inner reminiscence. The ensuing input/output verbal exchange (or I/O) among speedy inner reminiscence and slower exterior reminiscence (such as disks) could be a significant functionality bottleneck. Algorithms and information constructions for exterior reminiscence surveys the state-of-the-art within the layout and research of exterior reminiscence (or EM) algorithms and knowledge buildings, the place the aim is to take advantage of locality and parallelism so as to decrease the I/O expenses. numerous EM paradigms are thought of for fixing batched and on-line difficulties successfully in exterior reminiscence. Algorithms and information buildings for exterior reminiscence describes numerous priceless paradigms for the layout and implementation of effective EM algorithms and knowledge buildings. the matter domain names thought of comprise sorting, permuting, FFT, clinical computing, computational geometry, graphs, databases, geographic details platforms, and textual content and string processing. Algorithms and knowledge buildings for exterior reminiscence is a useful reference for anyone drawn to, or undertaking study within the layout, research, and implementation of algorithms and information buildings.
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Extra resources for Algorithms and Data Structures for External Memory
The current step consists of reading the next blocks of Σ that are already in the prefetch buﬀers. That is, suppose blocks bi+1 , bi+2 , . . , bj are in the prefetch buﬀers, but bj+1 is still on a disk. Then blocks bi+1 , bi+2 , . . , bj are read and removed from the prefetch buﬀers. The second part of the current step involves input from the disks. 3 Prefetching, Caching, and Applications to Sorting 351 input step 1 2 3 4 5 6 7 8 9 l o p q r e g h n buffer pool f i a b c d j k m Fig. 5 Greedy prefetch schedule for sequence Σ = a, b, c, .
However, disk striping devotes too much internal memory (namely, 2RD blocks) to cache blocks not yet merged, and thus the eﬀective order of the merge is reduced to R = Θ(m/D) (cf. 2)), which gives a nonoptimal result. A better approach is the simple randomized merge sort (SRM) algorithm of Barve et al. [68, 72], referred to as “randomized striping” by Knuth . It uses much less space in internal memory for caching blocks and thus allows R to be much larger. Each run is striped across the disks, but with a random starting point (the only place in the algorithm where randomness is utilized).
The buckets are sorted individually in the second pass. An even better way to do distribution sort, and deterministically at that, is the BalanceSort method developed by Nodine and Vitter . During the partitioning process, the algorithm keeps track of how evenly each bucket has been distributed so far among the disks. It maintains an invariant that guarantees good distribution across the disks for each bucket. For each bucket 1 ≤ b ≤ S and disk 1 ≤ d ≤ D, let num b be the total number of items in bucket b processed so far during the partitioning and let num b (d) be the number of those items 1 We use the notation ln d to denote the natural (base e) logarithm loge d.
Algorithms and Data Structures for External Memory by Jeffrey Scott Vitter