Algorithms for Memory Hierarchies: Advanced Lectures by Peter Sanders (auth.), Ulrich Meyer, Peter Sanders, Jop

By Peter Sanders (auth.), Ulrich Meyer, Peter Sanders, Jop Sibeyn (eds.)

Algorithms that experience to procedure huge facts units need to needless to say the price of reminiscence entry relies on the place the information is kept. conventional set of rules layout is predicated at the von Neumann version the place accesses to reminiscence have uniform price. real machines more and more deviate from this version: whereas looking forward to reminiscence entry, these days, microprocessors can in precept execute a thousand additions of registers; for hard disk drive entry this issue can succeed in six orders of magnitude.

The sixteen coherent chapters during this monograph-like instructional publication introduce and survey algorithmic options used to accomplish excessive functionality on reminiscence hierarchies; emphasis is put on equipment fascinating from a theoretical in addition to very important from a realistic element of view.

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2 Lookup Using One External Memory Access In the previous section we looked at hashing schemes with good expected lookup behavior. Of course, an expected bound may not be good enough for some applications where a firm guarantee on throughput is needed. In this and the following section we investigate how added resources may provide dictionaries in which lookups take just the time of a single I/O in the worst case. In particular, we consider dictionaries using more internal memory, and dictionaries using external memory that allows two I/Os to be performed in parallel.

Output stream (b) 2 4 7 8 12 16 19 27 37 44 48 61 1 3 5 11 17 21 22 35 40 55 57 62 2 4 7 8 1 3 5 11 (c) 2 4 7 8 12 16 19 27 37 44 48 61 1 3 5 11 17 21 22 35 40 55 57 62 5 11 7 8 1 2 3 4 Fig. 1. Merging two sorted sequences. (a) The initial situation: The two lists are stored on disk. Two empty input buffers and an empty output buffer have been allocated in main memory. The output sequence does not contain any data yet. (b) The first block from each input sequence has been loaded into main memory. (c) The first B elements have been moved from the input buffers to the output buffer.

Whenever a block at level d has run full, it is split into two blocks at level d + 1 using hd +1 . In case d = d we first need to double the size of the directory. Conversely, if two blocks at level d , with keys having the same function value under hd −1 , contain less than B keys in total, these blocks are merged. If no blocks are left at level d, the size of the directory is halved. 2. Basic External Memory Data Structures 31 Using a Predecessor Dictionary. If one is willing to increase internal computation from a constant to expected O(log log N ) time per dictionary operation, both internal and external space usage can be made better than that of extendible hashing.

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