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

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

Algorithms that experience to strategy huge info units need to understand that the price of reminiscence entry will depend 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 rate. genuine machines more and more deviate from this version: whereas awaiting reminiscence entry, these days, microprocessors can in precept execute a thousand additions of registers; for hard drive entry this issue can succeed in six orders of magnitude.

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

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Additional resources for Algorithms for Memory Hierarchies: Advanced Lectures

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This results in a sorted list of blocks of elements that form the new children of v. If there are too few or too many children, rebalancing operations are performed, similar to the ones described for Btrees (see [52] for details). Each node involved in a rebalancing operation has its buffer flushed before the rebalancing is done. In this way, the content of the buffers need not be considered when splitting, fusing, and sharing. The cost of flushing a buffer is O(M/B) I/Os for reading the buffer, and O(M/B) I/Os for writing the operations to the buffers of the children.

For details we refer to [99, 661, 749]. String B-trees. We have assumed that the keys stored in a B-tree have fixed length. In some applications this is not the case. Most notably, in String Btrees [296] the keys are strings of unbounded length. It turns out that all the usual B-tree operations, as well as a number of operations specific to strings, can be efficiently supported in this setting. String B-trees are presented in Chapter 7. 2. , the answer to a query is provided immediately after the query is issued.

What consequence does this have for the height of the B-tree? 3 On the Optimality of B-trees As seen in Chapter 1 the bound of O(logB N ) I/Os for searching is the best we can hope for if we consider algorithms that use only comparisons of keys to guide searches. If we have a large amount of internal memory and are willing to use it to store the top M/B nodes of the B-tree, the number of I/Os for searches and updates drops to O(logB (N/M )). 12. How large should internal memory be to make O(logB (N/ M )) asymptotically smaller than O(logB N )?

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