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.)

ISBN-10: 3540008837

ISBN-13: 9783540008835

Algorithms that experience to method huge info units need to remember that the price of reminiscence entry depends upon the place the knowledge is saved. conventional set of rules layout is predicated at the von Neumann version the place accesses to reminiscence have uniform fee. genuine machines more and more deviate from this version: whereas expecting reminiscence entry, these days, microprocessors can in precept execute one thousand additions of registers; for hard disk drive entry this issue can achieve six orders of magnitude.

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

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To implement an efficient queue we use two buffers of size B, a read buffer and a write buffer. Remove operations work on the read buffer until it is empty, in which case the least recently written external memory block is read into the buffer. ) Insertions are done to the read buffer which when full is written to external memory. Similar to before, we get at most 1/B I/O per operation. 2. Above we saw how to implement stacks and queues having a fixed bound on the maximum number of elements. Show how to efficiently implement external stacks and queues with no bound on the number of elements.

N/B } that maps at most B keys to each block. Note that if we store key k in block p(k) and the B-perfect hash function resides in internal memory, we need only a single I/O to look up k. Mairson 30 Rasmus Pagh showed that such a function can be implemented using O(N log(B)/B) bits of internal memory. ) If the number of that only shows up when the key set K has size 2B external blocks is only N/B and we want to be able to handle every possible key set, this is also the best possible [525].

This can be done by first searching for the key a, which will lead to the smallest key x ≥ a. We then traverse the linked list starting with x and report all keys smaller than b (whenever we encounter 2. Basic External Memory Data Structures 21 a block with a key larger than b the search is over). The number of I/Os used for reporting Z keys from the linked list is O(Z/B), where Z/B is the minimum number of I/Os we could hope for. The feature that the number of I/Os used for a query depends on the size of the result is called output sensitivity.

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