Download e-book for iPad: 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.)

ISBN-10: 3540008837

ISBN-13: 9783540008835

Algorithms that experience to technique huge facts 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 expense. real machines more and more deviate from this version: whereas anticipating reminiscence entry, these days, microprocessors can in precept execute a thousand additions of registers; for harddisk entry this issue can succeed in six orders of magnitude.

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

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As an example, if the auxiliary data structure can be constructed by scanning the entire subtree in O(W/B) I/Os, the amortized cost per update is O( B1 logB N ) I/Os, which is negligible. 11. Modify the rebalancing scheme to support the following type of weight balance condition: A B-tree node at level i < h is the root of a subtree having Θ((B/(2 + ))i ) leaves, where > 0 is a constant. 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.

1 − for some constant > 0) and if B is not too small, the expected average is very close to 1. In fact, the asymptotic probability of having to use k > 1 I/Os for a lookup is 2−Ω(B(k−1)) . 4 we will consider the problem of keeping the load factor in a certain range, shrinking and expanding the hash table according to the size of the set. Chaining with Separate Lists. In chaining with separate lists we again hash to a table of size approximately N/(αB) to achieve load factor α. Each block in the hash table is the start of a linked list of keys hashing to that block.

However, more efficient ways of reorganizing the hash table are important in practice to keep constant factors down. The basic idea is to introduce more “gentle” ways of changing the hash function. Linear Hashing. Litwin [508] proposed a way of gradually increasing and decreasing the range of hash functions with the size of the set. The basic idea for hashing to a range of size r is to extract b = log r bits from a “mother” hash function. If the extracted bits encode an integer k less than r, this is used as the hash value.

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

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