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 approach huge information units need to remember that the price of reminiscence entry is determined by 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 price. genuine machines more and more deviate from this version: whereas looking ahead to reminiscence entry, these days, microprocessors can in precept execute a 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 ebook 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 realistic element of view.

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Again, a direct implementation of the internal memory data structure could behave poorly in external memory: When traversing the list, the algorithm may need to perform one I/O every time a pointer is followed. (The task of traversing an entire linked list on external memory can be performed more efficiently. , elements that are near each other in the list must tend to be stored in the same block. An immediate idea would be to put chunks of B consecutive elements together in each block and link these blocks together.

This means that we are not able to control exactly the relative sizes of the set and hash table. On the other hand, uniformity means that we will be able to achieve the performance of linear hashing using a smaller hash table. As in linear hashing we extract the hash function value for all ranges from a “mother” hash function φ : U → {0, . . , R − 1}. The factor between consecutive hash table sizes will be between 1+ 1 and 1+ 2, where 2 > 1 > 0 are arbitrary constants. The size R of the range of φ is chosen as follows.

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. Note 26 Rasmus Pagh that there is a cost of a constant number of I/Os for each child – this is the reason for making the number of children equal to the I/O-cost of reading the buffer. Thus, flushing costs O(1/B) I/Os per operation in the buffer, and since the depth of the tree is O(log M ( N B )), the total cost of all flushes is B O( B1 log M ( N )) I/Os per operation.

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