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 information units need to remember the fact 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 expense. real machines more and more deviate from this version: whereas watching for 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 publication introduce and survey algorithmic recommendations used to accomplish excessive functionality on reminiscence hierarchies; emphasis is put on tools attention-grabbing from a theoretical in addition to vital from a pragmatic element of view.

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Examples of decomposable problems are dictionaries and priority queues. The basic idea of the logarithmic method is to maintain a collection of data structures of different sizes, and periodically merge a number data structures into one, in order to keep the number of data structures to be queried low. In internal memory, the number of data structures for a set of size N is typically O(log N ), explaining the name of the method. We refer to [109, 110, 600] and the references therein for more background.

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. Making Use of Internal Memory. An important design principle in external memory algorithms is to make full use of internal memory for data structures that reduce the number of external memory accesses.

Clearly, extendible hashing provides lookups using a single I/O and constant internal processing time. Analyzing its space usage is beyond the scope of this chapter, but we mention some results. Flajolet [305] has shown that √ B N . , in case B ≥ log N the number of bits used is less than 8N log(N )/B. In comparison, the optimal space bound for perfect hashing to exactly N/B external memory blocks is 12 N log(B)/B + Θ(N/B) bits. The expected external space usage can be shown to be around N/(B ln 2) blocks, which means that about 69% of the space is utilized [285, 545].

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