By Peter Sanders (auth.), Ulrich Meyer, Peter Sanders, Jop Sibeyn (eds.)
Algorithms that experience to procedure huge info units need to remember that the price of reminiscence entry relies on the place the information is kept. conventional set of rules layout relies 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 one 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 educational 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 very important from a realistic element of view.
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Sample text
The expected space utilization in external memory is about 69% rather than the 100% achieved by Mairson’s scheme. Extendible hashing employs an internal structure called a directory to determine which external block to search. The directory is an array of 2d pointers to external memory blocks, for some parameter d. Let h : K → {0, 1}r be a truly random hash function, where r ≥ d. Lookup of a key k is performed by using h(k)d , the function returning the d least significant bits of h(k), to determine an entry in the directory, which in turn specifies the external block to be searched.
C} × {1, . . , L}, where C is an upper bound of the number of arrays we will ever use and L is an upper bound on the length of any array. We wish the ith block of array c to be returned from the dictionary when looking up the key (c, i). In case the block has never been written to, the key will not be present, and some standard block content may be returned. Allocation of an array consists of choosing c ∈ {1, . . , C} not used for any other array (using a counter, say), and associating a linked list of length 0 with the key (c, 0).
This increases the number of I/Os needed for a sequential scan by at most a factor of three. Insertions can be done in a single I/O except for the case where the block supposed to hold the new element is full. If either neighbor of the block has spare capacity, we may push an element to this block. In case both neighbors are full, we split the block into two blocks of about B/2 elements each. Clearly this maintains the invariant (in fact, at least B/6 deletions will be needed before the invariant is violated in this place again).