Algorithms and Theory of Computation Handbook by Richard E. Klima, Neil Sigmon, Ernest Stitzinger

By Richard E. Klima, Neil Sigmon, Ernest Stitzinger

As well as conventional themes, this finished compendium of algorithms, facts constructions, and conception of computation covers:oapplications parts the place algorithms and information structuring ideas are of precise significance ograph drawingorobot algorithmsoVLSI layoutovision and picture processing algorithmsoschedulingoelectronic cashodata compressionodynamic graph algorithmsoon-line algorithmsomultidimensional info structuresocryptographyoadvanced subject matters in combinatorial optimization and parallel/distributed computingUnique insurance of Algorithms and concept of Computation instruction manual makes it a vital reference for researchers and practitioners in those functions components.

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ACM, 34, 596–615, 1987. H. , Birkhäuser, Boston, 1990. , Addison-Wesley, Reading, MA, 1997. , Addison-Wesley, Reading, MA, 1997. , Addison-Wesley, Reading, MA, 1997. , “Some techniques for solving recurrences,” Computing Surveys, 12, 419–436, 1980. , Data Structures and Algorithms 1: Sorting and Searching, Springer-Verlag, Berlin, 1984. M. , Data Structures in Pascal, Little, Brown and Company, Boston, 1986. , Combinatorial Algorithms, Theory and Practice, Prentice-Hall, Englewood Cliffs, NJ, 1977.

That is, we use a parallel RAM (PRAM) model. Can we speed up binary search? First, we have to define how the memory is accessed in a concurrent way. The most used model is CREW, that is, concurrent read, but exclusive write (otherwise it is difficult to know the final value of a memory cell after a writing operation). In a CREW PRAM, we can use the following simple parallel binary search. We divide the sorted set in p + 1 segments (then, there are p internal segment boundaries). Processor i compares the key to the element stored in the i-th boundary and writes in a variable ci a 0 if it is greater or a 1 if it is smaller (in case of equality the search ends).

3 Sorted Array Search In the off-line case we can search faster if we allow some time to preprocess the set and the elements can be ordered. Certainly, if we sort the set (using O(n log n) comparisons in the worst-case) and we store it in an array, we can use the well-known binary search. Binary search uses divide and conquer to quickly discard half of the elements by comparing the searched key with the element in the middle of the array, and if not equal, following the search recursively either on the first half or the second half (if the searched key was smaller or larger, respectively).

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