By Justin R. Smith
This article for college students and pros in laptop technology presents a useful review of present wisdom bearing on parallel algorithms. those desktop operations have lately received elevated significance as a result of their skill to augment the ability of desktops through allowing a number of processors to paintings on assorted elements of an issue independently and at the same time. This procedure has resulted in suggestions of inauspicious difficulties in a few important fields, together with man made intelligence, picture processing, and differential equations. because the first up to date precis of the subject, this ebook should be wanted through researchers, computing device technological know-how execs, and complicated scholars serious about parallel computing and parallel algorithms.
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Extra resources for The Design and Analysis of Parallel Algorithms
Cn , Dn }; 24 2. MODELS OF PARALLEL COMPUTATION 4. Sorting this result requires at most 1 parallel step, interchanging Ci with Di−1 for some values of i. 8. Let n be a power of 2 and let A1 , . . , An and B1 , . . , Bn be two sorted sequences such that A1 ≤ B1 . Merge the sequences A1 , A3 , A5 , . . and B1 , B3 , B5 , . . to form C1 , . . , Cn and the sequences A2 , A4 , A6 , . . and B2 , B4 , B6 , . . to form D1 , . . , Dn . Now shuffle the C-sequence with the D- sequence to get C1 , D1 , C2 , D2 , .
Here is an example of the simulation of a CRCW-write operation: Processor Target D (i ) 0 2 3 1 6 4 2 3 5 3 1 6 4 5 7 5 7 8 6 1 9 7 0 0 Here D (i ) is the data that processor i wants to write to location a(i ). This is converted into a list of pairs: (0,2), (6,1), (3,2), (1,3), (5,4), (7,5), (7,6), (0,7) This list is sorted by the second element in each pair: (0,7), (1,3), (2,0), (3,2), (5,4), (6,1), (7,5), (7,6) 5. RELATIONS BETWEEN PRAM MODELS 27 Suppose the ith pair in the sorted list is called ( a( ji ), ji ), and the memory in the ith processor is called Mi .
A problem will be said to be in Plogspace(k) if there exists an offline Turing machine that solves the problem using space that is O(lgk n). 5. e. any problem that can be solved on an offline Turing machine in space proportional to the logarithm of the complexityparameter can be solved in polynomial time on a conventional Turing machine. This is not hard to see — if the total amount of RAM used by a sequential algorithm is c lg n then the total number of possible states (or sets of data stored in memory) is a power of n.