R. Cole, Parallel Merge Sort, Proc. 27th IEEE Symposium on Foundations of Computer Science, 1986, pp. 511-516. 3.6 Bibliography 141  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Komlos and Szemeredi [AKS83] Leighton [L84] reduced the processor complexity in AKS to obtain a truly optimal deterministic algorithm. However the AKS has su ered due to astronomical constants involved in the construction the underlying network which is an expander graph. More recently Cole [C86] designed an elegant O(log n) time sorting algorithm which has virtually settled the problem of sorting on PRAM models; however Flashsort continues to remain the most practical algorithm for networks. The optimal sub logarithmic algorithm for pre x sum stated in lemma 3.5 was discovered by Cole ....

R. Cole, Parallel Merge Sort, Proc. 27th IEEE Symposium on Foundations of Computer Science, 1986, pp. 511-516. 3.6 Bibliography 141

....sequential algorithms for INTEGER SORT and optimal parallel algorithms for GENERAL SORT. Lemma 2.4 Stable INTEGER SORT of n keys can be done in time O(n) by a deterministic sequential RAM [1] Lemma 2. 5 GENERAL SORT of n keys can be performed in time O(log n) using n PRAM processors ( 4] and [8]) 3 An Optimal INTEGER SORT Algorithm In this section we present an optimal algorithm for INTEGER SORT. This algorithm employs n= log n processors and runs in time e O(log n) 3.1 Summary of the Algorithm The main idea behind our algorithm is radix sorting [15] As an example of radix ....

R. COLE, Parallel Merge Sort, Proc. 27th IEEE Symposium on Foundations of Computer Science, 1986, pp. 511-516.

....to a vertex in N(i) Gamma[i] is an array containing deg(i) 1 entries. Each entry corresponds to a vertex in Gamma(i) We assume the entries in the arrays N [i] s and Gamma[i] s are sorted in the increasing order. This can be done in O(log n) time with O(n m) processors from the input [8]. Given two arrays X[1: a] and Y [1: b] define diff L (X; Y ) minfi j X [i] 6= Y [i]g. If a b and X [i] Y [i] for all 1 i a, define diff L (X; Y ) a 1. If a = b and X [i] Y [i] for all 1 i a, diff L (X; Y ) is not defined. Define X L Y iff X [d] Y [d] where d = diff L (X; Y ....

....analogous to L . In order to implement Step 2, we need to find the f classes of V . We sort the set of the arrays fN [i] j 1 i ng by L . Since i f j iff N [i] N [j] each f class corresponds to a contiguous block in the sorted list. We use the O(log n) time sorting algorithm in [8]. For an array N [i] of size k = deg(i) we assign k processors. The comparison between two arrays N [i] and N [j] can be done in O(1) time using the processors assigned to them. The total number of processors needed is P n i=1 deg(i) 2m. So this step takes O(log n) time with O(m) processors. ....

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R. Cole, Parallel Merge Sort, Proc. 27th IEEE Symposium on Foundation of Computer Science, 1986, pp. 511-517.

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