An Optimal Parallel Algorithm for Selection
An Optimal Parallel Algorithm for Selection
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In our eReader you can find the full English version of the book. Read An Optimal Parallel Algorithm for Selection Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book An Optimal Parallel Algorithm for Selection
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L. G. That log^n is an integer. Problem . Compute their sum. Algorithm . "Plant" a balanced binary tree with n leaves. Every node of the tree is denoted [h, j]. See Fig. 1. Leaf [0, j] corresponds to A(j). Associate a number B[h, j] with every node of the tree. Initialization . For all 1 < j < n pardo B [, j ] : = A( j ) . For h := 1 to^ log n for all 1 < j < 2^o§ ^ ~ ^ pardo B[h, j] := B[h-l, 2j-l] + B[h-l, 2j]. It is easy to verify that B[log n, I] holds the desired sum. Think first about an n processor implementation of this summation algorithm. It runs in O(log n) time. Then apply the proof of Brent's theorem to get an alternative implementation that uses only n/log n -7- processors and runs in O(log n) time. This summation algorithm can be extended to solve the following partial-sum problem. Input . As for the summation problem. Problem . Compute / A(j) for all 1 < i < n. Algorithm . Perform the summation algorithm given above. An additional "down-sweep" of the tree (from the root to the leaves), which roughly amounts to reversing the operation of the summation algorithm, will complete the job: Associate another number C[h, j] with each node [h, j].
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To quickly assess the difficulty of the text, read a short excerpt:
L. G. That log^n is an integer. Problem . Compute their sum. Algorithm . "Plant" a balanced binary tree with n leaves. Every node of the tree is denoted [h, j]. See Fig. 1. Leaf [0, j] corresponds to A(j). Associate a number B[h, j] with every node of the tree. Initialization . For all 1 < j < n pardo B [, j ] : = A( j ) . For h := 1 to^ log n for all 1 < j < 2^o§ ^ ~ ^ pardo B[h, j] := B[h-l, 2j-l] + B[h-l, 2j]. It is easy to verify that B[log n, I] holds the desired sum. Think first about an n processor implementation of this summation algorithm. It runs in O(log n) time. Then apply the proof of Brent's theorem to get an alternative implementation that uses only n/log n -7- processors and runs in O(log n) time. This summation algorithm can be extended to solve the following partial-sum problem. Input . As for the summation problem. Problem . Compute / A(j) for all 1 < i < n. Algorithm . Perform the summation algorithm given above. An additional "down-sweep" of the tree (from the root to the leaves), which roughly amounts to reversing the operation of the summation algorithm, will complete the job: Associate another number C[h, j] with each node [h, j].
What to read after An Optimal Parallel Algorithm for Selection?
You can find similar books in the "Read Also" column, or choose other free books by U Vishkin to read online
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