Supersaturated Paracomputer Algorithms

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Supersaturated Paracomputer Algorithms
Clyde Kruskal
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(1) Create an array C of size N initialized to 0.
(2) Count how many items have each value by incrementing Page 17 (via replace-add) C(A(i)) for all i e {1, ... , N}.
(3) Apply integer summing to C and then set D(i) = C(i-l) (and D(l) = 0), so that D(i) is the number of items less than i.
(4) Copy A into a temporary array T.
(5) The final location j of the ith original item is obtained as replace-add (D (T ( i )), 1 ) . Set A(j) equal to T(i) .
To illustrate this algorithm consider the problem
...of sorting the array A = (2, 1, 5, 3, 2). After step (2) above C = (1, 2, 1, 0, 1), where C(i) is the number of items with value i (e. G. Two items have value 2 and no items have value 4). At step (3) summing is applied to transform C into (1, 3, 4, 4, 5); C(i) now represents the number of items less than or equal to i. D = (0, 1, 3, 4, 4) is derived from C by shifting the values of C right one position and represents the number of items less than i. At step (4) A is copied into T. Finally at step (5) the ith item of T determines its final location by r eplace-adding 1 to D(T(i)).

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