By Fănică Gavril
Communications of the ACM,
October 1975,
Vol. 18 No. 10, Pages 588-591
10.1145/361020.361216
Comments
Consider two linearly ordered sets A, B, | A | = m, | B | = n, m ≤ n, and p, p ≤ m, parallel processors working synchronously. The paper presents an algorithm for merging A and B with the p parallel processors, which requires at most 2⌈log2(2m + 1)⌉ + ⌊3m/p⌋ + [m/p][log2(n/m)] steps. If n = 2&bgr;m (&bgr; an integer), the algorithm requires at most 2[log2(m + 1)] + [m/p](2 + &bgr;) steps. In the case where m and n are of the same order of magnitude, i.e. n = km with k being a constant, the algorithm requires 2[log2(m + 1)] + [m/p](3 + k) steps. These performances compare very favorably with the previous best parallel merging algorithm, Batcher's algorithm, which requires n/p + ((m + n)/2p)log2m steps in the general case and km/p + ((k + 1)/2)(m/p)log2m in the special case where n = km.
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