Lower Bounds on Merging Networks

Andrew Chi-Chih Yao, Foong Frances Yao

Abstract: Let M(m, n) be the minimum number or comparators needed in an (m, n)-merging network. It is shown that M(m, n) ≥ n(lg(m + 1))/2, which implies that Batcher's merging networks are optimal up to a factor of 2 + ε for almost all values of m and n. The limit rm = limn→∞ M(m, n)/n is determined to within 1. It is also proved that M(2, n) = [3n/2].