Periodic Sorting Using Minimum Delay, Recursively Constructed Merging Networks

Let α and β be a partition of {1, . . . , n} into two blocks. A merging network is a network of comparators which allows as input arbitrary real numbers and has the property that, whenever the input sequence x1, x2, . . . , xn is such that the subsequence in the positions α and the subsequence in the positions β are each sorted, the output sequence will be sorted. We study the class of “recursively constructed” merging networks and characterize those with delay log2 n (the best possible delay for all merging networks). When n is a power of 2, we show that at least 3n/2−1 of these nets are log-periodic sorters; that is, they sort any input sequence after log2 n passes through the net. (Two of these have appeared previously in the literature.) 1991 AMS Classification Number. Primary: 68P10 

• Type: Journal
• Year: 1998
• Where: COMBINATORICS
• Authors: Edward A. Bender, S. Gill Williamson
• Keywords: Arbitrary Real Numbers, COMBINATORICS 1998, Input Sequence, Output Sequence