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 3 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 the electronic journal of combinatorics 5 (1998), #R5 2