Periodic Sorting

Let and be a partition of f1; : : : ; ng 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 x 1 ; x 2 ; : : : ; x n is such that the subse-quence in the positions and the subsequence in the positions are each sorted, the output sequence will be sorted. We study the class of \recursively constructed" merging networks and characterize those with delay dlog 2 ne (the best possible delay for all merging networks). When n is a power of 2, we show that at least 3 n=2?1 of these nets are log-periodic sorters; that is, they sort any input sequence after log 2 n passes through the net. (Two of these have appeared previously in the literature.)