We introduce pairwise cardinality networks, networks of comparators, derived from pairwise sorting networks, which express cardinality constraints. We show that pairwise cardinality networks are superior to the cardinality networks introduced in previous work which are derived from odd-even sorting networks. Our presentation identifies the precise relationship between odd-even and pairwise sort...

We present new parallel sorting networks for 17 to 20 inputs. For 17, 19, and 20 inputs these new networks are faster (i.e., they require less computation steps) than the previously known best networks. Therefore, we improve upon the known upper bounds for minimal depth sorting networks on 17, 19, and 20 channels. Furthermore, we show that our sorting network for 17 inputs is optimal in the sen...

This paper describes a more efficient paired comparison method that reduces the number of trials necessary for converting a table of paired comparisons into scaler data. Instead of comparing every pair of samples (the complete method), a partial method is used that makes more comparisons between closer samples than between more distant samples. A sorting algorithm is used to efficiently order t...

We are introducing a new sorting algorithm.