A neural network with O(N) neurons for ranking N numbers in O(1/N) time

In this paper, we propose a neural network for ranking a given set of N numbers in O(1/N) time. The ordering of a set of numbers based on their relative magnitudes, which is analogous to sorting, is a fundamental operation in many algorithms. In comparison with other sorting networks reported in the literature, the proposed network requires fewer neurons, and fewer interconnections between neurons. The interconnections use nonlinear synapses which are composed of comparators, and do not require any weighted interconnections between neurons, as used in conventional neural networks. The proposed network has many applications, including as a component of self-organizing feature maps and other systems where sorting is a frequent operation.