In this paper, we present an O(1) time neural network with O(n(1+ε)) neurons and links to sort n data, ε > O. For large-size problems, it is desirable to have low-cost hardware solutions. In order to solve the sorting problem in constant time and with less hardware-cost, we adopt Leighton's column sort  as the main architecture. Then we use Chen and Hsieh's neural network  with O(n3) complexity as the lowest-level sub-networks. By using recursive techniques properly, we are able to explore constant-time, low-complexity neural sorting networks.
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