On the complexity of min–max sorting networks

This paper extends previous work on sorting networks (SNs) based on min/max circuits. In particular, we have identified the complexity of both min/max-based sorting and merging networks showing that, depending on design choice, the time complexity of this kind of SN ranges from O(1) to O(log (n)) and spatial complexity from O(n2n) to O(n2), respectively. Moreover, we show that both AT and AT2 metrics of the proposed SN are better than those of Batcher’s SNs also for SNs with several hundreds of inputs. In addition to these results we show how to design a fast digital, serial, pipelined sorting network using FPGA technology. As expected, FPGA synthesis results confirm our theoretical analysis.