Area efficient layouts of the Batcher sorting networks

In the early 1980s, the grid area required by the sorting nets of Batcher for input vectors of length N was investigated by Thompson. He showed that the Ω(N2) area was necessary and sufficient, but the hidden constant factors, both for the lower and upper bounds, were not discussed. In this paper, a lower bound of (N − 1)2/2 is proven, for the area required by any sorting network. Upper bounds of 4N2 and 3N2 are shown for the bitonic sorter and the odd—even sorter, respectively. In the layouts, which are presented to establish these upper bounds, slanted lines are used and there are no knock‐knees. © 2001 John Wiley & Sons, Inc.