Layout of the Batcher Bitonic Sorter

The grid-area required by a sorting net for input vectors of length N is shown to be at least (N ? 1) 2 =2. Of all sorting nets which use o(N 2) comparators, the bitonic sorting net of Batcher has been known to have a layout of O(N 2), but the hidden constant factor has not been investigated. A straightforward use of known techniques leads to a layout of grid-area 20:25N 2. We present area-eecient layouts of the bitonic sorter. First, we describe a ip-bitonic sorting net { it is isomorphic to Batcher's bitonic sorter but leads naturally to a layout of grid-area less than 4N 2. Second, we present a butterry-based layout of the bitonic sorter with grid-area of 3N 2 + O(N). The former does not use knock-knees while the latter relies on them and is more compact.