An AT2 optimal mapping of sorting onto the mesh connected array without comparators

We present a parallel SIMD algorithm for sorting of N numbers of log N bits each on a mesh connected array without comparators. While most previous AT²-optimal sorting algorithms on the mesh explicitly or implicitly assume O(1) time comparison of two operands of O(log N) bits, our algorithm does not require O(1) time comparison. Rather we assume O(log N) time comparison, which makes our algorithm realizable with current VLSI technology. To retain the AT² optimality with increased (by a factor of O(log N)) comparison time, we develop a new mapping technique which combines radix sort, shear sort, block merge and column sort in a creative way. The time complexity of sorting of N numbers on a (two-dimensional) mesh of size N^1/2×N^1/2 without comparators is O(N^1/2 )