sorting networks, adjacent transposition sorting, comparators, swaps, miniswaps, sweeps.
A miniswap Si,1 ≤ i < n, compares two adjacent keys Пi, Пi+1 in the sequence (П1, ... , Пn), and transposes them if they are out of order. A full sweep is any composition of all n - 1 possible miniswaps. We prove that the composition of any n- 1 full sweeps is a sorting function.
Li, Xue Shirley and Morris, F. Lockwood, "A Non-Deterministric Parallel Sorting Algorithm" (1992). Electrical Engineering and Computer Science Technical Reports. 176.