Analysis of Sort_Bitonic(X)
The bitonic sorting network needs log n number of phases for performing task of sorting the numbers. The first n-1 phases of circuit can sort two n/2 numbers and the last phase uses a +BM (n) comparator having the depth of log n. As running time of sorting relies upon the total depth of the circuit so it can be stated as:
D (n) = D (n/2) + log n
Solving above written recurrence relation
D (n) = (log^{2} n + log n)/2 = O (log^{2} n)
So the complexity of solving a sorting algorithm employing a combinational circuit is O (log^{2}n).
One more famous sorting algorithm called merge sort based algorithm can also be solved with help of combinational circuit.