Statistical bound of bubble sort algorithm in serial and parallel computations

In some recent papers, the weight based statistical bounds have arguably explained time complexity better than the count based mathematical bounds. Sorting has been a profound area for the algorithmic researchers and many resources are invested to suggest more works for sorting algorithms. In this paper we conceptually study the, bubble sort algorithms and were observed in terms of the efficiency of the algorithmic complexity. It found that the parallel bubble sort gives the better processor utilization, load balancing and algorithmic efficiency.