Quicksort with median of medians is considered practical

Quicksort[2, 1, 3] is one of the most efficient and widely used sorting algorithms. The major drawback of quicksort is that worst case time complexity of naive implementations of quicksort is O(n2) with input size n. In order to avoid this worst case behavior, a variant of quicksort, so-called introsort[4] 1 , is often used. There exists another solution to keep the worst case complexity of quicksort O(n ln n). This is the use of median-of-medians or Blum-Floyd-Pratt-Rivest-Tarjan (BFPRT) algorithm — the pivot selection algorithm in the linear median finding algorithm[6]. Despite the theoretical importance of this scheme, because of its somewhat large constant factor, this method have been considered impractical to use as a pivot selection algorithm in quicksort. In this article, contrary to the above widespread view, we show that using BFPRT in quicksort is not inefficient, and moreover, considered practical. Indeed, we find that quicksort with median-of-medians shows comparable performance to the well-known optimized quicksort implementations[7, 8] for random sequence. We also show that the technique for improving performance is not only for the BFPRT but also available for other pivoting methods.