Randomized Median Finding and Quicksort

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 qui...

How Branch Mispredictions Affect Quicksort

We explain the counterintuitive observation that finding “good” pivots (close to the median of the array to be partitioned) may not improve performance of quicksort. Indeed, an intentionally skewed pivot improves performance. The reason is that while the instruction count decreases with the quality of the pivot, the likelihood that the direction of a branch is mispredicted also goes up. We anal...

A Noble Randomized Quicksort with a Random Number Generator

Sorting is a well-known computational problem. Sorting means arranging a set of records (or a list of keys) in some (increasing or decreasing) order. Randomized algorithms often have low complexity and are associated to robustness bounds, which are generally less conservative than the classical ones. This paper presents a noble randomized Quicksort with a random number generator. This randomize...

Chapter 13 Introduction to Randomized Algorithms: QuickSort and QuickSelect

Introduction to Randomized Algorithms: QuickSort and QuickSelect

QuickSort Hoare [1962] (A) Pick a pivot element from array (B) Split array into 3 subarrays: those smaller than pivot, those larger than pivot, and the pivot itself. (C) Recursively sort the subarrays, and concatenate them. Randomized QuickSort (A) Pick a pivot element uniformly at random from the array (B) Split array into 3 subarrays: those smaller than pivot, those larger than pivot, and the...