stable sorting algorithm

A stable sorting algorithm is any sorting algorithm that preserves the relative ordering of items with equal values. For instance, consider a list of ordered pairs

$L:=\{(A,3),(B,5),(C,2),(D,5),(E,4)\}.$

If a stable sorting algorithm sorts $L$ on the second value in each pair using the $\le$ relation, then the result is guaranteed to be $\{(C,2),(A,3),(E,4),(B,5),(D,5)\}$. However, if an algorithm is not stable, then it is possible that $(D,5)$ may come before $(B,5)$ in the sorted output.

Some examples of stable sorting algorithms are bubblesort and mergesort (although the stability of mergesort is dependent upon how it is implemented). Some examples of unstable sorting algorithms are heapsort and quicksort (quicksort could be made stable, but then it wouldn’t be quick any more). Stability is a useful property when the total ordering relation is dependent upon initial position. Using a stable sorting algorithm means that sorting by ascending position for equal keys is built-in, and need not be implemented explicitly in the comparison operator.

Title	stable sorting algorithm
Canonical name	StableSortingAlgorithm
Date of creation	2013-03-22 12:31:04
Last modified on	2013-03-22 12:31:04
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	9
Author	mathcam (2727)
Entry type	Definition
Classification	msc 68P10
Synonym	stable algorithm
Related topic	Bubblesort
Defines	unstable sorting algorithm