sorting problem

Let be a total ordering on the set S. Given a sequence of n elements, x1,x2,,xnS, find a sequence of distinct indices 1i1,i2,,inn such that xi1xi2xin.

The sorting problem is a heavily studied area of computer science, and many sorting algorithms exist to solve it. The most general algorithmsMathworldPlanetmath depend only upon the relationMathworldPlanetmath , and are called comparison-based sorts. It can be proved that the lower bound for sorting by any comparison-based sorting algorithm is Ω(nlogn).

A few other specialized sort algorithms rely on particular properties of the values of elements in S (such as their structureMathworldPlanetmath) in order to achieve lower time complexity for sorting certain sets of elements. Examples of such a sorting algorithm are the bucket sort and the radix sort.

Title sorting problem
Canonical name SortingProblem
Date of creation 2013-03-22 11:43:37
Last modified on 2013-03-22 11:43:37
Owner Logan (6)
Last modified by Logan (6)
Numerical id 10
Author Logan (6)
Entry type Algorithm
Classification msc 68P10
Classification msc 82C35
Related topic TotalOrder
Related topic PartialOrder
Related topic Relation
Related topic HeapsortMathworldPlanetmath
Related topic Bubblesort
Related topic BinarySearch
Related topic InPlaceSortingAlgorithm
Related topic InsertionSort
Related topic LandauNotation
Related topic QuicksortMathworldPlanetmath
Related topic SelectionSort