### Abstract

It is well known that n integers in the range [1, n^{c}] can be sorted in O(n) time in the RAM model using radix sorting. More generally, integers in any range [1, U] can be sorted in O(n√log log n) time [5]. However, these algorithms use O(n) words of extra memory. Is this necessary? We present a simple, stable, integer sorting algorithm for words of size O(log n), which works in O(n) time and uses only O(1) words of extra memory on a RAM model. This is the integer sorting case most useful in practice. We extend this result with same bounds to the case when the keys are read-only, which is of theoretical interest. Another interesting question is the case of arbitrary c. Here we present a black-box transformation from any RAM sorting algorithm to a sorting algorithm which uses only O(1) extra space and has the same running time. This settles the complexity of in-place sorting in terms of the complexity of sorting.

Original language | English (US) |
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Title of host publication | Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings |

Publisher | Springer Verlag |

Pages | 194-205 |

Number of pages | 12 |

ISBN (Print) | 9783540755197 |

DOIs | |

State | Published - 2007 |

Event | 15th Annual European Symposium on Algorithms, ESA 2007 - Eilat, Israel Duration: Oct 8 2007 → Oct 10 2007 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4698 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 15th Annual European Symposium on Algorithms, ESA 2007 |
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Country | Israel |

City | Eilat |

Period | 10/8/07 → 10/10/07 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings*(pp. 194-205). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4698 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-75520-3_19