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 \(O(n\sqrt{\log\log n})\) 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(logn), 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.
A full version of this paper is available as arXiv:0706.4107.
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© 2007 Springer-Verlag Berlin Heidelberg
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Franceschini, G., Muthukrishnan, S., Pǎtraşcu, M. (2007). Radix Sorting with No Extra Space. In: Arge, L., Hoffmann, M., Welzl, E. (eds) Algorithms – ESA 2007. ESA 2007. Lecture Notes in Computer Science, vol 4698. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75520-3_19
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DOI: https://doi.org/10.1007/978-3-540-75520-3_19
Publisher Name: Springer, Berlin, Heidelberg
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