An Upper Bound on the Number of Circular Transpositions to Sort a Permutation release_y352bmohnbfvxl6mjhpy5dmdpe

by Anke van Zuylen, James Bieron, Frans Schalekamp, Gexin Yu

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2014  

Abstract

We consider the problem of upper bounding the number of circular transpositions needed to sort a permutation. It is well known that any permutation can be sorted using at most n(n-1)/2 adjacent transpositions. We show that, if we allow all adjacent transpositions, as well as the transposition that interchanges the element in position 1 with the element in the last position, then the number of transpositions needed is at most n^2/4. This answers an open question posed by Feng, Chitturi and Sudborough (2010).
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Date   2014-02-20
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arXiv  1402.4867v1
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