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arXiv · 1402.4867

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

Anke van Zuylen·James Bieron·Frans Schalekamp·Gexin Yu
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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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Anke van Zuylen, James Bieron, Frans Schalekamp, Gexin Yu. 2014-02-20. An Upper Bound on the Number of Circular Transpositions to Sort a Permutation. https://arxiv.org/abs/1402.4867

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