Computing rearrangement distance of every permutation in the symmetric group

Authors:
Gustavo Rodrigues Galvão;Zanoni Dias
Affiliations:
University of Campinas - Unicamp, Campinas, São Paulo, Brazil;University of Campinas - Unicamp, Campinas, São Paulo, Brazil
Venue:
Proceedings of the 2011 ACM Symposium on Applied Computing
Year:
2011

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Abstract

We consider the problem of computing rearrangement distance of every permutation in the symmetric group Sn and present a simple algorithm for doing it. By analysing the rearrangement distance distribution computed for different scenarios, we were able to correct the reversal distance distribution given by Kececioglu and Sankoff; disprove a conjecture of Walter, Dias and Meidanis on signed reversal and transposition diameter; and reinforce the conjecture of Dias and Meidanis on prefix transposition diameter. As an attempt to better characterize how rearrangement distances are distributed, two new measures are introduced: the traversal diameter and the longevity. We conjecture results on them and on the diameter of some rearrangement distances.