## A tight upper bound on the number of cyclically adjacent transpositions to sort a permutation

- Anke van Zuylen, James Bieron, Frans Schalekamp, Gexin Yu
- Inf. Process. Lett.
- 2016

Highly Influenced

@article{Feng2009SortingCP, title={Sorting Circular Permutations by Bounded Transpositions}, author={Xuerong Feng and Bhadrachalam Chitturi and Chunlei Liu}, journal={Advances in experimental medicine and biology}, year={2009}, volume={680}, pages={725-36} }

- Published 2009 in BIOCOMP
DOI:10.1007/978-1-4419-5913-3_81

A k-bounded (k ≥ 2) transposition is an operation that switches two elements that have at most k - 2 elements in between. We study the problem of sorting a circular permutation π of length n for k = 2, i.e., adjacent swaps and k = 3, i.e., short swaps. These transpositions mimic microrearrangements of gene order in viruses and bacteria. We prove a (1/4)n (2) lower bound for sorting by adjacent swaps. We show upper bounds of (5/32)n (2) + O(n log n) and (7/8)n + O(log n) for sequential and… CONTINUE READING