Sorting Circular Permutations by Bounded Transpositions

@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}
}
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