Two notes on genome rearrangement. Ozery-Flato, M. and Shamir, R. J Bioinform Comput Biol, 1(1):71–94, 2003.
abstract   bibtex   
A central problem in genome rearrangement is finding a most parsimonious rearrangement scenario using certain rearrangement operations. An important problem of this type is sorting a signed genome by reversals and translocations (SBRT). Hannenhalli and Pevzner presented a duality theorem for SBRT which leads to a polynomial time algorithm for sorting a multi-chromosomal genome using a minimum number of reversals and translocations. However, there is one case for which their theorem and algorithm fail. We describe that case and suggest a correction to the theorem and the polynomial algorithm. The solution of SBRT uses a reduction to the problem of sorting a signed permutation by reversals (SBR). The best extant algorithms for SBR require quadratic time. The common approach to solve SBR is by finding a safe reversal using the overlap graph or the interleaving graph of a permutation. We describe a family of signed permutations which proves a quadratic lower bound on the number of affected vertices in the overlap/interleaving graph during any optimal sorting scenario. This implies, in particular, an Omega(n3) lower bound for Bergeron's algorithm.
@Article{ozery-flato03two,
  author    = {Michal Ozery-Flato and Ron Shamir},
  title     = {Two notes on genome rearrangement.},
  journal   = {J Bioinform Comput Biol},
  year      = {2003},
  volume    = {1},
  number    = {1},
  pages     = {71--94},
  abstract  = {A central problem in genome rearrangement is finding a most parsimonious rearrangement scenario using certain rearrangement operations. An important problem of this type is sorting a signed genome by reversals and translocations (SBRT). Hannenhalli and Pevzner presented a duality theorem for SBRT which leads to a polynomial time algorithm for sorting a multi-chromosomal genome using a minimum number of reversals and translocations. However, there is one case for which their theorem and algorithm fail. We describe that case and suggest a correction to the theorem and the polynomial algorithm. The solution of SBRT uses a reduction to the problem of sorting a signed permutation by reversals (SBR). The best extant algorithms for SBR require quadratic time. The common approach to solve SBR is by finding a safe reversal using the overlap graph or the interleaving graph of a permutation. We describe a family of signed permutations which proves a quadratic lower bound on the number of affected vertices in the overlap/interleaving graph during any optimal sorting scenario. This implies, in particular, an Omega(n3) lower bound for Bergeron's algorithm.},
  file      = {Ozery-FlatoShamir_TwoNotesGenomeRearrangement_JBioinformComputBiol_2003.pdf:2003/Ozery-FlatoShamir_TwoNotesGenomeRearrangement_JBioinformComputBiol_2003.pdf:PDF},
  keywords  = {Gene Rearrangement; Genomics; Translocation, Genetic},
  optmonth  = apr,
  owner     = {truss},
  pmid      = {15290782},
  timestamp = {2006.12.20},
}
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