title: Maximum independent sets of commuting and noninterfering inversions.
abstract: BACKGROUND
  Given three signed permutations, an inversion median is a fourth permutation that minimizes the sum of the pairwise inversion distances between it and the three others. This problem is NP-hard as well as hard to approximate. Yet median-based approaches to phylogenetic reconstruction have been shown to be among the most accurate, especially in the presence of long branches. Most existing approaches have used heuristics that attempt to find a longest sequence of inversions from one of the three permutations that, at each step in the sequence, moves closer to the other two permutations; yet very little is known about the quality of solutions returned by such approaches.
  
  
  RESULTS
  Recently, Arndt and Tang took a step towards finding longer such sequences by using sets of commuting inversions. In this paper, we formalize the problem of finding such sequences of inversions with what we call signatures and provide algorithms to find maximum cardinality sets of commuting and noninterfering inversions.
  
  
  CONCLUSIONS
  Our results offer a framework in which to study the inversion median problem, faster algorithms to obtain good medians, and an approach to study characteristic events along an evolutionary path.
authors.affiliation: Laboratory for Computational Biology and Bioinformatics, School of Computer and Communication Sciences, Ecole Polytechnique Fédérale de Lausanne, Switzerland. krister.swenson@epfl.ch
authors.forename: Krister M
authors.initials: KM
authors.lastname: Swenson
authors.forename: Yokuki
authors.initials: Y
authors.lastname: To
authors.forename: Jijun
authors.initials: J
authors.lastname: Tang
authors.forename: Bernard M E
authors.initials: BM
authors.lastname: Moret
mesh_terms: D000465:Algorithms; D007446:Chromosome Inversion; D019295:Computational Biology / Q000379:methods; D019143:Evolution, Molecular; D010802:Phylogeny