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Adjacent Swaps on Strings

  • Bhadrachalam Chitturi
  • Hal Sudborough
  • Walter Voit
  • Xuerong Feng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)

Abstract

Transforming strings by exchanging elements at bounded distance is applicable in fields like molecular biology, pattern recognition and music theory. A reversal of length two at position i is denoted by (i i+1). When it is applied to π, where π = π 1,π 2, π 3,..., π i ,π i + 1, π n , it transforms π to π′, where π′ = π 1,π 2, π 3,..., π i − 1,π i + 1, π i , π i + 1, ..., π n . We call this operation an adjacent swap. We study the problem of computing the minimum number of adjacent swaps needed to transform one string of size n into another compatible string over an alphabet σ of size k, i.e. adjacent swap distance problem. O(nlog 2 n) time complexity algorithms are known for adjacent swap distance. We give an algorithm with O(nk) time for both signed and unsigned versions of this problem where k is the number of symbols. We also give an algorithm with O(nk) time for transforming signed strings with reversals of length up to 2, i.e. reversals of length 1 or 2.

Keywords

Optimum Pairing Intersection Count Circular Permutation Signed String Head Pointer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Bhadrachalam Chitturi
    • 1
  • Hal Sudborough
    • 1
  • Walter Voit
    • 1
  • Xuerong Feng
    • 2
  1. 1.University of Texas at DallasRichardsonUSA
  2. 2.Valdosta State UniversityValdostaUSA

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