Charge and reduce: A fixed-parameter algorithm for String-to-String Correction

  • Authors:

  • Faisal N. Abu-Khzam;Henning Fernau;Michael A. Langston;Serena Lee-Cultura;Ulrike Stege

  • Affiliations:

  • Department of Computer Science and Mathematics, Lebanese American University, Lebanon;Universität Trier, FB IV-Abteilung Informatik, D-54286 Trier, Germany;Department of Electrical Engineering and Computer Science, University of Tennessee, USA;Department of Computer Science, University of Victoria, Canada;Department of Computer Science, University of Victoria, Canada

  • Venue:
  • Discrete Optimization
  • Year:
  • 2011

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Abstract

String distance problems typically ask for a minimum number of permitted operations to transform one string into another. Such problems find application in a wide variety of areas, including error-correcting codes, parsing theory, speech recognition, and computational biology, to name a few. Here we consider a classic string distance problem, the NP-complete String-to-String Correction problem, first studied by Wagner some 35 years ago. In this problem, we are asked whether it is possible to transform string x into string y with at most k operations on x, where permitted operations are single-character deletions and adjacent character exchanges. We prove that String-to-String Correction is fixed-parameter tractable, for parameter k, and present a simple fixed-parameter algorithm that solves the problem in O(2^kn) time. We also devise a bounded search tree algorithm, and introduce a bookkeeping technique that we call charge and reduce. This leads to an algorithm whose running time is O(1.6181^kn).