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

Faisal Abu Khzam, Henning Fernau, M Langston, S Lee-Cultura, Ulrike Stege

Research output: Contribution to journalArticle

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 NPcomplete 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 fixedparameter tractable, for parameter k, and present a simple fixed-parameter algorithm that solves the problem in O(2kn) 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(1.6181kn).
Original languageEnglish
Pages (from-to)41-49
Number of pages9
JournalDiscrete Optimization
Volume8
Issue number1
DOIs
Publication statusPublished - 2011
Externally publishedYes

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