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 language | English |
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Pages (from-to) | 41-49 |
Number of pages | 9 |
Journal | Discrete Optimization |
Volume | 8 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2011 |
Externally published | Yes |