An FPT Algorithm for STRING-TO-STRING CORRECTION

Date

2011-08-24

Authors

Lee-Cultura, Serena Glyn

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Abstract

Parameterized string correction decision problems investigate the possibility of transforming a given string X into a target string Y using a fixed number of edit operations, k. There are four possible edit operations: swap, delete, insert and substi- tute. In this work we consider the NP--complete STRING-TO-STRING CORREC- TION problem restricted to deletes and swaps and parameterized by the number of allowed operations. Specifically, the problem asks whether there exists a trans- formation from X into Y consisting of at most k deletes or swaps. We present a fixed parameter algorithm that runs in O(2k(k + m)), where m is the length of the destination string. Further, we present an implementation of an extended version of the algorithm that constructs the transformation sequence ! of length ay most k, given its existence. This thesis concludes with a discussion comparing the practical run times obtained from our implementation with the proposed theoretical results. Efficient string correction algorithms have applications in several areas, for example computational linguistics, error detection and correction, and computational biology.

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Keywords

String Correction, Swaps and Deletes, fpt Algorithm

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