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arXiv · 1012.0280

String Matching with Inversions and Translocations in Linear Average Time (Most of the Time)

Szymon Grabowski·Simone Faro·Emanuele Giaquinta
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Abstract

We present an efficient algorithm for finding all approximate occurrences of a given pattern $p$ of length $m$ in a text $t$ of length $n$ allowing for translocations of equal length adjacent factors and inversions of factors. The algorithm is based on an efficient filtering method and has an $\bigO(nm\max(\alpha, \beta))$-time complexity in the worst case and $\bigO(\max(\alpha, \beta))$-space complexity, where $\alpha$ and $\beta$ are respectively the maximum length of the factors involved in any translocation and inversion. Moreover we show that under the assumptions of equiprobability and independence of characters our algorithm has a $\bigO(n)$ average time complexity, whenever $\sigma = \Omega(\log m / \log\log^{1-\epsilon} m)$, where $\epsilon > 0$ and $\sigma$ is the dimension of the alphabet. Experiments show that the new proposed algorithm achieves very good results in practical cases.

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Szymon Grabowski, Simone Faro, Emanuele Giaquinta. 2010-12-01. String Matching with Inversions and Translocations in Linear Average Time (Most of the Time). https://doi.org/10.1016/j.ipl.2011.02.015

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