String matching with inversions and translocations in linear average time (most of the time)

Authors:
Szymon Grabowski;Simone Faro;Emanuele Giaquinta
Affiliations:
Technical University of Łód, Computer Engineering Department, Al. Politechniki 11, 90-924 Łód, Poland;Universití di Catania, Dipartimento di Matematica e Informatica, Viale Andrea Doria 6, I-95125 Catania, Italy;Universití di Catania, Dipartimento di Matematica e Informatica, Viale Andrea Doria 6, I-95125 Catania, Italy
Venue:
Information Processing Letters
Year:
2011

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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 O(nmmax(@a,@b))-time complexity in the worst case and O(max(@a,@b,@s))-space complexity, where @a and @b are respectively the maximum length of the factors involved in any translocation and inversion, and @s is the alphabet size. Moreover we show that our algorithm has an O(n) average time complexity, whenever @s=@W(logm/loglog^1^-^@em), for @e0. Experiments show that the proposed algorithm achieves very good results in practical cases.