The longest common subsequence problem a finite automata approach

Authors:
Bořivoj Melichar;Tomá&scaron Polcar
Affiliations:
Department of Computer Science and Engineering, Faculty of Electrical Engineering, Czech Technical University, Prague 2, Czech Republic;Department of Computer Science and Engineering, Faculty of Electrical Engineering, Czech Technical University, Prague 2, Czech Republic
Venue:
CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
Year:
2003

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Abstract

A new algorithm that creates a common subsequence automaton for a set of strings is presented. Moreover, it is shown that a longest common subsequence of two strings over a constant alphabet can be found in O (|A| (|S1 + |S2| + Σa∈A|S1|a|S2|a)) time, where |A| is the size of the alphabet, |Si| is the length of the input string i, and |Si|a is the number of occurrences of a ∈ A in Si.