Faster algorithms for δ,γ-matching and related problems

Authors:
Peter Clifford;Raphaël Clifford;Costas Iliopoulos
Affiliations:
Department of Statistics, Oxford, UK;Algorithm Design Group, Department of Computer Science, King's College London, London, UK;Algorithm Design Group, Department of Computer Science, King's College London, London, UK
Venue:
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
Year:
2005

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Abstract

We present new faster algorithms for the problems of δ and (δ, γ)-matching on numeric strings. In both cases the running time of the proposed algorithms is shown to be O(δn log m), where m is the pattern length, n is the text length and δ a given integer. Our approach makes use of Fourier transform methods and the running times are independent of the alphabet size. $O(n\sqrt{m\log{m}})$ algorithms for the γ-matching and total-difference problems are also given. In all the above cases, we improve existing running time bounds in the literature.