Faster algorithms for δ,γ-matching and related problems

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√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. © Springer-Verlag Berlin Heidelberg 2005.