Faster algorithms for &delta, &gamma matching and related problemsP. Clifford, Raphael Clifford, C. S. Iliopoulos, Faster algorithms for &delta, &gamma matching and related problems. Proceedings of the 16th Annual Symposium on Combinatorial Pattern Matching (CPM). ISBN 3-540-26201-6, pp. 68–78. April 2005. No electronic version available.
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(δ n 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.