The Zooming Method: A Recursive Approach to Time-Space Efficient String-Matching

A new approach to time-space eecient string-matching is presented. The method is exible, its implementation depends whether or not the alphabet is linearly ordered. The only known linear-time constant-space algorithm for string-matching over nonordered alphabets is the Galil-Seiferas algorithm, see 8, 6] which is rather complicated. The zooming method gives probably the simplest string-matching algorithm working in constant space and linear time for nonordered alphabets. The novel feature of our algorithm is the application of the searching phase (which is usually simpler than preprocessing) in the preprocessing phase. The preprocessing has a recursive structure similar to selection in linear time, see 1]. For ordered alphabets the preprocessing part is much simpler, its basic component is a simple and well-known algorithm for nding the maximal suux, see 7]. Hence we demonstrate a new application of this algorithm, see also 5]. The idea of the zooming method was applied in 4] to two dimensional patterns.