Alphabet independent two dimensional matching

There are many solutions to the string matching problem which are strictly linear in the input size and independent of alphabet size. Furthermore, the model of computation for these algorithms is very weak: they allow only simple arithmetic and comparisons of equality between characters of the input. In contrast, algorithm for two dimensional matching have needed stronger models of computation, most notably assuming a totally ordered alphabet. The fastest algorithms for two dimensional matching have therefore had a logarithmic dependence on the alphabet size. In the worst case, this gives an algorithm that runs in O(n² log m) with O(m² log m) preprocessing. We show an algorithm for two dimensional matching with an O(n²) text scanning phase. Furthermore, the text scan requires no special assumptions about the alphabet, i.e. it runs on the same model as the standard linear time string matching algorithm.