Optimal on-line search and sublinear time update in string matching

We study in a dynamic setting the problem of online searching for the occurrences of an arbitrary pattern string P[1,p] in an indexed text string T[1,n]. That is, we assume that the text T may be updated by inserting or deleting an arbitrary string Y[1,y]. Our main contribution is presenting the first dynamic algorithm that achieves optimal time, i.e. Θ(p+occ), to find the occ occurrences of P, and sublinear time per update, i.e. O(√(n+y)), in the worst case. The required space is optimal Θ(n)