Real-Time streaming multi-pattern search for constant alphabet

In the streaming multi-pattern search problem, which is also known as the streaming dictionary matching problem, a set D = {P1, P2, . . . , Pd} of d patterns (strings over an alphabet ∑), called the dictionary, is given to be preprocessed. Then, a text T arrives one character at a time and the goal is to report, before the next character arrives, the longest pattern in the dictionary that is a current suffix of T. We prove that for a constant size alphabet, there exists a randomized Monte-Carlo algorithm for the streaming dictionary matching problem that takes constant time per character and uses O(d logm) words of space, where m is the length of the longest pattern in the dictionary. In the case where the alphabet size is not constant, we introduce two new randomized Monte-Carlo algorithms with the following complexities: O(log log |∑|) time per character in the worst case and O(d logm) words of space. O( 1/ ϵ ) time per character in the worst case and O(d|∑|ϵ log m/ϵ ) words of space for any 0 < ϵ≤1. These results improve upon the algorithm of Clifford et al. [12] which uses O(d logm) words of space and takes O(log log(m + d)) time per character.