On the weak prefix-search problem

The weak-prefix search problem asks for the strings in a dictionary S that are prefixed by a pattern P[1, p], if any, otherwise it admits any answer. Strings in S have average length l, are n in number, and are given in advance to be preprocessed, whereas pattern P is provided on-line. In this paper we solve this problem in the cache-oblivious model by using the optimal O(n log l) bits of space and O(p/B + logB n) I/Os. The searching algorithm is of Monte-Carlo type, so its answer is correct with high probability. We also extend our algorithmic scheme to the case in which a probability distribution over the queried prefixes is known, and eventually address the deterministic case too.