On building minimal automaton for subset matching queries

We address the problem of building an index for a set D of n strings, where each string location is a subset of some finite integer alphabet of size σ, so that we can answer efficiently if a given simple query string (where each string location is a single symbol) p occurs in the set. That is, we need to efficiently find a string d ∈ D such that p[i] ∈ d[i] for every i. We show how to build such index in O(nσ/∆ log(n)) average time, where ∆ is the average size of the subsets. Our methods have applications e.g. in computational biology (haplotype inference) and music information retrieval.