On building minimal automaton for subset matching queries

TL;DR

This paper introduces a method for constructing minimal automata to efficiently answer subset matching queries on sets of strings with subset-labeled positions, with applications in biology and music retrieval.

Contribution

It presents a novel indexing technique for subset matching queries, achieving sub-quadratic average construction time based on alphabet and subset sizes.

Findings

Index construction in O(n^{log_{σ/Δ}(σ)} log n) average time

Efficient subset matching query answering

Applications in computational biology and music information retrieval

Abstract

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 $\sigma$, 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 $d \in D$ such that $p[i] \in d[i]$ for every $i$. We show how to build such index in $O(n^{\log_{\sigma/\Delta}(\sigma)}\log(n))$ average time, where $\Delta$ is the average size of the subsets. Our methods have applications e.g.\ in computational biology (haplotype inference) and music information retrieval.