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On building minimal automaton for subset matching queries. (English) Zbl 1379.68371
Summary: 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.
MSC:
68W32 Algorithms on strings
68P20 Information storage and retrieval of data
68Q45 Formal languages and automata
Software:
PATRICIA
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