Abstract
Let S be a string over a finite, ordered alphabet Σ. For any substring S ′ of S, the set of distinct characters contained in S ′ is called its fingerprint. The text fingerprinting indexing problem is to construct a data structure for the string S in advance, so that on given any input subset C of Σ, we can answer the following queries efficiently: (1) determine if C represents a fingerprint of some substrings in S; (2) find all maximal substrings of S whose fingerprint is C. The best known results solved these two queries in Θ ( | Σ | ) and Θ ( | Σ | + K ) time, respectively, where K is the number of maximal substrings. In this paper, we propose two improved algorithms for the text fingerprinting indexing problem. The first one solves the two queries in O ( | C | log n ) and O ( | C | log n + K ) time, respectively. For the second one, the query time complexities are further reduced to O ( | C | log ( | Σ | / | C | ) ) and O ( | C | log ( | Σ | / | C | ) + K ) . Both results answer an open problem proposed by Amir et al.
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