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Succinct indexes for strings, binary relations, and multi-labeled trees

By Jérémy Barbay, Meng He, J. Ian Munro and SRINIVASA RAO SATTI


We define and design succinct indexes for several abstract data types (ADTs). The concept is to design auxiliary data structures that ideally occupy asymptotically less space than the information-theoretic lower bound on the space required to encode the given data, and support an extended set of operations using the basic operators defined in the ADT. The main advantage of succinct indexes as opposed to succinct (integrated data/index) encodings is that we make assumptions only on the ADT through which the main data is accessed, rather than the way in which the data is encoded. This allows more freedom in the encoding of the main data. In this paper, we present succinct indexes for various data types, namely strings, binary relations and multi-labeled trees. Given the support for the interface of the ADTs of these data types, we can support various useful operations efficiently by constructing succinct indexes for them. When the operators in the ADTs are supported in constant time, our results are comparable to previous results, while allowing more flexibility in the encoding of the given data. Using our techniques, we design a succinct encoding that represents a string of length n over an alphabet of size σ using nHk(S)+lgσ·o(n)+O ( nlgσ lglglgσ) bits to support access/rank/select operations in o((lglgσ)1+ɛ) time, for any fixed constant ɛ> 0. We also design a succinct text index using nH0(S)+O ( nlgσ) bits that lglg

Topics: Categories and Subject Descriptors, E.1 [Data, Data Structures—Arrays, Trees, E.4 [Data, Coding and Information Theory—Data compaction and compression, F.2.2 [Analysis of Algorithms and Problem Complexity, Nonnumerical Algorithms and Problems—Computations on discrete structures, E.2 [Data, Data Storage Representations, H.3.1 [Information Storage and Retrieval, Content Analysis and Indexing— Indexing methods General Terms, Algorithms, Design, Theory The preliminary versi
Publisher: ACM/SIAM
Year: 2007
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
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