A New Compressed Suffix Tree Supporting Fast Search and Its Construction Algorithm Using Optimal Working Space

@inproceedings{Kim2005ANC,
  title={A New Compressed Suffix Tree Supporting Fast Search and Its Construction Algorithm Using Optimal Working Space},
  author={Dong Kyue Kim and Heejin Park},
  booktitle={CPM},
  year={2005}
}
The compressed suffix array and the compressed suffix tree for a given string S are full-text index data structures occupying O(nlog|Σ|) bits where n is the length of S and Σ is the alphabet from which symbols of S are drawn. When they were first introduced, they were constructed from suffix arrays and suffix trees, which implies they were not constructed in optimal O(nlog|Σ|)-bit working space. Recently, several methods were developed for constructing compressed suffix arrays and compressed… 
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References

SHOWING 1-10 OF 39 REFERENCES
Compressed suffix arrays and suffix trees with applications to text indexing and string matching (extended abstract)
TLDR
An index structure is constructed that occupies only O(n) bits and compares favorably with inverted lists in space and achieves optimal O(m/log n) search time for sufficiently large m = ~(log a+~ n).
An Efficient Index Data Structure with the Capabilities of Suffix Trees and Suffix Arrays for Alphabets of Non-negligible Size
TLDR
The enhance suffix array is considered, which is almost as time/space-efficient as the suffix array but loses the capabilities of the suffix tree when the size of the alphabet is not negligible.
A Fast Algorithm for Constructing Suffix Arrays for Fixed-Size Alphabets
TLDR
This paper presents a fast algorithm for constructing suffix arrays for the fixed-size alphabet that constructs suffix arrays faster than any other algorithms developed for integer or general alphabets when the size of the alphabet is fixed.
Simple Linear Work Suffix Array Construction
TLDR
The skew algorithm for suffix array construction over integer alphabets that can be implemented to run in linear time using integer sorting as its only nontrivial subroutine is introduced.
Space Efficient Suffix Trees
TLDR
The development of techniques to use the succinct tree representation through balanced parentheses for suffix trees and several index structures for binary texts, with less space are given.
A Space and Time Efficient Algorithm for Constructing Compressed Suffix Arrays
TLDR
This paper initiates the study of constructing compressed suffix arrays directly from the text with a construction algorithm that uses only O(n) bits of working memory, and the time complexity is O( n log n).
A Space and Time Efficient Algorithm for Constructing Compressed Suffix Arrays
TLDR
This paper initiates the study of constructing compressed suffix arrays directly from text with the main contribution is a new construction algorithm that uses only O(n) bits of working memory, and more importantly, the time complexity remains the same as before.
Space Efficient Linear Time Construction of Suffix Arrays
TLDR
This work presents a linear time algorithm to sort all the suffixes of a string over a large alphabet of integers, which improves upon the best known direct algorithm for suffix sorting, which takes O(n log n) time.
On the sorting-complexity of suffix tree construction
TLDR
A recursive technique for building suffix trees that yields optimal algorithms in different computational models that match the sorting lower bound and for an alphabet consisting of integers in a polynomial range the authors get the first known linear-time algorithm.
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