# On the Construction of Classes of Suffix Trees for Square Matrices: Algorithms and Applications

@article{Giancarlo1996OnTC, title={On the Construction of Classes of Suffix Trees for Square Matrices: Algorithms and Applications}, author={Raffaele Giancarlo and Roberto Grossi}, journal={Inf. Comput.}, year={1996}, volume={130}, pages={151-182} }

Given an n × n TEXT matrix with entries defined over an ordered alphabet σ, we introduce 4n−1 classes of index data structures for TEXT. Those indices are informally the two-dimensional analog of the suffix tree of a string [15], allowing on-line searches and statistics to be performed on TEXT. We provide one simple algorithm that efficiently builds any chosen index in those classes in O(n2 log n) worst case time using O(n2) space. The algorithm can be modified to require optimal O(n2) expected…

## Figures from this paper

## 28 Citations

On-Line Construction of Two-Dimensional Suffix Trees in O(n2 log n) Time

- Computer ScienceAlgorithmica
- 2007

The main contribution in this paper is an O(log n) factor improvement in the time complexity of the GG algorithm, making it optimal for unbounded alphabets and leading to a major simplification of theGG algorithm.

A Simple Construction of Two-Dimensional Suffix Trees in Linear Time

- Computer Science, MathematicsCPM
- 2007

A new and simple algorithm to construct two-dimensional suffix trees in linear time by applying the skew scheme to square matrices is proposed.

Generalizations of suffix arrays to multi-dimensional matrices

- Computer ScienceTheor. Comput. Sci.
- 2003

Linear-Time Construction of Two-Dimensional Suffix Trees

- Computer ScienceICALP
- 1999

This work presents the first linear-time algorithm for constructing two-dimensional suffix trees, a compacted trie that represents all suffixes of S in two dimensions.

Optimal on-line search and sublinear time update in string matching

- Computer ScienceProceedings of IEEE 36th Annual Foundations of Computer Science
- 1995

This work is presenting the first dynamic algorithm that achieves optimal time to find the occ occurrences of P, and sublinear time per update, i.e. O(/spl radic/(n+y)), in the worst case.

The Burrows-Wheeler Transform : Ten Years Later

- Computer Science
- 2004

The FM-index is a succinct text index needing only O(Hkn) bits of space, with the constant factor depending only logarithmically on σ, which means in practice for all but very small alphabets, even with huge texts.

One-dimensional and multi-dimensional substring selectivity estimation

- Computer ScienceThe VLDB Journal
- 2000

This paper uses pruned count-suffix trees (PSTs) as the basic data structure for substring selectivity estimation and presents a novel technique called MO (Maximal Overlap), which is both practical and substantially superior to competing algorithms.

Multi-Dimensional Substring Selectivity Estimation

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- 1999

This paper develops a space and time eecient probabilis-tic algorithm to construct multi-dimensional pruned count-suux trees directly and demonstrates experimentally, using real data sets, that MO is substantially superior to GNO in the quality of the estimate.

A Note on a Tree-Based 2D Indexing

- Computer ScienceCIAA
- 2010

This work presents the transformation of 2D structures into the form of a tree, preserving the context of each element of the structure, and achieves the properties analogous to the results obtained in tree pattern matching and string indexing.

Two-dimensional pattern matching with rotations

- Computer ScienceTheor. Comput. Sci.
- 2004

An upper and lower bound on the number of such different possible rotated patterns is proved, given an m × m array and an n × n array over some finite alphabet Σ, yielding an O(n2m3) time algorithm for pattern matching with rotation.

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