# Parallel Construction and Query of Index Data Structures for Pattern Matching on Square Matrices

@article{Giancarlo1999ParallelCA, title={Parallel Construction and Query of Index Data Structures for Pattern Matching on Square Matrices}, author={Raffaele Giancarlo and Roberto Grossi}, journal={J. Complex.}, year={1999}, volume={15}, pages={30-71} }

We describe fast parallel algorithms for building index data structures that can be used to gather various statistics on square matrices. The main data structure is the Lsuffix tree, which is a generalization of the classical suffix tree for strings. Given ann×ntext matrixA, we build our data structures inO(logn) time withn2processors on a CRCW PRAM, so that we can quickly processAin parallel as follows: (i) report some statistical information aboutA, e.g., find the largest repeated square…

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SHOWING 1-10 OF 61 REFERENCES

Multi-Dimensional Pattern Matching with Dimensional Wildcards: Data Structures and Optimal On-Line Search Algorithms

- Computer ScienceJ. Algorithms
- 1997

A new multidimensional pattern matching problem that is a natural generalization of string matching, a well studied problem, and derives the first efficient sequential algorithms for the new problem.

An Index Data Structure For Matrices, with Applications to Fast Two-Dimensional Pattern Matching

- Computer ScienceWADS
- 1993

It is shown that the s-trees are optimal for space and within a log factor optimal for time.

Suffix arrays: a new method for on-line string searches

- Computer ScienceSODA '90
- 1990

A new and conceptually simple data structure, called a suffixarray, for on-line string searches is introduced in this paper, and it is believed that suffixarrays will prove to be better in practice than suffixtrees for many applications.

Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions

- Computer ScienceProceedings of 1993 IEEE 34th Annual Foundations of Computer Science
- 1993

An algorithm that computes a deterministic sample of a sufficiently long substring in constant time for string matching, solving the main open problem remaining in string matching.

Parallel Suffix-Prefix-Matching Algorithm and Applications

- Computer ScienceSIAM J. Comput.
- 1996

The techniques and algorithms are the first to preserve optimal speedup in the context of pattern matching in higher dimensions and are the only known ones to do so for dimensions $d > 2$.

A Generalization of the Suffix Tree to Square Matrices, with Applications

- Computer ScienceSIAM J. Comput.
- 1995

A new data structure is described, the Lsuffix tree, which generalizes McCreight's suffix tree for a string to a square matrix and gives efficient algorithms for the static versions of the following dual problems that arise in low-level image processing and visual databases.

On the Parallel Dynamic Dictionary Matching Problem: New Results with Applications

- Computer ScienceESA
- 1996

This paper provides the first parallel algorithm for the DDM problem which achieves optimal (amortized) work for the update operations in the case of both a constant sized and an unbounded alphabet.

A fast parallel algorithm to determine edit distance

- Computer Science
- 1988

An algorithm that runs in <9(logmlogrt) time and uses mn processors on a CRCW PRAM, where m and n are the lengths of the strings and the largest common submatrix of two matrices is considered and shown to be NP-hard.

Augmenting Suffix Trees, with Applications

- Computer ScienceESA
- 1998

This paper considers one algorithmic problem from each of these areas and presents highly efficient (linear or near linear time) algorithms for both problems, relying on augmenting the suffix tree, a fundamental data structure in string algorithmics.