A simple parallel cartesian tree algorithm and its application to parallel suffix tree construction

2014 ◽  
Vol 1 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Julian Shun ◽  
Guy E. Blelloch
Keyword(s):  
Suffix Tree ◽  
Tree Algorithm ◽  
Tree Construction ◽  
Cartesian Tree

Suffix Tree Data Structures for Matrices

1997 ◽  
Author(s):  
R. Giancarlo ◽  
R. Grossi
Keyword(s):  
Linear Space ◽  
Suffix Tree ◽  
Linear Time ◽  
Suffix Trees ◽  
Construction Time ◽  
Matching Problems ◽  
Tree Construction ◽  
The Matrix ◽  
Visual Databases ◽  
Efficient Construction

We discuss the suffix tree generalization to matrices in this chapter. We extend the suffix tree notion (described in Chapter 3) from text strings to text matrices whose entries are taken from an ordered alphabet with the aim of solving pattern-matching problems. This suffix tree generalization can be efficiently used to implement low-level routines for Computer Vision, Data Compression, Geographic Information Systems and Visual Databases. We examine the submatrices in the form of the text’s contiguous parts that still have a matrix shape. Representing these text submatrices as “suitably formatted” strings stored in a compacted trie is the rationale behind suffix trees for matrices. The choice of the format inevitably influences suffix tree construction time and space complexity. We first deal with square matrices and show that many suffix tree families can be defined for the same input matrix according to the matrix’s string representations. We can store each suffix tree in linear space and give an efficient construction algorithm whose input is both the matrix and the string representation chosen. We then treat rectangular matrices and define their corresponding suffix trees by means of some general rules which we list formally. We show that there is a super-linear lower bound to the space required (in contrast with the linear space required by suffix trees for square matrices). We give a simple example of one of these suffix trees. The last part of the chapter illustrates some technical results regarding suffix trees for square matrices: we show how to achieve an expected linear-time suffix tree construction for a constant-size alphabet under some mild probabilistic assumptions about the input distribution. We begin by defining a wide class of string representations for square matrices. We let Σ denote an ordered alphabet of characters and introduce another alphabet of five special characters, called shapes. A shape is one of the special characters taken from set {IN,SW,NW,SE,NE}. Shape IN encodes the 1x1 matrix generated from the empty matrix by creating a square.

OPTIMAL PARALLEL CONSTRUCTION OF MINIMAL SUFFIX AND FACTOR AUTOMATA

1996 ◽  
Vol 06 (01) ◽  
pp. 35-44 ◽  
Author(s):  
DANY BRESLAUER ◽  
RAMESH HARIHARAN
Keyword(s):  
Parallel Algorithms ◽  
Data Structures ◽  
Suffix Tree ◽  
Finite Automata ◽  
Suffix Trees ◽  
Deterministic Finite Automata ◽  
Tree Construction ◽  
Parallel Construction ◽  
Construction Algorithms

This paper gives optimal parallel algorithms for the construction of the smallest deterministic finite automata recognizing all the suffixes and the factors of a string. The algorithms use recently discovered optimal parallel suffix tree construction algorithms together with data structures for the efficient manipulation of trees, exploiting the well known relation between suffix and factor automata and suffix trees.

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