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.

scholarly journals Optimal Parallel Construction of Minimal Suffix and Factor Automata

1995 ◽  
Vol 2 (16) ◽  
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.

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.

From Suffix Trees to Suffix Vectors

2006 ◽  
Vol 17 (06) ◽  
pp. 1385-1402 ◽  
Author(s):  
Élise Prieur ◽  
Thierry Lecroq
Keyword(s):  
Data Structures ◽  
Suffix Tree ◽  
Suffix Trees ◽  
Linear Algorithms ◽  
Economical Alternative

We present a first formal setting for suffix vectors that are space economical alternative data structures to suffix trees. We give two linear algorithms for converting a suffix tree into a suffix vector and conversely. We enrich suffix vectors with formulas for counting the number of occurrences of repeated substrings. We also propose an alternative implementation for suffix vectors that should outperform the existing one.

THE VIRTUAL SUFFIX TREE

2009 ◽  
Vol 20 (06) ◽  
pp. 1109-1133 ◽  
Author(s):  
JIE LIN ◽  
YUE JIANG ◽  
DON ADJEROH
Keyword(s):  
Suffix Tree ◽  
Linear Time ◽  
Suffix Array ◽  
Intermediate Step ◽  
Suffix Trees ◽  
String Length ◽  
Space Requirement ◽  
Suffix Arrays ◽  
Tree Construction ◽  
Efficient Data

We introduce the VST (virtual suffix tree), an efficient data structure for suffix trees and suffix arrays. Starting from the suffix array, we construct the suffix tree, from which we derive the virtual suffix tree. Later, we remove the intermediate step of suffix tree construction, and build the VST directly from the suffix array. The VST provides the same functionality as the suffix tree, including suffix links, but at a much smaller space requirement. It has the same linear time construction even for large alphabets, Σ, requires O(n) space to store (n is the string length), and allows searching for a pattern of length m to be performed in O(m log |Σ|) time, the same time needed for a suffix tree. Given the VST, we show an algorithm that computes all the suffix links in linear time, independent of Σ. The VST requires less space than other recently proposed data structures for suffix trees and suffix arrays, such as the enhanced suffix array [1], and the linearized suffix tree [17]. On average, the space requirement (including that for suffix arrays and suffix links) is 13.8n bytes for the regular VST, and 12.05n bytes in its compact form.

scholarly journals Practical Wavelet Tree Construction

2021 ◽  
Vol 26 ◽  
pp. 1-67
Author(s):  
Patrick Dinklage ◽  
Jonas Ellert ◽  
Johannes Fischer ◽  
Florian Kurpicz ◽  
Marvin Löbel
Keyword(s):  
Parallel Algorithms ◽  
Shared Memory ◽  
Distributed Memory ◽  
Auxiliary Information ◽  
Parallel Computers ◽  
External Memory ◽  
Sequential Algorithms ◽  
Bottom Up ◽  
Memory Efficiency ◽  
Tree Construction

We present new sequential and parallel algorithms for wavelet tree construction based on a new bottom-up technique. This technique makes use of the structure of the wavelet trees—refining the characters represented in a node of the tree with increasing depth—in an opposite way, by first computing the leaves (most refined), and then propagating this information upwards to the root of the tree. We first describe new sequential algorithms, both in RAM and external memory. Based on these results, we adapt these algorithms to parallel computers, where we address both shared memory and distributed memory settings. In practice, all our algorithms outperform previous ones in both time and memory efficiency, because we can compute all auxiliary information solely based on the information we obtained from computing the leaves. Most of our algorithms are also adapted to the wavelet matrix , a variant that is particularly suited for large alphabets.

Deterministic finite automata with recursive calls and DPDAs

2003 ◽  
Vol 87 (4) ◽  
pp. 187-193
Author(s):  
Jean H. Gallier ◽  
Salvatore La Torre ◽  
Supratik Mukhopadhyay
Keyword(s):  
Finite Automata ◽  
Deterministic Finite Automata
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