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

1999 ◽  
Vol 15 (1) ◽  
pp. 30-71
Author(s):  
Raffaele Giancarlo ◽  
Roberto Grossi
Keyword(s):  
Pattern Matching ◽  
Data Structures ◽  
Index Data ◽  
Index Data Structures ◽  
Parallel Construction

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.

Pattern-matching and rewriting rules for group indexed data structures

2002 ◽  
Vol 37 (12) ◽  
pp. 76-87 ◽  
Author(s):  
Jean-Louis Giavitto ◽  
Olivier Michel ◽  
Julien Cohen
Keyword(s):  
Pattern Matching ◽  
Data Structures ◽  
Rewriting Rules

scholarly journals Parallel construction of binary tree based on sorting

2019 ◽  
Vol 18 (4) ◽  
pp. 449-454
Author(s):  
Ya. E. Romm ◽  
D. A. Chabanyuk
Keyword(s):  
Data Structures ◽  
Binary Tree ◽  
Time Complexity ◽  
Binary Data ◽  
Relational Databases ◽  
Input Sequence ◽  
Mutual Transformation ◽  
One To One ◽  
Parallel Construction ◽  
Address Sorting

Introduction. Algorithms for the parallel binary tree construction are developed. The algorithms are based on sorting and described in a constructive form. For the Nelement set, the time complexity has T(R) = O(1) and T(R) = O(log2N) estimates, where R = (N2-N)/2 is the number of processors. The tree is built with the uniqueness property. The algorithms are invariant with respect to the input sequence type. The work objective is to develop and study ways of accelerating the process of organizing and transforming the tree-like data structures on the basis of the stable maximum parallel sorting algorithms for their application to the basic operations of information retrieval on databases.Materials and Methods.A one-to-one relation between the input element set and the binary tree built for it is established using a stable address sorting. The sorting provides maximum concurrency, and, in an operator form, establishes a one-to-one mapping of input and output indices. On this basis, methods for the mutual transformation of the binary data structures are being developed.Research Results.An efficient parallel algorithm for constructing a binary tree based on the address sorting with time complexity of T(N2) = O(log2N) is obtained. From the well-known analogues, the algorithm differs in structure and logarithmic estimation of time complexity, which makes it possible to achieve the acceleration of O(Nα), α≥1 order analogues. As an advanced version, an algorithm modification, which provides the maximum parallel construction of the binary tree based on a stable address sorting and a priori calculation of the stored subtree root indices is suggested. The algorithm differs in structure and estimation of T(1) = O(1) time complexity. A similar estimate is achieved in a sequential version of the modified algorithm, which allows obtaining the acceleration of known analogs O(Nα), α>1 order.Discussion and Conclusions.The results obtained are focused on the creation of effective methods for the dynamic database processing. The proposed methods and algorithms can form an algorithmic basis for an advanced deterministic search on the relational databases and information systems.

scholarly journals A Note on Linear Time Simulation of Deterministic Two-Way Pushdown Automata

1977 ◽  
Vol 6 (75) ◽  
Author(s):  
Neil D. Jones
Keyword(s):  
Pattern Matching ◽  
Data Structures ◽  
Linear Time ◽  
Random Access ◽  
Simulation Algorithm ◽  
Pushdown Automaton ◽  
Matching Problems ◽  
Time Result ◽  
Time Simulation ◽  
Pushdown Automata

<p>Cook has shown that any deterministic two-way pushdown automaton could be simulated by a uniform-cost random access machine in time O(n) for inputs of length n. The result was of interest because such a machine is a natural model for a variety of backtracking algorithms, particularly as used in pattern matching problems. The linear time result was surprising because of the fact that such machines may run as many as 2n steps before halting; similar problems with 'combinatorial explosions' are well known to occur in applications of backtracking. Cook's result inspired the development of a number of efficient pattern matching algorithms.</p><p>However, it is impractical to use Cook's algorithm directly to do pattern matching, since it involves a large constant time factor and much storage. The purpose of this note is to present an alternate, simpler simulation algorithm which involves consideration only of the configurations actually reached by the automaton. It can be expected to run faster and use less storage (depending on the data structures used), thus bringing Cook's result a step closer to practical utility.</p>

scholarly journals First-class patterns

2009 ◽  
Vol 19 (2) ◽  
pp. 191-225 ◽  
Author(s):  
BARRY JAY ◽  
DELIA KESNER
Keyword(s):  
Pattern Matching ◽  
Data Structures ◽  
General Framework ◽  
Expressive Power ◽  
Training Data ◽  
Matching Algorithm ◽  
Recursive Functions ◽  
Pattern Polymorphism

AbstractPure pattern calculus supports pattern-matching functions in which patterns are first-class citizens that can be passed as parameters, evaluated and returned as results. This new expressive power supports two new forms of polymorphism. Path polymorphism allows recursive functions to traverse arbitrary data structures. Pattern polymorphism allows patterns to be treated as parameters which may be collected from various sources or generated from training data. A general framework for pattern calculi is developed. It supports a proof of confluence that is parameterised by the nature of the matching algorithm, suitable for the pure pattern calculus and all other known pattern calculi.

scholarly journals Indexing ordered trees for (nonlinear) tree pattern matching by pushdown automata

2012 ◽  
Vol 9 (3) ◽  
pp. 1125-1153
Author(s):  
J. Travnícek ◽  
J. Janousek ◽  
B. Melichar
Keyword(s):  
Pattern Matching ◽  
Data Structures ◽  
Input Pattern ◽  
Pushdown Automaton ◽  
Ordered Trees ◽  
Tree Pattern ◽  
Tree Patterns ◽  
Tree Pattern Matching ◽  
Ordered Tree ◽  
Pushdown Automata

Trees are one of the fundamental data structures used in Computer Science. We present a new kind of acyclic pushdown automata, the tree pattern pushdown automaton and the nonlinear tree pattern pushdown automaton, constructed for an ordered tree. These automata accept all tree patterns and nonlinear tree patterns, respectively, which match the tree and represent a full index of the tree for such patterns. Given a tree with n nodes, the numbers of these distinct tree patterns and nonlinear tree patterns can be at most 2n?1 +n and at most (2+v)n?1+2, respectively, where v is the maximal number of nonlinear variables allowed in nonlinear tree patterns. The total sizes of nondeterministic versions of the two pushdown automata are O(n) and O(n2), respectively. We discuss the time complexities and show timings of our implementations using the bit-parallelism technique. The timings show that for a given tree the running time is linear to the size of the input pattern.

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