Parallel Algorithms for the Boxed-Mesh Permutation Pattern Matching Problem

2019 ◽  
Vol 46 (4) ◽  
pp. 299-307
Author(s):  
Jihyo Choi ◽  
Youngho Kim ◽  
Joong Chae Na ◽  
Jeong Seop Sim
Keyword(s):  
Parallel Algorithms ◽  
Pattern Matching ◽  
Matching Problem ◽  
Permutation Pattern

scholarly journals Permutation Pattern matching in (213, 231)-avoiding permutations

2017 ◽  
Vol Vol. 18 no. 2, Permutation... (Permutation Patterns) ◽  
Author(s):  
Both Neou ◽  
Romeo Rizzi ◽  
Stéphane Vialette
Keyword(s):  
Pattern Matching ◽  
Related Problem ◽  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Matching Problem ◽  
Permutation Pattern ◽  
Special Case ◽  
Longest Subsequence

Given permutations σ of size k and π of size n with k < n, the permutation pattern matching problem is to decide whether σ occurs in π as an order-isomorphic subsequence. We give a linear-time algorithm in case both π and σ avoid the two size-3 permutations 213 and 231. For the special case where only σ avoids 213 and 231, we present a O(max(kn 2 , n 2 log log n)-time algorithm. We extend our research to bivincular patterns that avoid 213 and 231 and present a O(kn 4)-time algorithm. Finally we look at the related problem of the longest subsequence which avoids 213 and 231.

A SPACE EFFICIENT BIT-PARALLEL ALGORITHM FOR THE MULTIPLE STRING MATCHING PROBLEM

2006 ◽  
Vol 17 (06) ◽  
pp. 1235-1251 ◽  
Author(s):  
DOMENICO CANTONE ◽  
SIMONE FARO
Keyword(s):  
Parallel Algorithms ◽  
Parallel Algorithm ◽  
Pattern Matching ◽  
String Matching ◽  
Common Factors ◽  
Building Blocks ◽  
Parallel Simulation ◽  
Direct Simulation ◽  
Matching Problem ◽  
Multiple Pattern Matching

Finite (nondeterministic) automata are very useful building blocks in the field of string matching. This is particularly true in the case of multiple pattern matching, where the use of factor-based automata can reduce substantially the number of computational steps when the patterns have large common factors. Direct simulation of nondeterministic automata can be performed very efficiently using the bit-parallelism technique, though this is not necessarily true for factor-based automata. In this paper we present an algorithm for the multiple string matching problem, based on the bit-parallel simulation of nondeterministic factor-based automata which satisfy a particular ordering condition. We also show how to enforce such condition by suitably modifying a minimal initial automaton, through equivalence preserving transformations. The resulting automaton turns out to be smaller than the corresponding maximal automata used by existing bit-parallel algorithms, as they do not take any advantage of common factors in patterns.

PARALLEL PATTERN MATCHING WITH SCALING

2001 ◽  
Vol 11 (01) ◽  
pp. 125-138 ◽  
Author(s):  
H. MONGELLI ◽  
S. W. SONG
Keyword(s):  
Parallel Algorithms ◽  
Parallel Algorithm ◽  
Pattern Matching ◽  
Computing Time ◽  
Parallel Machine ◽  
Experimental Results ◽  
Coarse Grained ◽  
Matching Problem ◽  
Communication Round ◽  
Parallel Pattern

Given a text and a pattern, the problem of pattern matching consists of determining all the positions of the text where the pattern occurs. When the text and the pattern are matrices, the matching is termed bidimensional. There are variations of this problem where we allow the matching using a somehow modified pattern. A modification that we will allow is that the pattern can be scaled. We propose a new parallel algorithm for this problem, under the CGM (Coarse Grained Multicomputer) model. This algorithm requires linear local computing time in the input, linear memory and uses only one communication round, during which at most a linear amount of data is exchanged. To be the best of our knowledge, there are no known parallel algorithms for the bidimensional pattern matching problem with scaling in the literature. This proposed algorithm was implemented in C, using the PVM interface and was executed on a Parsytec PowerXplorer parallel machine. The experimental results obtained were very promising and showed significant speedups.

scholarly journals The Complexity of Pattern Matching for $321$-Avoiding and Skew-Merged Permutations

2016 ◽  
Vol Vol. 18 no. 2, Permutation... (Permutation Patterns) ◽  
Author(s):  
Michael H. Albert ◽  
Marie-Louise Lackner ◽  
Martin Lackner ◽  
Vincent Vatter
Keyword(s):  
Pattern Matching ◽  
Polynomial Time ◽  
Matching Problem ◽  
Polynomial Time Algorithms ◽  
Permutation Pattern ◽  
Special Cases ◽  
Np Complete

The Permutation Pattern Matching problem, asking whether a pattern permutation $\pi$ is contained in a permutation $\tau$, is known to be NP-complete. In this paper we present two polynomial time algorithms for special cases. The first algorithm is applicable if both $\pi$ and $\tau$ are $321$-avoiding; the second is applicable if $\pi$ and $\tau$ are skew-merged. Both algorithms have a runtime of $O(kn)$, where $k$ is the length of $\pi$ and $n$ the length of $\tau$.

A new algorithm for the small-field astrometric point-pattern matching problem

2018 ◽  
Vol 72 (1) ◽  
pp. 55-70 ◽  
Author(s):  
Cláudio P. Santiago ◽  
Carlile Lavor ◽  
Sérgio Assunção Monteiro ◽  
Alberto Kroner-Martins
Keyword(s):  
Pattern Matching ◽  
Point Pattern ◽  
Small Field ◽  
Matching Problem ◽  
Point Pattern Matching
Sign in / Sign up

Export Citation Format

Share Document