OpenMP Implementation of Parallel Longest Common Subsequence Algorithm for Mathematical Expression Retrieval

2021 ◽  
pp. 2150007
Author(s):  
Pavan Kumar Perepu
Keyword(s):  
Time Complexity ◽  
Mathematical Expression ◽  
Longest Common Subsequence ◽  
Retrieval Algorithm ◽  
Retrieval Process ◽  
Parallel Version ◽  
Mathematical Expressions ◽  
Common Subsequence ◽  
Text Processor ◽  
Performance Results

Given a mathematical expression in LaTeX or MathML format, retrieval algorithm extracts similar expressions from a database. In our previous work, we have used Longest Common Subsequence (LCS) algorithm to match two expressions of lengths, [Formula: see text] and [Formula: see text], which takes [Formula: see text] time complexity. If there are [Formula: see text] database expressions, total complexity is [Formula: see text], and an increase in [Formula: see text] also increases this complexity. In the present work, we propose to use parallel LCS algorithm in our retrieval process. Parallel LCS has [Formula: see text] time complexity with [Formula: see text] processors and total complexity can be reduced to [Formula: see text]. For our experimentation, OpenMP based implementation has been used on Intel [Formula: see text] processor with 4 cores. However, for smaller expressions, parallel version takes more time as the implementation overhead dominates the algorithmic improvement. As such, we have proposed to use parallel version, selectively, only on larger expressions, in our retrieval algorithm to achieve better performance. We have compared the sequential and parallel versions of our ME retrieval algorithm, and the performance results have been reported on a database of 829 mathematical expressions.

scholarly journals Automata Technique for The LCS Problem

2019 ◽  
Vol 35 (1) ◽  
pp. 21-37
Author(s):  
Trường Huy Nguyễn
Keyword(s):  
Dynamic Programming ◽  
Parallel Algorithms ◽  
Time Complexity ◽  
Dynamic Programming Algorithm ◽  
Longest Common Subsequence ◽  
Programming Algorithm ◽  
Worst Case ◽  
Common Subsequence ◽  
Input Strings ◽  
Upper Estimate

In this paper, we introduce two efficient algorithms in practice for computing the length of a longest common subsequence of two strings, using automata technique, in sequential and parallel ways. For two input strings of lengths m and n with m ≤ n, the parallel algorithm uses k processors (k ≤ m) and costs time complexity O(n) in the worst case, where k is an upper estimate of the length of a longest common subsequence of the two strings. These results are based on the Knapsack Shaking approach proposed by P. T. Huy et al. in 2002. Experimental results show that for the alphabet of size 256, our sequential and parallel algorithms are about 65.85 and 3.41m times faster than the standard dynamic programming algorithm proposed by Wagner and Fisher in 1974, respectively.

ALGORITHMS FOR THE CONSTRAINED LONGEST COMMON SUBSEQUENCE PROBLEMS

2005 ◽  
Vol 16 (06) ◽  
pp. 1099-1109 ◽  
Author(s):  
ABDULLAH N. ARSLAN ◽  
ÖMER EĞECIOĞLU
Keyword(s):  
Time Complexity ◽  
Edit Distance ◽  
Longest Common Subsequence ◽  
Longest Common Subsequence Problem ◽  
Common Subsequence ◽  
Definition Of

Given strings S1, S2, and P, the constrained longest common subsequence problem for S1 and S2 with respect to P is to find a longest common subsequence lcs of S1 and S2 which contains P as a subsequence. We present an algorithm which improves the time complexity of the problem from the previously known O(rn2m2) to O(rnm) where r, n, and m are the lengths of P, S1, and S2, respectively. As a generalization of this, we extend the definition of the problem so that the lcs sought contains a subsequence whose edit distance from P is less than a given parameter d. For the latter problem, we propose an algorithm whose time complexity is O(drnm).

Cross-lingual Text Reuse Detection Using Translation Plus Monolingual Analysis for English-Urdu Language Pair

2022 ◽  
Vol 21 (2) ◽  
pp. 1-18
Author(s):  
Iqra Muneer ◽  
Rao Muhammad Adeel Nawab
Keyword(s):  
Probabilistic Approach ◽  
Detailed Comparison ◽  
Longest Common Subsequence ◽  
Common Subsequence ◽  
Classification Tasks ◽  
N Gram ◽  
Cross Lingual ◽  
Recurrent Architecture ◽  
Translation Systems ◽  
Language Pair

Cross-Lingual Text Reuse Detection (CLTRD) has recently attracted the attention of the research community due to a large amount of digital text readily available for reuse in multiple languages through online digital repositories. In addition, efficient machine translation systems are freely and readily available to translate text from one language into another, which makes it quite easy to reuse text across languages, and consequently difficult to detect it. In the literature, the most prominent and widely used approach for CLTRD is Translation plus Monolingual Analysis (T+MA). To detect CLTR for English-Urdu language pair, T+MA has been used with lexical approaches, namely, N-gram Overlap, Longest Common Subsequence, and Greedy String Tiling. This clearly shows that T+MA has not been thoroughly explored for the English-Urdu language pair. To fulfill this gap, this study presents an in-depth and detailed comparison of 26 approaches that are based on T+MA. These approaches include semantic similarity approaches (semantic tagger based approaches, WordNet-based approaches), probabilistic approach (Kullback-Leibler distance approach), monolingual word embedding-based approaches siamese recurrent architecture, and monolingual sentence transformer-based approaches for English-Urdu language pair. The evaluation was carried out using the CLEU benchmark corpus, both for the binary and the ternary classification tasks. Our extensive experimentation shows that our proposed approach that is a combination of 26 approaches obtained an F 1 score of 0.77 and 0.61 for the binary and ternary classification tasks, respectively, and outperformed the previously reported approaches [ 41 ] ( F 1 = 0.73) for the binary and ( F 1 = 0.55) for the ternary classification tasks) on the CLEU corpus.

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