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

Abstract

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.