RMESH Algorithms for Parallel String Matching

String matching problem received much attention over the years due to its importance in various applications such as text/file comparison, DNA sequencing, search engines, and spelling correction. Especially with the introduction of search engines dealing with tremendous amount of textual information presented on the world wide web and the research on DNA sequencing, this problem deserves special attention and any algorithmic or hardware improvements to speed up the process will benefit these important applications. In this paper, we present three algorithms for string matching on reconfigurable mesh architectures. Given a text T of length n and a pattern P of length m, the first algorithm finds the exact matching between T and P in O(1) time on a 2-dimensional RMESH of size (n-m+1) * m. The second algorithm finds the approximate matching between T and P in O(k) time on a 2D RMESH, where k is the maximum edit distance between T and P. The third algorithm allows only the replacement operation in the calculation of the edit distance and finds an approximate matching between T and P in constant-time on a 3D RMESH

Fast matching statistics in small space

Computing the matching statistics of a string S with respect to a string T on an alphabet of size sigma is a fundamental primitive for a number of large-scale string analysis applications, including the comparison of entire genomes, for which space is a pressing issue. This paper takes from theory to practice an existing algorithm that uses just O(|T|log{sigma}) bits of space, and that computes a compact encoding of the matching statistics array in O(|S|log{sigma}) time. The techniques used to speed up the algorithm are of general interest, since they optimize queries on the existence of a Weiner link from a node of the suffix tree, and parent operations after unsuccessful Weiner links. Thus, they can be applied to other matching statistics algorithms, as well as to any suffix tree traversal that relies on such calls. Some of our optimizations yield a matching statistics implementation that is up to three times faster than a plain version of the algorithm, depending on the similarity between S and T. In genomic datasets of practical significance we achieve speedups of up to 1.8, but our fastest implementations take on average twice the time of an existing code based on the LCP array. The key advantage is that our implementations need between one half and one fifth of the competitor\u27s memory, and they approach comparable running times when S and T are very similar

Exact string matching algorithms for searching DNA and protein sequences and searching chemical databases

The enormous quantities of biological and chemical files and databases are likely to grow year on year, consequently giving rise to the need to develop string-matching algorithms capable of minimizing the searching response time. Being aware of this need, this thesis aims to develop string matching algorithms to search biological sequences and chemical structures by studying exact string matching algorithms in detail. As a result, this research developed a new classification of string matching algorithms containing eight categories according to the pre-processing function of algorithms and proposed five new string matching algorithms; BRBMH, BRQS, Odd and Even algorithm (OE), Random String Matching algorithm (RSMA) and Skip Shift New algorithm (SSN). The main purpose behind the proposed algorithms is to reduce the searching response time and the total number of comparisons. They are tested by comparing them with four well- known standard algorithms, Boyer Moore Horspool (BMH), Quick Search (QS), TVSBS and BRFS. This research applied all of the algorithms to sample data files by implementing three types of tests. The number of comparison tests showed a substantial difference in the number of comparisons our algorithms use compared to the non-hybrid algorithms such as QS and BMH. In addition, the tests showed considerable difference between our algorithms and other hybrid algorithm such as TVSBS and BRFS. For instance, the average elapsed search time tests showed that our algorithms presented better average elapsed search time than the BRFS, TVSBS, QS and BMH algorithms, while the average number of tests showed better number of attempts compared to BMH, QS, TVSBS and BRFS algorithms. A new contribution has been added by this research by using the fastest proposed algorithm, the SSN algorithm, to develop a chemical structure searching toolkit to search chemical structures in our local database. The new algorithms were paralleled using OpenMP and MPI parallel models and tested at the University of Science Malaysia (USM) on a Stealth Cluster with different number of threads and processors to improve the speed of searching pattern in the given text which, as we believe, is another contribution

Multivariate Fine-Grained Complexity of Longest Common Subsequence

We revisit the classic combinatorial pattern matching problem of finding a longest common subsequence (LCS). For strings $x$ and $y$ of length $n$, a textbook algorithm solves LCS in time $O(n^2)$, but although much effort has been spent, no $O(n^{2-\varepsilon})$-time algorithm is known. Recent work indeed shows that such an algorithm would refute the Strong Exponential Time Hypothesis (SETH) [Abboud, Backurs, Vassilevska Williams + Bringmann, K\"unnemann FOCS'15]. Despite the quadratic-time barrier, for over 40 years an enduring scientific interest continued to produce fast algorithms for LCS and its variations. Particular attention was put into identifying and exploiting input parameters that yield strongly subquadratic time algorithms for special cases of interest, e.g., differential file comparison. This line of research was successfully pursued until 1990, at which time significant improvements came to a halt. In this paper, using the lens of fine-grained complexity, our goal is to (1) justify the lack of further improvements and (2) determine whether some special cases of LCS admit faster algorithms than currently known. To this end, we provide a systematic study of the multivariate complexity of LCS, taking into account all parameters previously discussed in the literature: the input size $n:=\max\{|x|,|y|\}$, the length of the shorter string $m:=\min\{|x|,|y|\}$, the length $L$ of an LCS of $x$ and $y$, the numbers of deletions $\delta := m-L$ and $\Delta := n-L$, the alphabet size, as well as the numbers of matching pairs $M$ and dominant pairs $d$. For any class of instances defined by fixing each parameter individually to a polynomial in terms of the input size, we prove a SETH-based lower bound matching one of three known algorithms. Specifically, we determine the optimal running time for LCS under SETH as $(n+\min\{d, \delta \Delta, \delta m\})^{1\pm o(1)}$. [...]Comment: Presented at SODA'18. Full Version. 66 page

Automated schema matching techniques: an exploratory study

Manual schema matching is a problem for many database applications that use multiple data sources including data warehousing and e-commerce applications. Current research attempts to address this problem by developing algorithms to automate aspects of the schema-matching task. In this paper, an approach using an external dictionary facilitates automated discovery of the semantic meaning of database schema terms. An experimental study was conducted to evaluate the performance and accuracy of five schema-matching techniques with the proposed approach, called SemMA. The proposed approach and results are compared with two existing semi-automated schema-matching approaches and suggestions for future research are made

Comparing knowledge sources for nominal anaphora resolution

We compare two ways of obtaining lexical knowledge for antecedent selection in other-anaphora and definite noun phrase coreference. Specifically, we compare an algorithm that relies on links encoded in the manually created lexical hierarchy WordNet and an algorithm that mines corpora by means of shallow lexico-semantic patterns. As corpora we use the British National Corpus (BNC), as well as the Web, which has not been previously used for this task. Our results show that (a) the knowledge encoded in WordNet is often insufficient, especially for anaphor-antecedent relations that exploit subjective or context-dependent knowledge; (b) for other-anaphora, the Web-based method outperforms the WordNet-based method; (c) for definite NP coreference, the Web-based method yields results comparable to those obtained using WordNet over the whole dataset and outperforms the WordNet-based method on subsets of the dataset; (d) in both case studies, the BNC-based method is worse than the other methods because of data sparseness. Thus, in our studies, the Web-based method alleviated the lexical knowledge gap often encountered in anaphora resolution, and handled examples with context-dependent relations between anaphor and antecedent. Because it is inexpensive and needs no hand-modelling of lexical knowledge, it is a promising knowledge source to integrate in anaphora resolution systems