Taxonomies of regular tree algorithms

Algorithms for acceptance, pattern matching and parsing of regular trees and the tree automata used in these algorithms have many applications, including instruction selection in compilers, implementation of term rewriting systems, and model checking. Many such tree algorithms and constructions for such tree automata appear in the literature, but some deficiencies existed, including: inaccessibility of theory and algorithms; difficulty of comparing algorithms due to variations in presentation style and level of formality; and lack of reference to the theory in many publications. An algorithm taxonomy is an effective means of bringing order to such a field. We report on two taxonomies of regular tree algorithms that we have constructed to deal with the deficiencies. The complete work has been presented in the PhD thesis of the first author

Using human computation in dead-zone based 2D pattern matching

Abstract. This paper examines the application of human computation (HC) to twodimensional image pattern matching. The two main goals of our algorithm are to use turks as the processing units to perform an efficient pattern match attempt on a subsection of an image, and to divide the work using a version of dead-zone based pattern matching. In this approach, human computation presents an alternative to machine learning by outsourcing computationally difficult work to humans, while the dead-zone search offers an efficient search paradigm open to parallelization-making the combination a powerful approach for searching for patterns in two-dimensional images

On compile time Knuth-Morris-Pratt precomputation

Abstract. Many keyword pattern matching algorithms use precomputation subroutines to produce lookup tables, which in turn are used to improve performance during the search phase. If the keywords to be matched are known at compile time, the precomputation subroutines can be implemented to be evaluated at compile time versus at run time. This will provide a performance boost to run time operations. We have started an investigation into the use of metaprogramming techniques to implement such compile time evaluation, initially for the Knuth-Morris-Pratt (KMP) algorithm. We present an initial experimental comparison of the performance of the traditional KMP algorithm to that of an optimised version that uses compile time precomputation. During implementation and benchmarking, it was discovered that C++ is not well suited to metaprogramming when dealing with strings, while the related D language is. We therefore ported our implementation to the latter and performed the benchmarking with that version. We discuss the design of the benchmarks, the experience in implementing the benchmarks in C++ and D, and the results of the D benchmarks. The results show that under certain circumstances, the use of compile time precomputation may significantly improve performance of the KMP algorithm

Weak factor automata : the failure of failure factor oracles?

In indexing of, and pattern matching on, DNA and text sequences, it is often important to represent all factors of a sequence. One e cient, compact representation is the factor oracle (FO). At the same time, any classical deterministic nite automaton (DFA) can be transformed to a so-called failure one (FDFA), which may use failure transitions to replace multiple symbol transitions, potentially yielding a more compact representation. We combine the two ideas and directly construct a failure factor oracle (FFO) from a given sequence, in contrast to ex post facto transformation to an FDFA. The algorithm is suitable for both short and long sequences. We empirically compared the resulting FFOs and FOs on number of transitions for many DNA sequences of lengths 4 - 512, showing gains of up to 10% in total number of transitions, with failure transitions also taking up less space than symbol transitions. The resulting FFOs can be used for indexing, as well as in a variant of the FO-using backward oracle matching algorithm. We discuss and classify this pattern matching algorithm in terms of the keyword pattern matching taxonomies of Watson, Cleophas and Zwaan. We also empirically compared the use of FOs and FFOs in such backward reading pattern matching algorithms, using both DNA and natural language (English) data sets. The results indicate that the decrease in pattern matching performance of an algorithm using an FFO instead of an FO may outweigh the gain in representation space by using an FFO instead of an FO.http://www.journals.co.za/ej/ejour_comp.htmlam201

Solving String Problems on Graphs Using the Labeled Direct Product

Suffix trees are an important data structure at the core of optimal solutions to many fundamental string problems, such as exact pattern matching, longest common substring, matching statistics, and longest repeated substring. Recent lines of research focused on extending some of these problems to vertex-labeled graphs, either by using efficient ad-hoc approaches which do not generalize to all input graphs, or by indexing difficult graphs and having worst-case exponential complexities. In the absence of an ubiquitous and polynomial tool like the suffix tree for labeled graphs, we introduce the labeled direct product of two graphs as a general tool for obtaining optimal algorithms in the worst case: we obtain conceptually simpler algorithms for the quadratic problems of string matching (SMLG) and longest common substring (LCSP) in labeled graphs. Our algorithms run in time linear in the size of the labeled product graph, which may be smaller than quadratic for some inputs, and their run-time is predictable, because the size of the labeled direct product graph can be precomputed efficiently. We also solve LCSP on graphs containing cycles, which was left as an open problem by Shimohira et al. in 2011. To show the power of the labeled product graph, we also apply it to solve the matching statistics (MSP) and the longest repeated string (LRSP) problems in labeled graphs. Moreover, we show that our (worst-case quadratic) algorithms are also optimal, conditioned on the Orthogonal Vectors Hypothesis. Finally, we complete the complexity picture around LRSP by studying it on undirected graphs.Peer reviewe

Algorithms for Order-Preserving Matching

String matching is a widely studied problem in Computer Science. There have been many recent developments in this field. One fascinating problem considered lately is the order-preserving matching (OPM) problem. The task is to find all the substrings in the text which have the same length and relative order as the pattern, where the relative order is the numerical order of the numbers in a string. The problem finds its applications in the areas involving time series or series of numbers. More specifically, it is useful for those who are interested in the relative order of the pattern and not in the pattern itself. For example, it can be used by analysts in a stock market to study movements of prices.  In addition to the OPM problem, we also studied its approximate variation. In approximate order-preserving matching, we search for those substrings in the text which have relative order similar to the pattern, i.e., relative order of the pattern matches with at most k mismatches. With respect to applications of order-preserving matching, approximate search is more meaningful than exact search. We developed various advanced solutions for the problem and its variant. Special emphasis was laid on the practical efficiency of the solutions. Particularly, we introduced a simple solution for the OPM problem using filtration. We proved experimentally that our method was effective and faster than the previous solutions for the problem. In addition, we combined the Single Instruction Multiple Data (SIMD) instruction set architecture with filtration to develop competent solutions which were faster than our previous solution. Moreover, we proposed another efficient solution without filtration using the SIMD architecture. We also presented an offline solution based on the FM-index scheme. Furthermore, we proposed practical solutions for the approximate order-preserving matching problem and one of the solutions was the first sublinear solution on average for the problem