https://grfia.dlsi.ua.es/ml/algorithms/references/editsurvey_bille.pdf

A survey on tree edit distance and related problems

This book presents a practical approach to string matching problems, focusing on the algorithms and implementations that perform best in practice. It covers searching for simple, multiple, and extended strings, as well as regular expressions, exactly and approximately. It includes all of the most significant new developments in complex pattern searching. The clear explanations, step-by-step examples, algorithms pseudo-code, and implementation efficiency maps will enable researchers, professionals, and students in bioinformatics, computer science, and software engineering to choose the most appropriate algorithms for their applications.

Flexible Pattern Matching in Strings: Practical On-Line Search Algorithms for Texts and Biological Sequences

In a previous paper, an algorithm was presented for analyzing multiple RNA secondary structures utilizing a multiple string alignment algorithm. In this paper we present another approach to the problem of comparing many secondary structures by utilizing a very efficient tree-matching algorithm that will compare two trees in O([T1] X [T2] X L1 X L2) in the worst case and very close to O([T1] X [T2]) for average trees representing secondary structures. The result of the pairwise comparison algorithm is then used with a cluster algorithm to produce a multiple structure clustering which can be displayed in a taxonomy tree to show related structures.

Comparing multiple RNA secondary structures using tree comparisons

(MATH) This paper obtains the following results on pattern matching problems in which the text has length n and the pattern has length mAn O(nlog m) time deterministic algorithm for the String Matching with Wildcards problems, even when the alphabet is large.An O(klog2 m) time Las Vegas algorithm for the Sparse String Matching with Wildcards problem, where k«n is the number of non-zeros in the text. We also give Las Vegas algorithms for the higher dimensional version of this problem.As an application of the above, an O(nlog2 m) time Las Vegas algorithm for the Subset Matching and Tree Pattern Matching problems, and a Las Vegas algorithm for the Geometric Pattern Matching problem.Finally, an O(nlog2 m) time deterministic algorithm for Subset Matching and Tree Pattern Matching..The crucial new idea underlying the first three results above is that of confirming matches by convolving vectors obtained by coding characters in the alphabet with non-boolean (i.e., rational or even complex) entries; in contrast, almost all previous pattern matching algorithms consider only boolean codes for the alphabet. The crucial new idea underlying the fourth result is a simpler method of shifting characters which ensures that each character occurs as a singleton in some shift.

/pdf/verifying-candidate-matches-in-sparse-and-wildcard-matching-2ewmb109g6.pdf

Verifying candidate matches in sparse and wildcard matching

Periodic pattern mining or periodicity detection has a number of applications, such as prediction, forecasting, detection of unusual activities, etc. The problem is not trivial because the data to be analyzed are mostly noisy and different periodicity types (namely symbol, sequence, and segment) are to be investigated. Accordingly, we argue that there is a need for a comprehensive approach capable of analyzing the whole time series or in a subsection of it to effectively handle different types of noise (to a certain degree) and at the same time is able to detect different types of periodic patterns; combining these under one umbrella is by itself a challenge. In this paper, we present an algorithm which can detect symbol, sequence (partial), and segment (full cycle) periodicity in time series. The algorithm uses suffix tree as the underlying data structure; this allows us to design the algorithm such that its worstcase complexity is O(k.n2), where k is the maximum length of periodic pattern and n is the length of the analyzed portion (whole or subsection) of the time series. The algorithm is noise resilient; it has been successfully demonstrated to work with replacement, insertion, deletion, or a mixture of these types of noise. We have tested the proposed algorithm on both synthetic and real data from different domains, including protein sequences. The conducted comparative study demonstrate the applicability and effectiveness of the proposed algorithm; it is generally more time-efficient and noise-resilient than existing algorithms.

Efficient Periodicity Mining in Time Series Databases Using Suffix Trees

Recently R. Kosaraju gave an O(nmo.75polylog(m)) step algorithm for tree pattern matching. We improve this result by designing a simple O(n6 polylog(m)) algorithm.

Faster tree pattern matching

Recently, R. Kosaraju (Proc. 30th IEEE Symp. on Foundations of Computer Science, 1989, p.178-83) gave an O(nm/sup 0.75/ polylog(m))-step algorithm for tree pattern matching. The authors improve this result by designing a simple O(n square root m polylog (m)) algorithm. >

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