We define a tree pattern border array as a property of linearised trees analogous to border arrays from the string domain. We consider tree patterns with node wildcards and subtree wildcards. Then we use the tree patt...
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We define a tree pattern border array as a property of linearised trees analogous to border arrays from the string domain. We consider tree patterns with node wildcards and subtree wildcards. Then we use the tree pattern border array in a new forward tree pattern matching algorithm for ordered ranked trees. The algorithm finds all occurrences of a single linearised tree pattern in a linearised input tree. As with the classical Morris-Pratt algorithm for searching in strings, the tree pattern border array is used to determine shift lengths in the searching phase of the tree pattern matching algorithm. We compare this new algorithm with the best performing previously existing algorithms based on backward linearised tree pattern matching algorithms, (non-)linearised tree pattern matching algorithms using finite tree automata or stringpath matchers. We show that our new algorithm outperforms other tree pattern matching algorithms in single tree pattern matching. (c) 2024 Elsevier B.V. All rights reserved.
Regularities in indeterminate strings have recently been a matter of interest because of their use in the fields of molecular biology, musical text analysis, cryptanalysis and so on. In this paper, we study the proble...
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Regularities in indeterminate strings have recently been a matter of interest because of their use in the fields of molecular biology, musical text analysis, cryptanalysis and so on. In this paper, we study the problem of reconstructing an indeterminate string from a border array. We present two efficient algorithms to reconstruct an indeterminate string from a valid border array - one using an unbounded alphabet and the other using minimum sized alphabet. We also propose an O(n(2)) algorithm for reconstructing an indeterminate string from suffix array and LCP array. (C) 2011 Elsevier B.V. All rights reserved.
The parameterized longest previous factor (pLPF) problem as defined for parameterized strings (p-strings) adds a level of parameterization to the longest previous factor (LPF) problem originally defined for traditiona...
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The parameterized longest previous factor (pLPF) problem as defined for parameterized strings (p-strings) adds a level of parameterization to the longest previous factor (LPF) problem originally defined for traditional strings. In this work, we consider the construction of the pLPF data structure and identify the strong relationship between the pLPF linear time construction and several variations of the problem. Initially, we propose a taxonomy of classes for longest factor problems. Using this taxonomy, we show an interesting connection between the pLPF and popular data structures. It is shown that a subset of longest factor problems may be created with the pLPF construction. More specifically, the pLPF problem is used as a foundation to achieve the linear time construction of popular data structures such as the LCP, parameterized-LCP (pLCP), parameterized-border (p-border) array, and border array. We further generalize the permuted-LCP for p-strings and provide a linear time construction. A number of new variations of the pLPF problem are proposed and addressed in linear time for both p-strings and traditional strings, including the longest not-equal factor (LneF), longest reverse factor (LrF), and longest factor (LF). The framework of the pLPF construction is exploited to efficiently address a multitude of data structures with prospects in various applications. Finally, we implement our algorithms and perform various experiments to confirm theoretical results. (C) 2012 Elsevier B.V. All rights reserved.
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