1,720,997 research outputs found
Some Investigations on Similarity Measures Based on Absent Words
Full text linkIn this paper we investigate similarity measures based on minimal absent words, introduced by Chairungsee and Crochemore in [1]. They make use of a length-weighted index on a sample set corresponding to the symmetric difference M(x)ΔM(y) of the minimal absent words M(x) and M(y) of two sequences x and y, respectively. We first propose a variant of this measure by choosing as a sample set a proper subset (x, y) of M(x)ΔM(y), which appears to be more appropriate for distinguishing x and y. From the algebraic point of view, we prove that (x, y) is the base of the ideal generated by M(x)ΔM(y). We then remark that such measures are able to recognize whether the sequences x and y share a common structure, but they are not able to detect the difference on the number of occurrences of such a structure in the two sequences. In order to take into account such a multiplicity, we introduce the notion of multifactor, and define a new measure that uses both absent words and multifactors. Surprisingly, we prove that this similarity measure coincides with a distance on sequences introduced by Ehrenfeucht and Haussler in [2], in the context of block-moves strategies. In this way, our result creates a non trivial bridge between similarity measures based on absent words and those based on the block-moves approach
Sorting suffixes of a text via its Lyndon Factorization
No full textThe process of sorting the suffixes of a text plays a fundamental role in Text Algorithms. They are used for instance in the constructions of the Burrows-Wheeler transform and the suffix array, widely used in several fields of Computer Science. For this reason, several recent researches have been devoted to finding new strategies to obtain effective methods for such a sorting. In this paper we introduce a new methodology in which an important role is played by the Lyndon factorization, so that the local suffixes inside factors detected by this factorization keep their mutual order when extended to the suffixes of the whole word. This property suggests a versatile technique that easily can be adapted to different implementative scenarios
A new Combinatorial Approach to Sequence Comparison
No full textIn this paper we introduce a new alignment-free method for comparing sequences which is combinatorial by nature and does not use any compressor nor any information-theoretic notion. Such a method is based on an extension of the Burrows-Wheeler Transform, a transformation widely used in the context of Data Compression. The new extended transformation takes as input a multiset of sequences and produces as output a string obtained by a suitable rearrangement of the characters of all the input sequences. By using such a transformation we define a measure to compare sequences that takes into account how the characters coming from different input sequences are mixed in the output string. Such a method is tested on a real data set for the whole mitochondrial genome phylogeny problem. However, the goal of this paper is to introduce a new and general methodology for automatic categorization of sequences
Formal Languages and Automata: Models, Methods and Application. In Honour of the 70th Birthday of Antonio Restivo Preface
No full textAn extension of the Burrows-Wheeler Transform
No full textWe describe and highlight a generalization of the Burrows-Wheeler Transform (bwt) to a multiset of words. The extended transformation, denoted by ebwt, is reversible. Moreover, it allows to define a bijection between the words over a finite alphabet A and the finite multisets of conjugacy classes of primitive words in A*. Besides its mathematical interest, the extended transform can be useful for applications in the context of string processing. In the last part of this paper we illustrate one such application, providing a similarity measure between sequences based on ebwt
String attractors and combinatorics on words
Full text linkThe notion of string attractor has recently been introduced in [Prezza, 2017] and studied in [Kempa and Prezza, 2018] to provide a unifying framework for known dictionary-based compressors. A string attractor for a word w = w[1]w[2] · · · w[n] is a subset Γ of the positions 1, . . ., n, such that all distinct factors of w have an occurrence crossing at least one of the elements of Γ. While finding the smallest string attractor for a word is a NP-complete problem, it has been proved in [Kempa and Prezza, 2018] that dictionary compressors can be interpreted as algorithms approximating the smallest string attractor for a given word. In this paper we explore the notion of string attractor from a combinatorial point of view, by focusing on several families of finite words. The results presented in the paper suggest that the notion of string attractor can be used to define new tools to investigate combinatorial properties of the words
Sorting conjugates and Suffixes of Words in a Multiset
Full text linkIn this paper we are interested in the study of the combinatorial aspects related to the extension of the Burrows-Wheeler transform to a multiset of words. Such study involves the notion of suffixes and conjugates of words and is based on two different order relations, denoted by <_lex and ≺_ω, that, even if strictly connected, are quite different from the computational point of view. In particular, we introduce a method that only uses the <_lex sorting among suffixes of a multiset of words in order to sort their conjugates according to ≺_ω-order. In this study an important role is played by Lyndon words. This strategy could be used in applications specially in the field of Bioinformatics, where for instance the advent of "next-generation" DNA sequencing technologies has meant that huge collections of DNA sequences are now commonplace
Suffixes, Conjugates and Lyndon Words
No full textIn this paper we are interested in the study of the combinatorial aspects connecting three important constructions in the field of string algorithms: the suffix array, the Burrows-Wheeler transform (BWT) and the extended Burrows-Wheeler transform (EBWT). Such constructions involve the notions of suffixes and conjugates of words and are based on two different order relations, denoted by <_lex and ≺_ω , that, even if strictly connected, are quite different from the computational point of view. In this study an important role is played by Lyndon words. In particular, we improve the upper bound on the number of symbol comparisons needed to establish the ≺ ω order between two primitive words by using a preliminary knowledge of the <_lex order of the corresponding Lyndon conjugates. Moreover, we propose an algorithm that efficiently sorts, according to the ≺_ω order, the list of conjugates of a multiset of Lyndon words. Finally, we show that the Lyndon factorization of a word helps the construction of its suffix array, allowing a reduction of the number of symbol comparisons needed to lexicographically sort the suffixes of the word
An extension of the Burrows-Wheeler Transform and applications to sequence comparison and data compression
No full textWe introduce a generalization of the Burrows-Wheeler Transform (BWT) that can be applied to a multiset of words. The extended transformation, denoted by E, is reversible, but, differently from BWT, it is also surjective. The E transformation allows to give a definition of distance between two sequences, that we apply here to the problem of the whole mitochondrial genome phylogeny. Moreover we give some consideration about compressing a set of words by using the E transformation as preprocessing
A Comparison Between Similarity Measures Based on Minimal Absent Words: An Experimental Approach
Full text linkIn this paper we make some experimental considerations on the sets D(x, y), M(x)M(y), M(x) ∪ M(y) involving minimal absent words of two words x and y. This study is motivated by the computation of distances based on these sets
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