Search results for "Lexicographical order"
showing 10 items of 15 documents
Block Sorting-Based Transformations on Words: Beyond the Magic BWT
2018
The Burrows-Wheeler Transform (BWT) is a word transformation introduced in 1994 for Data Compression and later results have contributed to make it a fundamental tool for the design of self-indexing compressed data structures. The Alternating Burrows-Wheeler Transform (ABWT) is a more recent transformation, studied in the context of Combinatorics on Words, that works in a similar way, using an alternating lexicographical order instead of the usual one. In this paper we study a more general class of block sorting-based transformations. The transformations in this new class prove to be interesting combinatorial tools that offer new research perspectives. In particular, we show that all the tra…
Verbal ordinal classification with multicriteria decision aiding
2008
Abstract Professionals in neuropsychology usually perform diagnoses of patients’ behaviour in a verbal rather than in a numerical form. This fact generates interest in decision support systems that process verbal data. It also motivates us to develop methods for the classification of such data. In this paper, we describe ways of aiding classification of a discrete set of objects, evaluated on set of criteria that may have verbal estimations, into ordered decision classes. In some situations, there is no explicit additional information available, while in others it is possible to order the criteria lexicographically. We consider both of these cases. The proposed Dichotomic Classification (DC…
On the loopless generation of binary tree sequences
1998
Weight sequences were introduced by Pallo in 1986 for coding binary trees and he presented a constant amortized time algorithm for their generation in lexicographic order. A year later, Roelants van Baronaigien and Ruskey developed a recursive constant amortized time algorithm for generating Gray code for binary trees in Pallo's representation. It is common practice to find a loopless generating algorithm for a combinatorial object when enunciating a Gray code for this object. In this paper we regard weight sequences as variations and apply a Williamson algorithm in order to obtain a loopless generating algorithm for the Roelants van Baronaigien and Ruskey's Gray code for weight sequences.
A bijection between words and multisets of necklaces
2012
Two of the present authors have given in 1993 a bijection Phi between words on a totally ordered alphabet and multisets of primitive necklaces. At the same time and independently, Burrows and Wheeler gave a data compression algorithm which turns out to be a particular case of the inverse of Phi. In the present article, we show that if one replaces in Phi the standard permutation of a word by the co-standard one (reading the word from right to left), then the inverse bijection is computed using the alternate lexicographic order (which is the order of real numbers given by continued fractions) on necklaces, instead of the lexicographic order as for Phi(-1). The image of the new bijection, ins…
Universal Lyndon Words
2014
A word w over an alphabet Σ is a Lyndon word if there exists an order defined on Σ for which w is lexicographically smaller than all of its conjugates (other than itself). We introduce and study universal Lyndon words, which are words over an n-letter alphabet that have length n! and such that all the conjugates are Lyndon words. We show that universal Lyndon words exist for every n and exhibit combinatorial and structural properties of these words. We then define particular prefix codes, which we call Hamiltonian lex-codes, and show that every Hamiltonian lex-code is in bijection with the set of the shortest unrepeated prefixes of the conjugates of a universal Lyndon word. This allows us t…
A note on Sturmian words
2012
International audience; We describe an algorithm which, given a factor of a Sturmian word, computes the next factor of the same length in the lexicographic order in linear time. It is based on a combinatorial property of Sturmian words which is related with the Burrows-Wheeler transformation.
A Multi-Objective Approach to Optimize a Periodic Maintenance Policy
2012
The present paper proposes a multi-objective approach to find out an optimal periodic maintenance policy for a repairable and stochastically deteriorating multi-component system over a finite time horizon. The tackled problem concerns the determination of the system elements to replace at each scheduled and periodical system inspection by ensuring the simultaneous minimization of both the expected total maintenance cost and the expected global system unavailability time. It is assumed that in the case of system elements failure they are instantaneously detected and repaired by means of minimal repair actions in order to rapidly restore the system. A nonlinear integer mathematical programmi…
On generalized Lyndon words
2018
Abstract A generalized lexicographical order on infinite words is defined by choosing for each position a total order on the alphabet. This allows to define generalized Lyndon words. Every word in the free monoid can be factorized in a unique way as a nonincreasing factorization of generalized Lyndon words. We give new characterizations of the first and the last factor in this factorization as well as new characterization of generalized Lyndon words. We also give more specific results on two special cases: the classical one and the one arising from the alternating lexicographical order.
Parallel Algorithms for Listing Well-Formed Parentheses Strings
1998
We present two cost-optimal parallel algorithms generating the set of all well-formed parentheses strings of length 2n with constant delay for each generated string. In our first algorithm we generate in lexicographic order well-formed parentheses strings represented by bitstrings, and in the second one we use the representation by weight sequences. In both cases the computational model is based on an architecture CREW PRAM, where each processor performs the same algorithm simultaneously on a different set of data. Different processors can access the shared memory at the same time to read different data in the same or different memory locations, but no two processors are allowed to write i…
Reflections on the role and design of online dictionaries for specialised translation
2014
Este artículo trata de los diccionarios especializados de traducción. Basado en los principios de la teoría funcional, analiza las diversas fases y subfases del proceso traductivo desde una perspectiva lexicográfica mostrando que un diccionario de traducción, si realmente pretende resolver las complejas necesidades de sus usuarios, debe ser mucho más que un simple diccionario bilingüe. A continuación presenta un concepto global de diccionario de traducción que incluye diversos componentes monolingües y bilingües en ambas direcciones entre las dos lenguas en cuestión. Finalmente, el artículo debate cómo este concepto puede aplicarse en Internet con el fin de desarrollar diccionarios de tradu…