相关论文: String Comparison in $V$-Order: New Lexicographic …
We say that a family $\mathcal{W}$ of strings over $\Sigma^+$ forms a Unique Maximal Factorization Family (UMFF) if and only if every $w \in \mathcal{W}$ has a unique maximal factorization. Further, an UMFF $\mathcal{W}$ is called a…
The 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…
In this note we consider the concept of alphabet ordering in the context of string factoring. We propose a greedy-type algorithm which produces Lyndon factorizations with small numbers of factors along with a modification for large numbers…
The Burrows-Wheeler Transform is a string transformation that plays a fundamental role for the design of self-indexing compressed data structures. Over the years, researchers have successfully extended this transformation outside the…
In this paper we compare two finite words $u$ and $v$ by the lexicographical order of the infinite words $u^\omega$ and $v^\omega$. Informally, we say that we compare $u$ and $v$ by the infinite order. We show several properties of Lyndon…
In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…
A generalized lexicographic order on words is a lexicographic order where the total order of the alphabet depends on the position of the comparison. A generalized Lyndon word is a finite word which is strictly smallest among its class of…
We evaluate the influence of different alphabet orderings on the Lyndon factorization of a string. Experiments with Pizza & Chili datasets show that for most alphabet reorderings, the number of Lyndon factors is usually small, and the…
Suffix sort plays a critical role in various computational algorithms including genomics as well as in frequently used day to day software applications. The sorting algorithm becomes tricky when we have lot of repeated characters in the…
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…
Ordering the collection of states of a given automaton starting from an order of the underlying alphabet is a natural move towards a computational treatment of the language accepted by the automaton. Along this path, Wheeler \emph{graphs}…
Large-alphabet strings are common in scenarios such as information retrieval and natural-language processing. The efficient storage and processing of such strings usually introduces several challenges that are not witnessed in…
This dissertation focuses on two fundamental sorting problems: string sorting and suffix sorting. The first part considers parallel string sorting on shared-memory multi-core machines, the second part external memory suffix sorting using…
We introduce a new family of compressed data structures to efficiently store and query large string dictionaries in main memory. Our main technique is a combination of hierarchical Front-coding with ideas from longest-common-prefix…
Recently Kubica et al. (Inf. Process. Let., 2013) and Kim et al. (submitted to Theor. Comp. Sci.) introduced order-preserving pattern matching. In this problem we are looking for consecutive substrings of the text that have the same "shape"…
Sequential word order is important when processing text. Currently, neural networks (NNs) address this by modeling word position using position embeddings. The problem is that position embeddings capture the position of individual words,…
Given a string of characters, the Burrows-Wheeler Transform rearranges the characters in it so as to produce another string of the same length which is more amenable to compression techniques such as move to front, run-length encoding, and…
We extend the left-to-right Lyndon factorisation of a word to the left Lyndon tree construction of a Lyndon word. It yields an algorithm to sort the prefixes of a Lyndon word according to the infinite ordering defined by Dolce et al.…
Relative worst order analysis is a supplement or alternative to competitive analysis which has been shown to give results more in accordance with observed behavior of online algorithms for a range of different online problems. The…
The Lyndon array stores, at each position of a word, the length of the longest maximal Lyndon subword starting at that position, and plays an important role in combinatorics on words, for example in the construction of fundamental data…