Search results for "Run-length encoding"
showing 4 items of 4 documents
Measuring the clustering effect of BWT via RLE
2017
Abstract The Burrows–Wheeler Transform (BWT) is a reversible transformation on which are based several text compressors and many other tools used in Bioinformatics and Computational Biology. The BWT is not actually a compressor, but a transformation that performs a context-dependent permutation of the letters of the input text that often create runs of equal letters (clusters) longer than the ones in the original text, usually referred to as the “clustering effect” of BWT. In particular, from a combinatorial point of view, great attention has been given to the case in which the BWT produces the fewest number of clusters (cf. [5] , [16] , [21] , [23] ). In this paper we are concerned about t…
Burrows-Wheeler transform and Run-Length Enconding
2017
In this paper we study the clustering effect of the Burrows-Wheeler Transform (BWT) from a combinatorial viewpoint. In particular, given a word w we define the BWT-clustering ratio of w as the ratio between the number of clusters produced by BWT and the number of the clusters of w. The number of clusters of a word is measured by its Run-Length Encoding. We show that the BWT-clustering ratio ranges in ]0, 2]. Moreover, given a rational number \(r\,\in \,]0,2]\), it is possible to find infinitely many words having BWT-clustering ratio equal to r. Finally, we show how the words can be classified according to their BWT-clustering ratio. The behavior of such a parameter is studied for very well-…
String attractors and combinatorics on words
2019
The notion of \emph{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 $w=w[1]w[2]\cdots w[n]$ is a subset $\Gamma$ of the positions $\{1,\ldots,n\}$, such that all distinct factors of $w$ have an occurrence crossing at least one of the elements of $\Gamma$. 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 noti…
Binary jumbled string matching for highly run-length compressible texts
2012
The Binary Jumbled String Matching problem is defined as: Given a string $s$ over $\{a,b\}$ of length $n$ and a query $(x,y)$, with $x,y$ non-negative integers, decide whether $s$ has a substring $t$ with exactly $x$ $a$'s and $y$ $b$'s. Previous solutions created an index of size O(n) in a pre-processing step, which was then used to answer queries in constant time. The fastest algorithms for construction of this index have running time $O(n^2/\log n)$ [Burcsi et al., FUN 2010; Moosa and Rahman, IPL 2010], or $O(n^2/\log^2 n)$ in the word-RAM model [Moosa and Rahman, JDA 2012]. We propose an index constructed directly from the run-length encoding of $s$. The construction time of our index i…