Search results for " Combinatorics on words"

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…

Novel Results on the Number of Runs of the Burrows-Wheeler-Transform

2021

The Burrows-Wheeler-Transform (BWT), a reversible string transformation, is one of the fundamental components of many current data structures in string processing. It is central in data compression, as well as in efficient query algorithms for sequence data, such as webpages, genomic and other biological sequences, or indeed any textual data. The BWT lends itself well to compression because its number of equal-letter-runs (usually referred to as $r$) is often considerably lower than that of the original string; in particular, it is well suited for strings with many repeated factors. In fact, much attention has been paid to the $r$ parameter as measure of repetitiveness, especially to evalua…

Burrows-Wheeler transform and palindromic richness

2009

AbstractThe investigation of the extremal case of the Burrows–Wheeler transform leads to study the words w over an ordered alphabet A={a1,a2,…,ak}, with a1<a2<⋯<ak, such that bwt(w) is of the form aknkak−1nk−1⋯a2n2a1n1, for some non-negative integers n1,n2,…,nk. A characterization of these words in the case |A|=2 has been given in [Sabrina Mantaci, Antonio Restivo, Marinella Sciortino, Burrows-Wheeler transform and Sturmian words, Information Processing Letters 86 (2003) 241–246], where it is proved that they correspond to the powers of conjugates of standard words. The case |A|=3 has been settled in [Jamie Simpson, Simon J. Puglisi, Words with simple Burrows-Wheeler transforms, Electronic …

Quasi-linear time computation of the abelian periods of a word

2012

Computing abelian periods in words

2011

International audience

A New Class of Searchable and Provably Highly Compressible String Transformations

2019

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 domains of strings. However, efforts to find non-trivial alternatives of the original, now 25 years old, Burrows-Wheeler string transformation have met limited success. In this paper we bring new lymph to this area by introducing a whole new family of transformations that have all the "myriad virtues" of the BWT: they can be computed and inverted in linear time, they produce provably highly compressible strings, and they support linear time pattern search direc…

Balanced Words Having Simple Burrows-Wheeler Transform

2009

The investigation of the "clustering effect" of the Burrows-Wheeler transform (BWT) leads to study the words having simple BWT , i.e. words w over an ordered alphabet $A=\{a_1,a_2,\ldots,a_k\}$, with $a_1 < a_2 < \ldots <a_k$, such that $bwt(w)$ is of the form $a_k^{n_k} a_{k-1}^{n_{k-1}} \cdots a_1^{n_1}$, for some non-negative integers $n_1, n_2, \ldots, n_k$. We remark that, in the case of binary alphabets, there is an equivalence between words having simple BWT, the family of (circular) balanced words and the conjugates of standard words. In the case of alphabets of size greater than two, there is no more equivalence between these notions. As a main result of this paper we prove that, u…