Search results for "Equal-letter runs"
showing 2 items of 2 documents
Burrows-Wheeler Transform on Purely Morphic Words
2022
The study of the compressibility of repetitive sequences is an issue that is attracting great interest. We consider purely morphic words, which are highly repetitive sequences generated by iterating a morphism φ that admits a fixed point (denoted by φ^∞(a) ) starting from a given character a belonging to the finite alphabet A , i.e. φ^∞(a)=lim_{i→∞}φ^i(a) . Such morphisms are called prolongable on a . Here we focus on the compressibility via the Burrows-Wheeler Transform (BWT) of infinite families of finite sequences generated by morphisms. In particular, denoted by r(w) the number of equal-letter runs of a word w , we provide new upper bounds on r(bwt(φ^i(a))) , i.e. the number of equal-le…
Logarithmic Equal-Letter Runs for BWT of Purely Morphic Words
2022
In this paper we study the number r(bwt) of equal-letter runs produced by the Burrows-Wheeler transform (BWT) when it is applied to purely morphic finite words, which are words generated by iterating prolongable morphisms. Such a parameter r(bwt) is very significant since it provides a measure of the performances of the BWT, in terms of both compressibility and indexing. In particular, we prove that, when BWT is applied to whichever purely morphic finite word on a binary alphabet, r(bwt) is O(log n), where n is the length of the word. Moreover, we prove that r(bwt) is Theta(log n) for the binary words generated by a large class of prolongable binary morphisms. These bounds are proved by pro…