54 research outputs found
Linear pattern matching on sparse suffix trees
Packing several characters into one computer word is a simple and natural way
to compress the representation of a string and to speed up its processing.
Exploiting this idea, we propose an index for a packed string, based on a {\em
sparse suffix tree} \cite{KU-96} with appropriately defined suffix links.
Assuming, under the standard unit-cost RAM model, that a word can store up to
characters ( the alphabet size), our index takes
space, i.e. the same space as the packed string itself.
The resulting pattern matching algorithm runs in time ,
where is the length of the pattern, is the actual number of characters
stored in a word and is the number of pattern occurrences
On the number of Dejean words over alphabets of 5, 6, 7, 8, 9 and 10 letters
We give lower bounds on the growth rate of Dejean words, i.e. minimally
repetitive words, over a k-letter alphabet, for k=5, 6, 7, 8, 9, 10. Put
together with the known upper bounds, we estimate these growth rates with the
precision of 0,005. As an consequence, we establish the exponential growth of
the number of Dejean words over a k-letter alphabet, for k=5, 6, 7, 8, 9, 10.Comment: 13 page
Finding approximate repetitions under Hamming distance
The problem of computing tandem repetitions with possible mismatches is studied. Two main definitions are considered, and for both of them an algorithm is proposed ( the size of the output). This improves, in particular, the bound obtained in \citeLS93. Finally, other possible definions are briefly analyzed.
On the sum of exponents of maximal repetitions in a word
Rapport interne.This paper continues the study presented in {KolpakovKucherovRI98}, where it was proved that the number of maximal repetitions in a word is linearly-bounded in the word length. Here we strengthen this result and prove that the sum of exponents of maximal repetitions is linearly-bounded too. Similarly to {KolpakovKucherovRI98}, we first estimate the sum of exponents of maximal repetitions in Fibonacci words. Then we prove that the sum of exponents of all maximal repetitions in general words is linearly-bounded. Finally, some algorithmic applications of this results are discussed
On repetition-free binary words of minimal density
Colloque avec actes et comité de lecture.In \cite{KolpakovKucherovMFCS97}, a notion of minimal proportion (density) of one letter in -th power-free binary words has been introduced and some of its properties have been proved. In this paper, we proceed with this study and substantially extend some of these results. First, we introduce and analyse a general notion of minimal letter density for any infinite set of words which don't contain a specified set of ``prohibited'' subwords. We then prove that for -th power-free binary words, the density function is refining the estimate from \cite{KolpakovKucherovMFCS97}. Following \cite{KolpakovKucherovMFCS97}, we also consider a natural generalization of -th power-free words to -th power-free words for real argument . We prove that the minimal proportion of one letter in -th power-free binary words, considered as a function of , is discontinuous at all integer points . Finally, we give an estimate of the size of the jumps
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