19 research outputs found
Algorithms for Computing Abelian Periods of Words
Constantinescu and Ilie (Bulletin EATCS 89, 167--170, 2006) introduced the
notion of an \emph{Abelian period} of a word. A word of length over an
alphabet of size can have distinct Abelian periods.
The Brute-Force algorithm computes all the Abelian periods of a word in time
using space. We present an off-line
algorithm based on a \sel function having the same worst-case theoretical
complexity as the Brute-Force one, but outperforming it in practice. We then
present on-line algorithms that also enable to compute all the Abelian periods
of all the prefixes of .Comment: Accepted for publication in Discrete Applied Mathematic
Fast Computation of Abelian Runs
Given a word and a Parikh vector , an abelian run of period
in is a maximal occurrence of a substring of having
abelian period . Our main result is an online algorithm that,
given a word of length over an alphabet of cardinality and a
Parikh vector , returns all the abelian runs of period
in in time and space , where is the
norm of , i.e., the sum of its components. We also present an
online algorithm that computes all the abelian runs with periods of norm in
in time , for any given norm . Finally, we give an -time
offline randomized algorithm for computing all the abelian runs of . Its
deterministic counterpart runs in time.Comment: To appear in Theoretical Computer Scienc
Counting distinct palindromes in a word in linear time
International audienceWe design an algorithm to count the number of distinct palindromes in a word w in time O(|w|), by adapting an algorithm to detect all occurrences of maximal palindromes in a given word and using the longest previous factor array. As a direct consequence, this shows that the palindromic richness (or fullness) of a word can be checked in linear time
Multiplions et divisons avec des bâtons : Les réglettes de Genaille et Lucas.
http://www.apmep.asso.fr/spip.php?page=article&id_article=3624National audienceLes réglettes de Genaille et Lucas ont été inventées par l'ingénieur Henri Genaille en 1885 sur une proposition du mathématicien Édouard Lucas. Il existe des réglettes pour les multiplications et pour les divisions entières. Ces réglettes furent beaucoup utilisées jusque dans les années 1920, période d'apparition des règles à calcul qui précédèrent les calculatrices. Les réglettes présentées dans ce document permettent d'effectuer rapidement de grandes multiplications ou divisions sans calculer de tête. Nous expliquons comment les manipuler et les construire
Combining MEDLINE and publisher data to create parallel corpora for the automatic translation of biomedical text
International audienc
Computing abelian periods in words
International audienc
Online Computation of Abelian Runs
To appear in the Proceedings of LATA 2015Given a word and a Parikh vector , an abelian run of period in is a maximal occurrence of a substring of having abelian period . We give an algorithm that finds all the abelian runs of period in a word of length in time and space
A note on easy and efficient computation of full abelian periods of a word
International audienc