Quasi-linear Time Computation of the Abelian Periods of a Word
نویسندگان
چکیده
In the last couple of years many research papers have been devoted to Abelian complexity of words. Recently, Constantinescu and Ilie (Bulletin EATCS 89, 167–170, 2006) introduced the notion of Abelian period. In this article we present two quadratic brute force algorithms for computing Abelian periods for special cases and a quasi-linear algorithm for computing all the Abelian periods of a word.
منابع مشابه
Identifying All Abelian Periods of a String in quadratic Time and Relevant Problems
Abelian periodicity of strings has been studied extensively over the last years. In 2006 Constantinescu and Ilie defined the abelian period of a string and several algorithms for the computation of all abelian periods of a string were given. In contrast to the classical period of a word, its abelian version is more flexible, factors of the word are considered the same under any internal permuta...
متن کاملA Note on Easy and Efficient Computation of Full Abelian Periods of a Word
Constantinescu and Ilie (Bulletin of the EATCS 89, 167–170, 2006) introduced the idea of an Abelian period with head and tail of a finite word. An Abelian period is called full if both the head and the tail are empty. We present a simple and easy-to-implement O(n log logn)-time algorithm for computing all the full Abelian periods of a word of length n over a constant-size alphabet. Experiments ...
متن کاملA Note on Efficient Computation of All Abelian Periods in a String
We derive a simple efficient algorithm for Abelian periods knowing all Abelian squares in a string. An efficient algorithm for the latter problem was given by Cummings and Smyth in 1997. By the way we show an alternative algorithm for Abelian squares. We also obtain a linear time algorithm finding all “long” Abelian periods. The aim of the paper is a (new) reduction of the problem of all Abelia...
متن کاملComputation of Minimum Hamming Weight for Linear Codes
In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$ which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...
متن کاملFast computation of abelian runs
Given a word w and a Parikh vector P , an abelian run of period P in w is a maximal occurrence of a substring of w having abelian period P . Our main result is an online algorithm that, given a word w of length n over an alphabet of cardinality σ and a Parikh vector P , returns all the abelian runs of period P in w in time O(n) and space O(σ + p), where p is the norm of P , i.e., the sum of its...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012