Results 1  10
of
29
Fast Algorithms to Generate Necklaces, Unlabeled Necklaces, and Irreducible Polynomials over GF(2)
, 2000
"... this paper ## Sawada 23 developed an algorithm to generate kary bracelets in constant ## amortized time. Proskurowski et al. 17 show that the orbits of the ' Z. Z. Z . composition of b and d can be generated in amortized Oktime, which is CAT if k is fixed. It remains an interesting challenge to de ..."
Abstract

Cited by 18 (8 self)
 Add to MetaCart
this paper ## Sawada 23 developed an algorithm to generate kary bracelets in constant ## amortized time. Proskurowski et al. 17 show that the orbits of the ' Z. Z. Z . composition of b and d can be generated in amortized Oktime, which is CAT if k is fixed. It remains an interesting challenge to develop efficient algorithms for the other compositions
Average cost of Duval's algorithm for generating Lyndon words
, 1992
"... Berstel, J. and M. Pocchiola, Average cost of Duval’s algorithm for generating Lyndon words, Theoretical Computer Science 132 (1994) 415425. The average cost of Duval’s algorithm for generating all Lyndon words up to a given length in lexicographic order is proved to be asymptotically equal to (q+ ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
Berstel, J. and M. Pocchiola, Average cost of Duval’s algorithm for generating Lyndon words, Theoretical Computer Science 132 (1994) 415425. The average cost of Duval’s algorithm for generating all Lyndon words up to a given length in lexicographic order is proved to be asymptotically equal to (q+ l)/(q l), where 4 is the size of the underlying alphabet. In particular, the average cost is independent of the length of the words generated. A precise evaluation of the constants is also given. 1.
The Zooming Method: A Recursive Approach to TimeSpace Efficient StringMatching
 Comput. Sci
, 1995
"... A new approach to timespace efficient stringmatching is presented. The method is flexible, its implementation depends whether or not the alphabet is linearly ordered. The only known lineartime constantspace algorithm for stringmatching over nonordered alphabets is the GalilSeiferas algorithm, s ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
A new approach to timespace efficient stringmatching is presented. The method is flexible, its implementation depends whether or not the alphabet is linearly ordered. The only known lineartime constantspace algorithm for stringmatching over nonordered alphabets is the GalilSeiferas algorithm, see [8, 6] which is rather complicated. The zooming method gives probably the simplest stringmatching algorithm working in constant space and linear time for nonordered alphabets. The novel feature of our algorithm is the application of the searching phase (which is usually simpler than preprocessing) in the preprocessing phase. The preprocessing has a recursive structure similar to selection in linear time, see [1]. For ordered alphabets the preprocessing part is much simpler, its basic component is a simple and wellknown algorithm for finding the maximal suffix, see [7]. Hence we demonstrate a new application of this algorithm, see also [5]. The idea of the zooming method was applied in [...
Generating Bracelets in Constant Amortized Time
 SIAM JOURNAL ON COMPUTING
, 2001
"... A bracelet is the lexicographically smallest element in an equivalence class of strings under string rotation and reversal. We present a fast, simple, recursive algorithm for generating (i.e., listing) kary bracelets. Using simple bounding techniques, we prove that the algorithm is optimal in the s ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
A bracelet is the lexicographically smallest element in an equivalence class of strings under string rotation and reversal. We present a fast, simple, recursive algorithm for generating (i.e., listing) kary bracelets. Using simple bounding techniques, we prove that the algorithm is optimal in the sense that the running time is proportional to the number of bracelets produced. This is an improvement by a factor of n (where n is the length of the bracelets being generated) over the fastest, previously known algorithm to generate bracelets.
Lyndon Words and Singular Factors of Sturmian Words
"... Two different factorizations of the Fibonacci infinite word were given independently in [10] and [6]. In a certain sense, these factorizations reveal a selfsimilarity property of the Fibonacci word. We first describe the intimate links between these two factorizations. We then propose a generalizat ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
Two different factorizations of the Fibonacci infinite word were given independently in [10] and [6]. In a certain sense, these factorizations reveal a selfsimilarity property of the Fibonacci word. We first describe the intimate links between these two factorizations. We then propose a generalization to characteristic sturmian words.
A Fast Average Case Algorithm For Lyndon Decomposition
 Internat. J. Computer Math
, 1995
"... A simple algorithm, called LD, is described for computing the Lyndon decomposition of a word of length n. Although LD requires time O(nlogn) in the worst case, it is shown to require only \Theta(n) worstcase time for words which are "1decomposable", and \Theta(n) averagecase time for words whose ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
A simple algorithm, called LD, is described for computing the Lyndon decomposition of a word of length n. Although LD requires time O(nlogn) in the worst case, it is shown to require only \Theta(n) worstcase time for words which are "1decomposable", and \Theta(n) averagecase time for words whose length is small with respect to alphabet size. The main interest in LD resides in its application to the problem of computing the canonical form of a circular word. For this problem, LD is shown to execute significantly faster than other known algorithms on important classes of words. Further, experiment suggests that, when applied to arbitrary words, LD on average outperforms the other known canonization algorithms in terms of two measures: number of tests on letters and execution time. KEYWORDS combinatorial, algorithm, word, string, monoid, Lyndon, decomposition, factorization, canonization, canonical form, lexicographically least, circular, average case. AMS SUBJECT CLASSIFICATION 68C...
A Fast Algorithm for Generating NonIsomorphic Chord Diagrams
 SIAM J. Discrete Math
"... Using a new string representation, we develop two algorithms for generating nonisomorphic chord diagrams. Experimental evidence indicates that the latter of the two algorithms runs in constant amortized time. In addition, we use simple counting techniques to derive a formula for the number of nonis ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
Using a new string representation, we develop two algorithms for generating nonisomorphic chord diagrams. Experimental evidence indicates that the latter of the two algorithms runs in constant amortized time. In addition, we use simple counting techniques to derive a formula for the number of nonisomorphic chord diagrams. 1.
Lyndon Factorization of Infinite Words
"... Infinite Lyndon words have been introduced in [1], where the authors proved a factorization theorem for infinite words: any infinite word can be written as a non increasing product of Lyndon words, finite and/or infinite. After giving a new characterization of infinite Lyndon words, we concentrate o ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
Infinite Lyndon words have been introduced in [1], where the authors proved a factorization theorem for infinite words: any infinite word can be written as a non increasing product of Lyndon words, finite and/or infinite. After giving a new characterization of infinite Lyndon words, we concentrate on three well known infinite words and give their factorization. We conclude by giving an application to !division of infinite words.
Generating Lyndon brackets: a basis for the nth homogeneous component of the free Lie algebra
 Journal of Algorithms
, 2001
"... this paper, we develop an algorithm which generates the standard bracketing for all Lyndon words of length n, thus constructing a basis for the nth homogeneous component of the free Lie algebra. The algorithm runs in linear amortized time; i.e., O(n) time per basis element ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
this paper, we develop an algorithm which generates the standard bracketing for all Lyndon words of length n, thus constructing a basis for the nth homogeneous component of the free Lie algebra. The algorithm runs in linear amortized time; i.e., O(n) time per basis element