Abstract not found

this paper ## Sawada 23 developed an algorithm to generate k-ary 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

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 + 1)=(q \Gamma 1), where q 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 Introduction Several years ago, J.-P. Duval [4] has presented an amazingly simple algorithm for generating all Lyndon words up to a given length in lexicographic order. He observed that the worst-case behavior of his algorithm, for computing the next Lyndon word is linear, and he left as an open problem to determine the average-case running time. We answer this question by showing that the average number of operations required for computing a Lyndon word of length at most n is constant, and independent of n. More precisely, we show that the cost is asymptotically equal to (q + 1)=(q \Gamma 1), where q is the size of the alphab...

A new approach to time-space efficient string-matching is presented. The method is flexible, its implementation depends whether or not the alphabet is linearly ordered. The only known linear-time constant-space algorithm for string-matching over nonordered alphabets is the GalilSeiferas algorithm, see [8, 6] which is rather complicated. The zooming method gives probably the simplest string-matching 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 well-known 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 [...

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) k-ary 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.

Two different factorizations of the Fibonacci infinite word were given independently in [10] and [6]. In a certain sense, these factorizations reveal a self-similarity 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 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) worst-case time for words which are "1-decomposable", and \Theta(n) average-case 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...

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 non-isomorphic chord diagrams. 1.

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.

In this paper we present external memory algorithms for some string problems. External memory algorithms have been developed in many research areas, as the speed gap between fast internal memory and slow external memory continues to grow. The goal of external memory algorithms is to minimize the number of input/output operations between internal memory and external memory. These years the sizes of strings such as DNA sequences are rapidly increasing. However, external memory algorithms have been developed for only a few string problems. In this paper we consider five string problems and present external memory algorithms for them. They are the problems of finding the maximum suffix, string matching, period finding, Lyndon decomposition, and finding the minimum of a circular string. Every algorithm that we present here runs in a linear number of I/Os in the external memory model with one disk, and they run in an optimal number of disk I/Os in the external memory model with multiple disks.