In this paper we consider the problem of computing the longest common abelian factor (LCAF) between two given strings. We present a simple O(σ n 2 ) time algorithm, where n is the length of the strings and σ is the alphabet size, and a sub-quadratic running time solution for the binary string case, both having linear space requirement. Furthermore, we present a modified algorithm applying some interesting tricks and experimentally show that the resulting algorithm runs faster.

Please cite this article in press as: A. Alatabbi et al., Inferring an indeterminate string from a prefix graph, Journal of Discrete Algorithms (2014), http://dx.doi.org/10. 1016/j.jda.2014.12.006 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. It is known from [6] that every feasible array is a prefix table of some indetermintate string. A prefix graph P = Py is a labelled simple graph whose structure is determined by a feasible array y. In this paper we show, given a feasible array y, how to use Py to construct a lexicographically least indeterminate string on a minimum alphabet whose prefix table π = y. Inferring an Indeterminate String from a Prefix Graph

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Abstract. An indeterminate string x = x[1..n] on an alphabet Σ is a sequence of nonempty subsets of Σ; x is said to be regular if every subset is of size one. A proper substring u of regular x is said to be a cover of x iff for every i ∈ 1..n, an occurrence of u in x includes x[i]. The cover array γ = γ[1..n] of x is an integer array such that γ[i] is the longest cover of x[1..i]. Fifteen years ago a complex, though nevertheless linear-time, algorithm was proposed to compute the cover array of regular x based on prior computation of the border array of x. In this paper we first describe a linear-time algorithm to compute the cover array of regular x based on the prefix table of x. We then extend this result to indeterminate strings.

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