# Inferring an indeterminate string from a prefix graph

Alatabbi, A., Sohel Rahman, M. and Smyth, W.F. (2014) Inferring an indeterminate string from a prefix graph. Journal of Discrete Algorithms, 32 . pp. 6-13.

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Link to Published Version: http://dx.doi.org/10.1016/j.jda.2014.12.006
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## Abstract

An indeterminate string (or, more simply, just a string ) x=x[1..n] on an alphabet σ is a sequence of nonempty subsets of σ. We say that x[i1] and x[i2] match (written x[i1]≈x[i2]) if and only if x[i1]∩x[i2]≠θ. A feasible array is an array y=y[1..n] of integers such that y[1]=n and for every i∈2..n, y[i]∈0..n-i+1. A prefix table of a string x is an array π=π[1..n] of integers such that, for every i∈1..n, π[i]=j if and only if x[i..i+j-1] is the longest substring at position i of x that matches a prefix of x It is known from [6] that every feasible array is a prefix table of some indeterminate 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.

Publication Type: Journal Article School of Engineering and Information Technology Elsevier © 2014 Elsevier B.V. http://researchrepository.murdoch.edu.au/id/eprint/25187
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