Inferring an indeterminate string from a prefix graph

Abstract

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

A prefix array for parameterized strings

“…Example 8. For Y = AABBAABB, we have P A=(8, 1, 0, 0, 4, 1, 0, 0), P OS= (1,2,5,6), and LEN =(8, 1, 4, 1).…”

“…Consider the parameterized suffix tree (pST ) [7]. We walk the path T [1], T [2], ..., T [n] and when at symbol T [i], we say that all p-suffixes (say at k) that differentiate at this node have plcp(1, k, T ) = i. The problem with the pST approach is that like the traditional suffix tree [44,32,1], the pST suffers from a large practical footprint.…”

“…For an n-length T , P A [i] is the length of the longest prefix common between T and T [i...n]. The P A computation is powerful for traditional pattern matching applications and, unlike the related-border array [44], where each border [i] is the length of the longest prefix of T [1...i] that matches a suffix of T [1...i], the P A is able to also support indeterminate pattern matching [45,18,22,2]. The P A has even been represented more compactly [45].…”

“…Baker [8] identifies three types of pattern matching: (1) exact matching, (2) parameterized matching (p-match), and (3) matching with modifications. In this work, we focus on (2) and a new fusion between (2) and (3). The first p-match breakthroughs revolved around suffix structures on the previous (prev) encoding.…”

Computing covers using prefix tables

“…Here x does not have a border of length β[β [3]] = 1; on the other hand, π = 320 correctly identifies all the borders of every prefix of x.…”