Constructing an indeterminate string from its associated graph

Helling, Joel; Ryan, Patrick J.; Smyth, W. Franklin; Soltys, Michael

doi:10.1016/j.tcs.2017.02.016

Cited by 9 publications

(11 citation statements)

References 23 publications

(26 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first string reverse engineering problem was introduced by Franȇk et al [7] who proposed a method to check if any integer array was the border array of some string. Since then a plethora of string inference problems have been studied in the literature (e.g., [4,[8][9][10][11][12][13][14][15][16]).…”

Section: Introductionmentioning

confidence: 99%

Counting and Verifying Abelian Border Arrays of Binary Words

Habib¹,

Shamil²,

Rahman³

2021

Preprint

View full text Add to dashboard Cite

In this note, we consider the problem of counting and verifying abelian border arrays of binary words. We show that the number of valid abelian border arrays of length n is 2 n−1 . We also show that verifying whether a given array is the abelian border array of some binary word reduces to computing the abelian border array of a specific binary word. Thus, assuming the word-RAM model, we present an O n 2 log 2 n time algorithm for the abelian border array verification problem.

show abstract

Section: Introductionmentioning

confidence: 99%

Counting and Verifying Abelian Border Arrays of Binary Words

Habib¹,

Shamil²,

Rahman³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…In addition, other aspects of indeterminate strings have been studied, such as their border arrays [13], cover arrays [14], prefix arrays [15,16] and suffix arrays [17,13]. The computation of an indeterminate string from its prefix graph was recently considered in [18].…”

Section: Introductionmentioning

confidence: 99%

A New Approach to Regular & Indeterminate Strings

Louza,

Mhaskar,

Smyth

2020

Preprint

View full text Add to dashboard Cite

In this paper we propose a new, more appropriate definition of regular and indeterminate strings. A regular string is one that is "isomorphic" to a string whose entries all consist of a single letter, but which nevertheless may itself include entries containing multiple letters. A string that is not regular is said to be indeterminate. We begin by proposing a new model for the representation of strings, regular or indeterminate, then go on to describe a linear time algorithm to determine whether or not a string x = x[1..n] is regular and, if so, to replace it by a lexicographically least (lex-least) string y whose entries are all single letters. Furthermore, we connect the regularity of a string to the transitive closure problem on a graph, which in our special case can be efficiently solved. We then introduce the idea of a feasible palindrome array MP of a string, and prove that every feasible MP corresponds to some (regular or indeterminate) string. We describe an algorithm that constructs a string x corresponding to given feasible MP, while ensuring that whenever possible x is regular and if so, then lex-least. A final section outlines new research directions suggested by this changed perspective on regular and indeterminate strings.

show abstract

“…Let Θ n (m) be the largest possible θ(G) for G ∈ G n (m). In [3,Problem 11] the authors pose the following problem: describe the function Θ n (m) for every given n, and they provide as an example a graph for Θ 7 (m), where m ranges over {0, 1, . .…”

Section: Introductionmentioning

confidence: 99%

“…We already know from [3] that for each n, the global maximum is reached at m = ⌊n 2 /4⌋. The reason for this is that ⌊n 2 /4⌋ is the largest number of edges that can fit in a graph on n vertices without forcing any triangles; note that such a graph is simply a complete bipartite graph.…”

Section: Introductionmentioning

confidence: 99%

“…We also establish Algorithm 1, which computes Θ n (m) in linear time. Our motivation comes from [3], where Θ n (m) would be used as an upper bound for the size of a minimal alphabet for an indeterminate string based on the edge and vertex counts of said string's corresponding undirected graph. The hope, of course, is that exploration of the structural causes behind the upper bound of θ(G) will help us to better understand the problem of finding a minimal or nearminimal clique cover, which corresponds directly to finding a small alphabet for an indeterminate string.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An exact upper bound on the size of minimal clique covers

McIntyre,

Soltys

2017

Preprint

Self Cite

View full text Add to dashboard Cite

Indeterminate strings have received considerable attention in the recent past; see for example [1] and [3]. This attention is due to their applicability in bioinformatics, and to the natural correspondence with undirected graphs. One aspect of this correspondence is the fact that the minimal alphabet size of indeterminates representing any given undirected graph corresponds to the size of the minimal clique cover of this graph. This paper solves a related problem proposed in [3]: compute Θn(m), which is the size of the largest possible minimal clique cover (i.e., an exact upper bound), and hence alphabet size of the corresponding indeterminate, of any graph on n vertices and m edges.

show abstract

Constructing an indeterminate string from its associated graph

Cited by 9 publications

References 23 publications

Counting and Verifying Abelian Border Arrays of Binary Words

Counting and Verifying Abelian Border Arrays of Binary Words

A New Approach to Regular & Indeterminate Strings

An exact upper bound on the size of minimal clique covers

Contact Info

Product

Resources

About