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Counting and Verifying Abelian Border Arrays of Binary Words
Mursalin Habib, Md. Salman Shamil, M. Sohel Rahman
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…
Multidimensional segment trees can do range updates in poly-logarithmic time
Nabil Ibtehaz, M. Kaykobad, M. Sohel Rahman
Updating and querying on a range is a classical algorithmic problem with a multitude of applications. The Segment Tree data structure is particularly notable in handling the range…
Algorithms to Compute the Lyndon Array
Frantisek Franek, A. S. M. Sohidull Islam, M. Sohel Rahman +1
We first describe three algorithms for computing the Lyndon array that have been suggested in the literature, but for which no structured exposition has been given. Two of these al…
String Comparison in -Order: New Lexicographic Properties & On-line Applications
Ali Alatabbi, Jacqueline W. Daykin, M. Sohel Rahman +1
-order is a global order on strings related to Unique Maximal Factorization Families (UMFFs), which are themselves generalizations of Lyndon words. -order has recently been p…
Linear Algorithms for Computing the Lyndon Border Array and the Lyndon Suffix Array
Ali Alatabbi, Jacqueline W. Daykin, M. Sohel Rahman
We consider the problem of finding repetitive structures and inherent patterns in a given string $\s{s}$ of length over a finite totally ordered alphabet. A border $\s{u}$ of a…
Enhanced Covers of Regular & Indeterminate Strings using Prefix Tables
Ali Alatabbi, A. S. Sohidull Islam, M. Sohel Rahman +2
A \itbf{cover} of a string is a proper substring of such that can be constructed from possibly overlapping instances of . A recent paper \cite{FIKPPST1…