Abstract
The data explosion problem continues to escalate requiring novel and ingenious solutions. Pattern inference focusing on repetitive structures in data is a vigorous field of endeavor aimed at shrinking volumes of data by means of concise descriptions. The Burrows–Wheeler transformation computes a permutation of a string of letters over an alphabet, and is wellsuited to compressionrelated applications due to its invertability and data clustering properties. For space efficiency the input to the transform can be preprocessed into Lyndon factors. Rather than this classic deterministic approach for letter based strings, we consider scenarios with uncertainty regarding the data: a position in an indeterminate or degenerate string is a set of letters. We first define indeterminate Lyndon words and establish their associated unique string factorization; then we introduce the novel degenerate Burrows–Wheeler transformation which may apply the indeterminate Lyndon factorization. A core computation in Burrows–Wheeler type transforms is the linear sorting of all conjugates of the input string—we achieve this in the degenerate case with lexextension ordering. Like the original forms, indeterminate Lyndon factorization and the degenerate transform and its inverse can all be computed in linear time and space with respect to total input size of degenerate strings. Regular molecular biological strings yield a wealth of applications of big data—an important motivation for generalizing to degenerate strings is their extensive use in expressing polymorphism in DNA sequences.
Original language  English 

Pages (fromto)  209218 
Number of pages  10 
Journal  Mathematics in Computer Science 
Volume  11 
Issue number  2 
Early online date  02 Feb 2017 
DOIs  
Publication status  Published  01 Jun 2017 
Externally published  Yes 
Keywords
 degenerate biological string
 degenerate BurrowsWheeler transform
 indeterminate Lyndon word
 indeterminate suffix array
 inverse transform
 lexextension order
 linear
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Jacqueline Daykin
 Faculty of Business and Physcial Sciences, Department of Computer Science  Honorary Research Fellow
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