A linear partitioning algorithm for Hybrid Lyndons using V-order

Authors:
David E. Daykin;Jacqueline W. Daykin;W. F. Smyth
Affiliations:
Department of Mathematics, University of Reading, UK;Department of Computer Science, Royal Holloway, University of London, UK and Department of Informatics, Kings College, University of London, UK;Department of Informatics, Kings College, University of London, UK and Algorithms Research Group, Department of Computing & Software, McMaster University, Hamilton ON L8S 4K1, Canada
Venue:
Theoretical Computer Science
Year:
2013

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Abstract

In this paper we extend previous work on unique maximal factorization families (UMFFs) and a total (but non-lexicographic) ordering of strings called V-order. We present new combinatorial results for V-order, in particular concatenation under V-order. We propose linear-time RAM algorithms for string comparison in V-order and for Lyndon-like factorization of a string into V-words. This asymptotic efficiency thus matches that of the corresponding algorithms for lexicographical order. Finally, we introduce Hybrid Lyndon words as a generalization of standard Lyndon words, and hence propose extensions of factorization algorithms to other forms of order.