A linear partitioning algorithm for Hybrid Lyndons using V-order

Authors Organisations
  • David E. Daykin(Author)
    University of Reading
  • Jacqueline Daykin(Author)
    Royal Holloway, University of London
    King's College London
  • William F. Smyth(Author)
    King's College London
    McMaster University
Type Article
Original languageEnglish
Pages (from-to)149-161
Number of pages13
JournalTheoretical Computer Science
Early online date10 Feb 2012
Publication statusPublished - 29 Apr 2013
Externally publishedYes
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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 Lyndonlike 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.


  • algorithm, alphabet, circ-UMFF, concatenate, factor, hybrid lyndon, lexicographic order, lyndon, maximal, RAM, string, total order, UMFF, V, -order, word, V, -word