A linear partitioning algorithm for Hybrid Lyndons using V-order

David E. Daykin, Jacqueline W. Daykin, William F. Smyth

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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.
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


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


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