Applications of V-Order: Suffix Arrays, the Burrows-Wheeler Transform & the FM-index

  • Ali Alatabbi
  • Jacqueline W. Daykin
  • Neerja MhaskarEmail author
  • M. Sohel Rahman
  • W. F. Smyth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11355)


V-order is a total order on strings that determines an instance of Unique Maximal Factorization Families (UMFFs), a generalization of Lyndon words. The fundamental V-comparison of strings can be done in linear time and constant space. V-order has been proposed as an alternative to lexicographic order (lexorder) in the computation of suffix arrays and in the suffix-sorting induced by the Burrows-Wheeler transform (BWT). In line with the recent interest in the connection between suffix arrays and the Lyndon factorization, we in this paper make a first attempt to obtain similar results for the V-order factorization. Indeed, we show that the results describing the connection between suffix arrays and the Lyndon factorization are matched by analogous V-order processing. We then apply the V-BWT to implement pattern matching in V-order after suitably modifying the FM-index.


Combinatorics Lexorder String comparison V-order Suffix sorting V-BWT Pattern matching FM-index 



The third and fifth authors were funded by NSERC Grant Number: 10536797. The fourth author was partially supported by a grant from Pubali Bank Ltd., Bangladesh. The second author was part-funded by the European Regional Development Fund through the Welsh Government, Grant Number 80761-AU-137 (West): Open image in new window


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ali Alatabbi
    • 1
  • Jacqueline W. Daykin
    • 1
    • 2
    • 3
    • 4
  • Neerja Mhaskar
    • 6
    Email author
  • M. Sohel Rahman
    • 5
  • W. F. Smyth
    • 1
    • 6
    • 7
  1. 1.Department of InformaticsKing’s College LondonLondonUK
  2. 2.Department of Computer ScienceAberystwyth UniversityAberystwythWales
  3. 3.Department of Computer ScienceAberystwyth UniversityFlic en FlacMauritius
  4. 4.Department of Information ScienceStellenbosch UniversityStellenboschSouth Africa
  5. 5.Department of CSEBUETDhakaBangladesh
  6. 6.Algorithms Research Group, Department of Computing and SoftwareMcMaster UniversityHamiltonCanada
  7. 7.School of Engineering and Information TechnologyMurdoch UniversityPerthWestern Australia

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