String Comparison and Lyndon-Like Factorization Using V-Order in Linear Time

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 describe linear-time algorithms for string comparison and Lyndon factorization based on V-order. We propose extensions of these algorithms to other forms of order.

[1]  Jacqueline W. Daykin,et al.  Properties and Construction of Unique Maximal Factorization Families for Strings , 2008, Int. J. Found. Comput. Sci..

[2]  William F. Smyth,et al.  Computing Patterns in Strings , 2003 .

[3]  Joseph Gil,et al.  A Bijective String Sorting Transform , 2012, ArXiv.

[4]  Jacqueline W. Daykin,et al.  Lyndon-like and V-order factorizations of strings , 2003, J. Discrete Algorithms.

[5]  Maxime Crochemore,et al.  A note on the Burrows - CWheeler transformation , 2005, Theor. Comput. Sci..

[6]  Ludovic Perret.  A Chosen Ciphertext Attack on a Public Key Cryptosystem Based on Lyndon Words , 2005, IACR Cryptol. ePrint Arch..

[7]  Eric Rivals,et al.  STAR: an algorithm to Search for Tandem Approximate Repeats , 2004, Bioinform..

[8]  Costas S. Iliopoulos,et al.  Parallel RAM Algorithms for Factorizing Words , 1994, Theor. Comput. Sci..

[9]  David E. Daykin,et al.  Ordered Ranked Posets, Representations of Integers and Inequalities from Extremal Poset Problems , 1985 .

[10]  M. Lothaire.  Combinatorics on words: Bibliography , 1997 .

[11]  W. F. Smyth,et al.  Optimal Algorithms for Computing the canonical form of a circular string , 1992, Theor. Comput. Sci..

[12]  Marc Chemillier.  Periodic musical sequences and Lyndon words , 2004, Soft Comput..

[13]  R. Lyndon,et al.  Free Differential Calculus, IV. The Quotient Groups of the Lower Central Series , 1958 .

[14]  Jean Pierre Duval,et al.  Factorizing Words over an Ordered Alphabet , 1983, J. Algorithms.

[15]  William F. Smyth,et al.  Combinatorics of Unique Maximal Factorization Families (UMFFs) , 2009, Fundam. Informaticae.