Simple Linear Comparison of Strings in V-Order - (Extended Abstract)

In this paper we focus on a total (but non-lexicographic) ordering of strings called V-order. We devise a new linear-time algorithm for computing the V-comparison of two finite strings. In comparison with the previous algorithm in the literature, our algorithm is both conceptually simpler, based on recording letter positions in increasing order, and more straightforward to implement, requiring only linked lists.

[1]  Costas S. Iliopoulos,et al.  Generic Algorithms for Factoring Strings , 2013, Information Theory, Combinatorics, and Search Theory.

[2]  Veli Mäkinen,et al.  Indexing Finite Language Representation of Population Genotypes , 2010, WABI.

[3]  Costas S. Iliopoulos Optimal Cost Parallel Algorithms for Lexicographical Ordering , 1986 .

[4]  Donald L. Kreher,et al.  Combinatorial algorithms: generation, enumeration, and search , 1998, SIGA.

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

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

[7]  Amar Mukherjee,et al.  The Burrows-Wheeler Transform:: Data Compression, Suffix Arrays, and Pattern Matching , 2008 .

[8]  D. E. Daykin,et al.  Ordering Integer Vectors for Coordinate Deletions , 1997 .

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

[10]  Jacques-Olivier Lachaud,et al.  Lyndon + Christoffel = digitally convex , 2009, Pattern Recognit..

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

[12]  Peter Sanders,et al.  Linear work suffix array construction , 2006, JACM.

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

[14]  William F. Smyth,et al.  A bijective variant of the Burrows-Wheeler Transform using V-order , 2014, Theor. Comput. Sci..

[15]  Ge Nong,et al.  Linear Suffix Array Construction by Almost Pure Induced-Sorting , 2009, 2009 Data Compression Conference.

[16]  Carla Savage,et al.  A Survey of Combinatorial Gray Codes , 1997, SIAM Rev..

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

[18]  Maxime Crochemore,et al.  Two-way string-matching , 1991, JACM.

[19]  Gonzalo Navarro,et al.  Compressed full-text indexes , 2007, CSUR.

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

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

[22]  William F. Smyth,et al.  String Comparison and Lyndon-Like Factorization Using V-Order in Linear Time , 2011, CPM.

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

[24]  Charlotte Truchet,et al.  Computation of words satisfying the "rhythmic oddity property" (after Simha Arom's works) , 2003, Inf. Process. Lett..

[25]  William F. Smyth,et al.  A linear partitioning algorithm for Hybrid Lyndons using VV-order , 2013, Theor. Comput. Sci..

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

[27]  Filippo Mignosi,et al.  Simple Real-Time Constant-Space String Matching , 2011, CPM.

[28]  Srinivas Aluru,et al.  Space efficient linear time construction of suffix arrays , 2003, J. Discrete Algorithms.

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

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