A Note on a Tree-Based 2D Indexing

A new approach to the 2D pattern matching and specifically to 2D text indexing is proposed. We present the transformation of 2D structures into the form of a tree, preserving the context of each element of the structure. The tree can be linearised using the prefix notation into the form of a text (a string) and we do the pattern matching in this text. Over this representation pushdown automata indexing the 2D text are constructed. They allow to search for 2D prefixes, suffixes, or factors of the 2D text in time proportional to the size of the representation of a 2D pattern. This result achieves the properties analogous to the results obtained in tree pattern matching and string indexing.

[1]  Dong Kyue Kim,et al.  Generalizations of suffix arrays to multi-dimensional matrices , 2003, Theor. Comput. Sci..

[2]  Roberto Grossi,et al.  Suffix tree data structures for matrices , 1997, Pattern Matching Algorithms.

[3]  Niklaus Wirth,et al.  Algorithms and Data Structures , 1989, Lecture Notes in Computer Science.

[4]  Amihood Amir,et al.  Two-Dimensional Dictionary Matching , 1992, Inf. Process. Lett..

[5]  Antonio Restivo,et al.  Two-Dimensional Languages , 1997, Handbook of Formal Languages.

[6]  Jan Janousek,et al.  String Suffix Automata and Subtree Pushdown Automata , 2009, Stringology.

[7]  Raffaele Giancarlo.  A Generalization of the Suffix Tree to Square Matrices, with Applications , 1995, SIAM J. Comput..

[8]  Roberto Grossi,et al.  On the Construction of Classes of Suffix Trees for Square Matrices: Algorithms and Applications , 1995, ICALP.

[9]  Grzegorz Rozenberg,et al.  Handbook of Formal Languages , 1997, Springer Berlin Heidelberg.

[10]  Dong Kyue Kim,et al.  Constructing Suffix Arrays for Multi-dimensional Matrices , 1998, CPM.

[11]  Roberto Grossi,et al.  Multi-Dimensional Pattern Matching with Dimensional Wildcards: Data Structures and Optimal On-Line Search Algorithms , 1997, J. Algorithms.

[12]  Raffaele Giancarlo,et al.  An Index Data Structure For Matrices, with Applications to Fast Two-Dimensional Pattern Matching , 1993, WADS.

[13]  Hubert Comon,et al.  Tree automata techniques and applications , 1997 .

[14]  Katsushi Inoue,et al.  Some properties of two-dimensional on-line tessellation acceptors , 1977, Inf. Sci..

[15]  Joong Chae Na,et al.  On-Line Construction of Two-Dimensional Suffix Trees in O(n2 log n) Time , 1997, Algorithmica.

[16]  Z. Galil,et al.  Pattern matching algorithms , 1997 .

[17]  Roberto Grossi,et al.  On the Construction of Classes of Suffix Trees for Square Matrices: Algorithms and Applications , 1995, Inf. Comput..