# Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

# Indexed Two-Dimensional String Matching

• Joong Chae Na
• Paolo Ferragina
• Raffaele Giancarlo
• Kunsoo Park
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_442

## Years and Authors of Summarized Original Work

• 2007; Na, Giancarlo, Park

• 2011; Kim, Na, Sim, Park

## Problem Definition

This entry is concerned with designing and building indexes of a two-dimensional matrix, which is basically the generalization of indexes of a string, the suffix tree [12] and the suffix array [11], to a two-dimensional matrix. This problem was first introduced by Gonnet [7]. Informally, a two-dimensional analog of the suffix tree is a tree data structure storing all submatrices of an n × m matrix, n ≥ m. The submatrix tree [2] is an incarnation of such indexes. Unfortunately, building such indexes requires $$\Omega$$

## Keywords

Index data structures for matrices or images Indexing for matrices or images Two-dimensional indexing for pattern matching Two-dimensional index data structures
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1. 1.
Cole R, Hariharan R (2003) Faster suffix tree construction with missing suffix links. SIAM J Comput 33:26–42
2. 2.
Giancarlo R (1993) An index data structure for matrices, with applications to fast two-dimensional pattern matching. In: Proceedings of workshop on algorithm and data structures, Montréal. Springer Lecture notes in computer science, vol 709, pp 337–348Google Scholar
3. 3.
Giancarlo R (1995) A generalization of the suffix tree to square matrices, with application. SIAM J Comput 24:520–562
4. 4.
Giancarlo R, Grossi R (1996) On the construction of classes of suffix trees for square matrices: algorithms and applications. Inf Comput 130:151–182
5. 5.
Giancarlo R, Grossi R (1997) Suffix tree data structures for matrices. In: Apostolico A, Galil, Z (eds) Pattern matching algorithms, ch. 11. Oxford University Press, Oxford, pp 293–340Google Scholar
6. 6.
Giancarlo R, Guaiana D (1999) On-line construction of two-dimensional suffix trees. J Complex 15:72–127
7. 7.
Gonnet GH (1988) Efficient searching of text and pictures. Technical report OED-88-02, University of WaterlooGoogle Scholar
8. 8.
Kim DK, Kim YA, Park K (1998) Constructing suffix arrays for multi-dimensional matrices. In: Proceedings of the 9th symposium on combinatorial pattern matching, Piscataway, pp 249–260Google Scholar
9. 9.
Kim DK, Kim YA, Park K (2003) Generalizations of suffix arrays to multi-dimensional matrices. Theor Comput Sci 302:401–416
10. 10.
Kim DK, Na JC, Sim JS, Park K (2011) Linear-time construction of two-dimensional suffix trees. Algorithmica 59:269–297
11. 11.
Manber U, Myers G (1993) Suffix arrays: a new method for on-line string searches. SIAM J Comput 22:935–948
12. 12.
McCreight EM (1976) A space-economical suffix tree construction algorithms. J ACM 23:262–272
13. 13.
Na JC, Giancarlo R, Park K (2007) On-line construction of two-dimensional suffix trees in O(n2log n) time. Algorithmica 48:173–186
14. 14.
Storer JA (1996) Lossless image compression using generalized LZ1-type methods. In: Proceedings of data compression conference, Snowbird, pp 290–299Google Scholar

© Springer Science+Business Media New York 2016

## Authors and Affiliations

• Joong Chae Na
• 1
Email author
• Paolo Ferragina
• 2
• Raffaele Giancarlo
• 3
• Kunsoo Park
• 4
1. 1.Department of Computer Science and EngineeringSejong UniversitySeoulKorea
2. 2.Department of Computer ScienceUniversity of PisaPisaItaly
3. 3.Department of Mathematics and ApplicationsUniversity of PalermoPalermoItaly
4. 4.School of Computer Science and EngineeringSeoul National UniversitySeoulKorea