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 \(\Omega\)(nm2) time [2]. Therefore, much of the attention paid has been restricted to square matrices and submatrices, the important special case in which much better results are available.
For square matrices, the Lsuffix tree and its array form, storing all square submatrices of an n × n matrix, have been proposed [3, 9, 10]. Moreover, the general framework for...
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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Recommended Reading
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Na, J., Ferragina, P., Giancarlo, R., Park, K. (2016). Indexed Two-Dimensional String Matching. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_442
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DOI: https://doi.org/10.1007/978-1-4939-2864-4_442
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