Improving on-line construction of two-dimensional suffix trees for square matrices
- Authors
- Na, Joong Chae; Kim, Namhee; Sim, Jeong Seop; Kim, Dong Kyue
- Issue Date
- Apr-2009
- Publisher
- ELSEVIER
- Keywords
- Design of algorithms; Two-dimensional suffix trees; Index data structures; On-line algorithms; Randomized algorithms
- Citation
- INFORMATION PROCESSING LETTERS, v.109, no.10, pp.504 - 508
- Indexed
- SCIE
SCOPUS
- Journal Title
- INFORMATION PROCESSING LETTERS
- Volume
- 109
- Number
- 10
- Start Page
- 504
- End Page
- 508
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/177040
- DOI
- 10.1016/j.ipl.2009.01.026
- ISSN
- 0020-0190
- Abstract
- The two-dimensional (2-D) suffix tree of an n x n square matrix A is a compacted trie that represents all square submatrices of A. We consider constructing 2-D suffix trees on-line, which means, instead of giving the whole matrix A in advance, A is separated and each part of A is given at different time as algorithms proceed. In general, developing an on-line algorithm is more difficult than developing an off-line algorithm. Moreover, the smaller the input grain size is, the harder it is to develop an on-line algorithm. In the case of 2-D suffix tree construction, dealing with a character at a time is harder than dealing with a row or a column at a time. In this paper we propose a randomized linear-time algorithm for constructing 2-D suffix trees on-line. This algorithm is superior to previous algorithms in two ways: (1) This is the first linear-time algorithm for constructing 2-D suffix trees on-line. Although there have been some linear-time algorithms for off-line construction, there were no linear-time algorithms for on-line construction. (2) We deal with the most fine-grain on-line case, i.e., our algorithm can construct a 2-D suffix tree even though only one character of A is given at a time, while previous on-line algorithms require at least a row and/or a column at a time.
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