A Generalization of the Linearized Suffix Tree to Square Matrices

  • Received : 2010.11.24
  • Accepted : 2010.12.28
  • Published : 2010.12.30

Abstract

The linearized suffix tree (LST) is an array data structure supporting traversals on suffix trees. We apply this LST to two dimensional (2D) suffix trees and obtain a space-efficient substitution of 2D suffix trees. Given an $n{\times}n$ text matrix and an $m{\times}m$ pattern matrix over an alphabet ${\Sigma}$, our 2D-LST provides pattern matching in $O(m^2log{\mid}{\Sigma}{\mid})$ time and $O(n^2)$ space.

Keywords

Acknowledgement

Supported by : Korea Research Foundation

References

  1. M.I. Abouelhoda, S. Kurtz, and E. Ohlebusch, "Replacing suffix trees with enhanced suffix arrays," Journal of Discrete Algorithms, Vol.2, No.1, pp. 53-86, 2004. https://doi.org/10.1016/S1570-8667(03)00065-0
  2. D.K. Kim, M. Kim, and H. Park, "Linearized suffix tree: an efficient index data structure with the capabilities of suffix trees and suffix arrays," Algorithmica, Vol.52, No.3, pp. 350- 377, 2008. https://doi.org/10.1007/s00453-007-9061-2
  3. E.M. McCreight, "A space-economical suffix tree construction algorithm," Journal of the ACM, Vol.23, No.2, pp. 262-272, 1976. https://doi.org/10.1145/321941.321946
  4. E. Ukkonen, "On-line construction of suffix trees," Algorithmica, Vol.14, No.3, pp. 249- 260, 1995. https://doi.org/10.1007/BF01206331
  5. U. Manber and G. Myers, "Suffix arrays: a new method for on-line string searches," SIAM Journal on Computing, Vol.22, No.5, pp. 935-948, 1993. https://doi.org/10.1137/0222058
  6. K. Sadakane, "Compressed suffix trees with full functionality," Theory of Computing Systems, Vol.41, No.4, pp. 589-607, 2007. https://doi.org/10.1007/s00224-006-1198-x
  7. L. Russo, G. Navarro, and A. Oliveira, "Fully- Compressed suffix trees," In LATIN, pp. 362-373, 2008.
  8. J. Fischer, V. Maakinen, and G. Navarro, "An(other) Entropy-Bounded compressed suffix tree," In CPM, pp. 152-165, 2008.
  9. R. Giancarlo, "A generalization of the suffix tree to square matrices, with applications," SIAM Journal on Computing, Vol.24, No.3, pp. 520-562, 1995. https://doi.org/10.1137/S0097539792231982
  10. D.K. Kim, J.C. Na, J.S. Sim, and K. Park, "Linear-time construction of two-dimensional suffix trees," Algorithmica, To Appear.
  11. D.K. Kim, Y.A. Kim, and K. Park, "Generalizations of suffix arrays to multi-dimensional matrices," Theoretical Computer Science, Vol.302, No.1-3, pp. 223-238, 2003. https://doi.org/10.1016/S0304-3975(02)00828-9