Minimum unique substrings and maximum repeats

Fundamenta Informaticae

Volumn 110, Issue 1-4, 2011, Pages 183-195

  Ilie, Lucian ^a   Smyth, William F ^b,c  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

^b MCMASTER UNIVERSITY   (Canada)

^c CURTIN UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

COMBINATORIAL PROPERTIES; FAST COMPUTATION; OPEN PROBLEMS; OPTIMAL ALGORITHM; STRINGOLOGY; STRONG DUALITY; SUB-STRINGS;

BIOINFORMATICS;

EID: 80052848353     PISSN: 01692968     EISSN: None     Source Type: Journal    
DOI: 10.3233/FI-2011-536     Document Type: Article

References (28)

1. M. I. Abouelhoda, S. Kurtz, and E. Ohlebusch, Replacing suffix trees with enhanced suffix arrays, J. Discrete Algorithms 2 (2004) 53-86.
2. A. Apostolico and F. P. Preparata, Optimal off-line detection of repetitions in a string, Theoret. Comput. Sci. 22 (1983) 297-315.
3. A. Bakalis, C. S. Iliopoulos, C. Makris, S. Sioutas, E. Theodoridis, A. K. Tsakalidis and K. Tsichlas, Locating maximum multirepeats in multiple strings under various constraints, The Computer Journal 50-2 (2007) 178-185. (Pubitemid 46416424)
4. G. S. Brodal, R. B. Lyngsoø, C. N. S. Pedersen and J. Stoye, Finding maximum pairs with bounded gap, J. Discrete Algorithms 1 (2000) 77-103.
5. J. Craig Venter et al., The Sequence of the Human Genome, Science 291 (5507) (2001) 1304-1351. (Pubitemid 32173090)
6. N. G. de Bruijn, A combinatorial problem, Proc. Konin. Neder. Akad. Wet. 49 (1946) 758-764.
7. M. Crochemore, An optimal algorithm for computing all the repetitions in a word, Inform. Process. Lett. 12-5 (1981) 244-248.
8. M. Crochemore, C. S. Iliopoulos, M. Mohamed and M.-F. Sagot, Longest repeats with a block of k don't cares, Theoret. Comput. Sci. 362-1 (2006) 248-254. (Pubitemid 44399794)
9. F. Franek, W. F. Smyth and Y. Tang, Computing all repeats using suffix arrays, J. Automata, Languages and Combinatorics 8-4 (2003) 579-591.
10. S. Gräf, F. G. G. Nielsen, S. Kurtz, M. A. Huynen, E. Birney, H. Stunnenberg and P. Flicek, Optimized design and assessment of whole genome tiling arrays, Bioinformatics 23-13 (2007) i195-i204.
11. D. Gusfield, Algorithms on Strings, Trees, and Sequences, Cambridge University Press (1997) 534 pp.
12. B. Haubold, N. Pierstorff, F. Möller and T. Wiehe, Genome comparison without alignment using shortest unique substrings, BMC Bioinformatics 6 (2005) 123-133.
13. C. S. Iliopoulos,W. F. Smyth and M. Yusufu, Faster algorithms for computing maximum multirepeats in multiple sequences, Fundamenta Informaticae 97-3 (2009) 311-320.
14. T. Kasai, G. Lee, H. Arimura, S. Arikawa, and K. Park, Linear-time longest-common-prefix computation in suffix arrays and its applications, Proc. 12th Annual Symp. Combinatorial Pattern Matching, LNCS 2089 (2001) 181-192. (Pubitemid 33298873)
15. E. S. Lander et al., Initial sequencing and analysis of the human genome, Nature 409 (2001) 860-921. (Pubitemid 32165345)
16. A. Lefebvre and T. Lecroq, A heuristic for computing repeats with a factor oracle: Application to biological sequences, Internat. J. Comput. Math. 79-12 (2002) 1303-1315. (Pubitemid 41710584)
17. M. G.Main and R. J. Lorentz, An O(n log n) algorithmfor finding all repetitions in a string, J. Algorithms 5 (1984) 422-432.
18. U. Manber and G. W. Myers, Suffix arrays: A new method for on-line string searches, Proc. First Annual ACM-SIAM Symp. Discrete Algs. (1990) 319-327.
19. K. Narisawa, S. Inenaga, H. Bannai andM. Takeda, Efficient computation of substring equivalence classes with suffix arrays, Proc. 18th Annual Symp. Combinatorial Pattern Matching, LNCS 4580 (2007) 340-351.
20. G. Nong, S. Zhang and W. H. Chan, Linear time suffix array construction using D-critical substrings, Proc. 20th Annual Symp. Combinatorial Pattern Matching, LNCS 5577 (2009) 54-67.
21. S. J. Puglisi, W. F. Smyth and A. H. Turpin, A taxonomy of suffix array construction algorithms, ACM Computing Surveys 39-2 (2007) 1-31.
22. S. J. Puglisi, W. F. Smyth and M. Yusufu, Fast, practical algorithms for computing all the repeats in a string, Math. Comput. Sci. 3 (2010) 373-389.
23. S. J. Puglisi and A. H. Turpin, Space-time tradeoffs for longest-common-prefix array computation, Proc. 19th Internat. Symp. Algs. and Computation, LNCS 5369 (2008) 124-135.
24. S. Rahmann, Fast large scale oligonucleotide selection using the longest common factor approach, J. Bioinformatics and Computational Biology 1-2 (2003) 343-361.
25. B. Smyth, Computing Patterns in Strings, Pearson Addison-Wesley (2003) 423 pp.
26. A. Thue, Über unendliche zeichenreihen, Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana 7 (1906) 1-22.
27. P. Weiner, Linear pattern matching algorithms, Proc. 14th Annual IEEE Symp. Switching and Automata Theory (1973) 1-11.
28. J. Zheng, T. J. Close, T. Jiang and S. Lonardi, Efficient selection of unique and popular oligos for large EST databases Proc. 14th Annual Symp. Combinatorial Pattern Matching, LNCS 2676 (2003) 273-283.