Forbidden factors and fragment assembly
Mignosi, F. ; Restivo, A. ; Sciortino, M.
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001), p. 565-577 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

In this paper methods and results related to the notion of minimal forbidden words are applied to the fragment assembly problem. The fragment assembly problem can be formulated, in its simplest form, as follows: reconstruct a word w from a given set I of substrings (fragments) of a word w. We introduce an hypothesis involving the set of fragments I and the maximal length m(w) of the minimal forbidden factors of w. Such hypothesis allows us to reconstruct uniquely the word w from the set I in linear time. We prove also that, if w is a word randomly generated by a memoryless source with identical symbol probabilities, m(w) is logarithmic with respect to the size of w. This result shows that our reconstruction algorithm is suited to approach the above problem in several practical applications e.g. in the case of DNA sequences.

Publié le : 2001-01-01
Classification:  68Q45,  68R15 
@article{ITA_2001__35_6_565_0,
     author = {Mignosi, F. and Restivo, A. and Sciortino, M.},
     title = {Forbidden factors and fragment assembly},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     volume = {35},
     year = {2001},
     pages = {565-577},
     mrnumber = {1922296},
     zbl = {1005.68122},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ITA_2001__35_6_565_0}
}

Mignosi, F.; Restivo, A.; Sciortino, M. Forbidden factors and fragment assembly. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) pp. 565-577. http://gdmltest.u-ga.fr/item/ITA_2001__35_6_565_0/

[1] A.V. Aho, J.E. Hopcroft and J.D. Ullman, Data Structures and Algorithms. Addison Wesley, Reading, Mass (1983). | MR 666695 | Zbl 0487.68005

[2] M.-P. Béal, F. Mignosi, A. Restivo and M. Sciortino, Forbidden Words in Symbolic Dynamics. Adv. in Appl. Math. 25 (2000) 163-193. | MR 1780764 | Zbl 0965.37014

[3] A. Blumer, J. Blumer, A. Ehrenfeucht, D. Haussler, M.T. Chen and J. Seiferas, The smallest automaton recognizing the subwords of a text. Theoret. Comput. Sci. 40 (1985) 31-55. | MR 828515 | Zbl 0574.68070

[4] A. Carpi, A. De Luca and S. Varricchio, Words, univalent factors, and boxes. Acta Inform. (to appear). | Zbl 1025.68052

[5] M. Crochemore and C. Hancart, Automata for matching patterns, in Handbook of Formal Languages, Vol. 2, Chap. 9, edited by G. Rosenberg and A. Salomaan. Springer (1997) 399-462. | MR 1470014

[6] M. Crochemore, F. Mignosi and A. Restivo, Automata and forbidden words. Inform. Process. Lett. 67 (1998) 111-117. | MR 1638178

[7] M. Crochemore, F. Mignosi, A. Restivo and S. Salemi, Data compression using antidictionaries, in Proc. of the IEEE, Special Issue on Lossless Data Compression, Vol. 88, edited by J.A. Storer (2000) 1756-1768.

[8] A. Frieze and B.V. Halldórsson, Optimal Sequencing by Hybridization in Rounds, in Proc. of RECOMB 2001, edited by T. Lengauer, D. Sankoff, S. Istrail, P. Pevzner and M. Waterman. ACM Press (2001) 141-148

[9] D. Gusfield, Algorithms on strings, trees, and sequences: Computer science and computational biology. Cambridge University Press (1997). | MR 1460730 | Zbl 0934.68103

[10] R. Idury and M. Waterman, A new algorithm for DNA sequence assembly. J. Comput. Biol. 2 (1995) 291-306.

[11] F. Mignosi and A. Restivo, Periodicity, in M. Lothaire, Algebraic Combinatorics on Words, Chap. 8. Cambridge University Press (to appear) 237-274. Also available at url: http://www-igm.univ-mlv.fr/~berstel/Lothaire/index.html | MR 1905123

[12] F. Mignosi, A. Restivo and M. Sciortino, Forbidden Factors and Fragment Assembly. Lecture Notes in Comput. Sci. (2001). Proceedings of DLT'01. | Zbl 1073.68704

[13] F. Mignosi, A. Restivo and M. Sciortino, Words and Forbidden Factors. Theoret. Comput. Sci. 273 (2002) 99-117. | MR 1872445 | Zbl 0997.68093

[14] F. Mignosi, A. Restivo, M. Sciortino and J. Storer, On Sequence Assembly, Technical Report cs-00-210. Brandeis University (2000).

[15] S. Muthukrishnan and S.C. Sahinalp, Approximate nearest neighbors and sequence comparison with block operations. ACM Press (2000). Proceedings of STOC 2000. | MR 2115277 | Zbl 1296.68082

[16] G. Myers, Whole-Genome DNA Sequencing, IEEE Comput. Engrg. Sci. 3 (1999) 33-43.

[17] H. Peltola, H. Soderlund and E. Ukkonen, SEQAID: A DNA Sequence Assembly Program Based on a Mathematical Model. Nucl. Acids Res. 12 (1984) 307-321.

[18] M. Peltola, H. Soderlund, J. Tarhio and E. Ukkonen, Algorithms for some string matching problems arising in molecular genetics, in Proc. of the 9th IFIP World Computer Congress (1983) 59-64.

[19] P.A. Pevzner, H. Tang and M. Waterman, A New Approach Fragment Assembly in DNA Sequencing, in Proc. of RECOMB 2001, edited by T. Lengauer, D. Sankoff, S. Istrail, P. Pevzner and M. Waterman. ACM Press (2001) 141-148.

[20] R. Shamir and D. Tsur, Large Scale Sequencing by Hybridization, in Proc. of RECOMB 2001, edited by T. Lengauer, D. Sankoff, S. Istrail, P. Pevzner and M. Waterman. ACM Press (2001) 269-278.

[21] M.S. Waterman, Introduction to computational biology: Maps, sequences and genomes. Chapman & Hall (1995). | Zbl 0831.92011