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1 results

  • Forbidden Factors and Fragment Assembly

  • F. Mignosi, A. Restivo, M. Sciortino
  • Journal:
    RAIRO - Theoretical Informatics and Applications / Volume 35 / Issue 6 / November 2001
    Published online by Cambridge University Press:
    15 July 2002, pp. 565-577
    Print publication:
    November 2001

  • In this paper methods and results related to the notion of minimalforbidden words are applied to the fragment assembly problem. Thefragment assembly problem can be formulated, in its simplest form,as follows: reconstruct a word w from a given set I ofsubstrings (fragments) of a word w. We introduce anhypothesis involving the set of fragments I and the maximallength m(w) of the minimal forbidden factors of w. Suchhypothesis allows us to reconstruct uniquely the word w from theset I in linear time. We prove also that, if w is a wordrandomly generated by a memoryless source with identical symbolprobabilities, m(w) is logarithmic with respect to the size ofw. This result shows that our reconstruction algorithm is suitedto approach the above problem in several practical applicationse.g. in the case of DNA sequences.