# Forbidden factors and fragment assembly

• Volume: 35, Issue: 6, page 565-577
• ISSN: 0988-3754

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## Abstract

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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 $m\left(w\right)$ 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, $m\left(w\right)$ 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.

## How to cite

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Mignosi, F., Restivo, A., and Sciortino, M.. "Forbidden factors and fragment assembly." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 35.6 (2001): 565-577. <http://eudml.org/doc/92685>.

@article{Mignosi2001,
abstract = {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.},
author = {Mignosi, F., Restivo, A., Sciortino, M.},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {factor automaton; minimal forbidden factor; fragment assembly; minimal forbidden words},
language = {eng},
number = {6},
pages = {565-577},
publisher = {EDP-Sciences},
title = {Forbidden factors and fragment assembly},
url = {http://eudml.org/doc/92685},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Mignosi, F.
AU - Restivo, A.
AU - Sciortino, M.
TI - Forbidden factors and fragment assembly
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2001
PB - EDP-Sciences
VL - 35
IS - 6
SP - 565
EP - 577
AB - 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.
LA - eng
KW - factor automaton; minimal forbidden factor; fragment assembly; minimal forbidden words
UR - http://eudml.org/doc/92685
ER -

## References

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