Forbidden Factors and Fragment Assembly

Issue		RAIRO-Theor. Inf. Appl. Volume 35, Number 6, November-December 2001 A tribute to Aldo de Luca


Page(s)		565 - 577
DOI		10.1051/ita:2001132

DOI: 10.1051/ita:2001132

Theoret. Informatics Appl. 35, 565-577 (2001)

Forbidden Factors and Fragment Assembly

F. Mignosi, A. Restivo and M. Sciortino

University of Palermo, Dipartimento di Matematica ed Applicazioni, Via Archirafi 34, 90123 Palermo, Italy; mignosi@math.unipa.it.restivo@math.unipa.it.mari@math.unipa.it.

(Received June 26, 2001. Revised February 21, 2002.)

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.

Mathematics Subject Classification. 68Q45, 68R15.

Key words: Factor automaton -- minimal forbidden factor -- fragment assembly.

© EDP Sciences 2001

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