Forbidden Factors and Fragment Assembly

Abstract

In this paper we approach the fragment assembly problem by using the notion of minimal forbidden factors introduced in previous paper. Denoting by M(w) the set of minimal forbidden factors of a word w, we first focus on the evaluation of the size of elements in M(w) and on designing of an algorithm to recover the word w from M(w). Actually we prove that for a word w randomly generated by a memoryless source with identical symbol probabilities, the maximal length m(w) of words in M(w) is logarithmic and that the reconstruction algorithm runs in linear time. These results have an interesting application to the fragment assembly problem, i.e. reconstruct a word w from a given set I of substrings (fragments). Indeed under a suitable hypothesis on the set of fragments I, one can detect the elements of M(w) by looking at the minimal forbidden factors of elements in I and then apply the reconstruction algorithm.

Partially supported by MURST projects: Modelli di calcolo innovativi: metodi sintattici e combinatori and Bioinformatica e Ricerca Genomica