0000000000384281
AUTHOR
Lorraine A.k. Ayad
Constructing Antidictionaries of Long Texts in Output-Sensitive Space
AbstractA wordxthat is absent from a wordyis calledminimalif all its proper factors occur iny. Given a collection ofkwordsy1, … ,ykover an alphabetΣ, we are asked to compute the set$\mathrm {M}^{\ell }_{\{y_1,\ldots ,y_k\}}$M{y1,…,yk}ℓof minimal absent words of length at mostℓof the collection {y1, … ,yk}. The set$\mathrm {M}^{\ell }_{\{y_1,\ldots ,y_k\}}$M{y1,…,yk}ℓcontains all the wordsxsuch thatxis absent from all the words of the collection while there existi,j, such that the maximal proper suffix ofxis a factor ofyiand the maximal proper prefix ofxis a factor ofyj. In data compression, this corresponds to computing the antidictionary ofkdocuments. In bioinformatics, it corresponds to c…
Constructing Antidictionaries in Output-Sensitive Space
A word $x$ that is absent from a word $y$ is called minimal if all its proper factors occur in $y$. Given a collection of $k$ words $y_1,y_2,\ldots,y_k$ over an alphabet $\Sigma$, we are asked to compute the set $\mathrm{M}^{\ell}_{y_{1}\#\ldots\#y_{k}}$ of minimal absent words of length at most $\ell$ of word $y=y_1\#y_2\#\ldots\#y_k$, $\#\notin\Sigma$. In data compression, this corresponds to computing the antidictionary of $k$ documents. In bioinformatics, it corresponds to computing words that are absent from a genome of $k$ chromosomes. This computation generally requires $\Omega(n)$ space for $n=|y|$ using any of the plenty available $\mathcal{O}(n)$-time algorithms. This is because a…