Reconstructing Words from Subwords in Linear Time

Abstract.

Almost 30 years ago, M. Schützenberger and L. Simon established that two n-words with letters drawn from a finite alphabet having identical sets of subwords of length up to ⌊ n/2 ⌋+1 are identical. In the context of coding theory, V.I. Levenshtein elaborated this result in a series of papers. And further elaborations dealing with alphabets and sequences with reverse complementation have been recently developed by P.L. Erdős, P. Ligeti, P. Sziklai, and D.C. Torney. However, the algorithmic complexity of actually (re)constructing a word from its subwords has apparently not yet explicitly been studied. This paper augments the work of M. Schützenberger and L. Simon by showing that their approach can be reworked so as to provide a linear-time solution of this reconstruction problem in the original setting studied in their work.