Reconstruction of a Word from a Finite Set of its Subwords under the unit Shift Hypothesis. I. Reconstruction without for Bidden Words1Please check captured article title, if appropriate.

Authors:
Y. G. Smetanin;M. V. Ulyanov
Affiliations:
Dorodnicyn Computing Center of RAS and Moscow Institute of Physics and Technology, Moscow, Russia;National Research University "Higher School of Economics" of the Moscow State University of Printing Arts, Moscow, Russia
Venue:
Cybernetics and Systems Analysis
Year:
2014

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Abstract

The problem of reconstruction of a word from a set of its subwords is considered. It is assumed that the set is generated by unit shifts of a fixed window along an unknown word. For the problem without constrains on the unknown word, a method of reconstruction is proposed based on the search for Euler paths or Euler cycles in a de Bruijn multidigraph. The search is based on symbolic multiplication of adjacency matrices with special operations of multiplication and addition of edge names. The method makes it possible to find reconstructed words and the number of reconstructions.