A new method of DNA reading was proposed at the end of 1988 by Lysov et al. According to the authors' claims it has certain advantages as compared to the Maxam-Gilbert and Sanger methods, which are revealed by automation and rapidity of DNA sequencing. Nevertheless its employment is hampered by a number of biological and mathematical problems. The present study proposes an algorithm that allows to overcome the computational difficulties occurring in the course of the method during reconstruction of the DNA sequence by its l-tuple composition. It is shown also that the biochemical problems connected with the loss of information about the l-tuple DNA composition during hybridization are not crucial and can be overcome by finding the maximal flow of minimal cost in the special graph.