Characterizing the reconstruction and enumerating the patterns of DNA sequences with repeats

A repeat in a DNA sequence is a substring that appears more than once. In DNA sequencing, the occurrence of repeats may hinder the unique reconstruction. In addition, the number of possible reconstructions depends on the pattern of repeats in a DNA sequence. Arratia et al. studied the patterns of DNA sequences with twofold repeats that result in k-way reconstructions. In this paper, multiple-fold repeats, including twofold repeats, are considered. For each pattern of DNA repeats, the possible reconstructions of the DNA sequence are enumerated by its reduced digraph. Then the reconstructions of DNA sequences with repeats are characterized using the pattern graphs. Finally, for DNA sequences with n repeats, the patterns of DNA repeats resulting in k-way reconstruction are enumerated. Dedicated to Professor Frank K. Hwang on the occasion of his 65th birthday.