Abstract:
An extension of the class of lattice graphs is considered. In order to become
close to the Euclidean metric, inclusion of additional ribs with weights
equal to the corresponding lengths of vectors in the Euclidean space is
performed in a neighborhood on the lattice. A correspondence between the
coordinates of nodes incident to the additional ribs and sequences of
irreducible Farey-Cauchy fractions is established. An algorithm for
constructing a set of the shortest paths on such a lattice is proposed. In
essence, this algorithm models the wave process of constructing the field
of all shortest paths from a set-source. Some estimates and examples are
given to illustrate the computer realization of the algorithm proposed.
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