  Algebraic curve interpolation is described by specifying the location of N
points in the plane and constructing an algebraic curve of a function f that
should pass through them. In this paper, we propose a novel approach to
construct the algebraic curve that interpolates a set of data (points or
neighborhoods). This approach aims to search the polynomial with the smallest
degree interpolating the given data. Moreover, the paper also presents an
efficient method to reconstruct the algebraic curve of integer coefficients
with the smallest degree and the least monomials that interpolates the provided
data. The problems are converted into optimization problems and are solved via
Lagrange multipliers methods and symbolic computation. Various examples are
presented to illustrate the proposed approaches.
