  The usual univariate interpolation problem of finding a monic polynomial f of
degree n that interpolates n given values is well understood. This paper
studies a variant where f is required to be composite, say, a composition of
two polynomials of degrees d and e, respectively, with de=n, and therefore
d+e-1 given values. Some special cases are easy to solve, and for the general
case, we construct a homotopy between it and a special case. We compute a
geometric solution of the algebraic curve presenting this homotopy, and this
also provides an answer to the interpolation task. The computing time is
polynomial in the geometric data, like the degree, of this curve. A consequence
is that for almost all inputs, a decomposable interpolation polynomial exists.
