  In this paper we generalize the $j$-invariant criterion for the semistable
reduction type of an elliptic curve to superelliptic curves $X$ given by
$y^{n}=f(x)$. We first define a set of tropical invariants for $f(x)$ using
symmetrized Pl\"{u}cker coordinates and we show that these invariants determine
the tree associated to $f(x)$. We then prove that this tree completely
determines the reduction type of $X$ for $n$ that are not divisible by the
residue characteristic. The conditions on the tropical invariants that
distinguish between the different types are given by half-spaces as in the
elliptic curve case. These half-spaces arise naturally as the moduli spaces of
certain Newton polygon configurations. We give a procedure to write down their
equations and we illustrate this by giving the half-spaces for polynomials
$f(x)$ of degree $d\leq{5}$.
