  Given a natural number $k\ge 2$, we consider the $k$-submodular cover problem
($k$-SC). The objective is to find a minimum cost subset of a ground set
$\mathcal{X}$ subject to the value of a $k$-submodular utility function being
at least a certain predetermined value $\tau$. For this problem, we design a
bicriteria algorithm with a cost at most $O(1/\epsilon)$ times the optimal
value, while the utility is at least $(1-\epsilon)\tau/r$, where $r$ depends on
the monotonicity of $g$.
