  In the first of this series of two articles, we studied some geometrical
aspects of the Birkhoff polytope, the compact convex set of all $n \times n$
doubly stochastic matrices, namely the Chebyshev center, and the Chebyshev
radius of the Birkhoff polytope associated with metrics induced by the operator
norms from $\ell_n^p$ to $\ell_n^p$ for $1 \leq p \leq \infty$. In the present
paper, we take another look at those very questions, but for a different family
of matrix norms, namely the Schatten $p$-norms, for $1 \leq p < \infty$. While
studying these properties, the intrinsic connection to the minimal trace, which
naturally appears in the assignment problem, is also established.
