  Let $R$ and $B$ be two disjoint sets of points in the plane where the points
of $R$ are colored red and the points of $B$ are colored blue, and let
$n=|R\cup B|$. A bichromatic spanning tree is a spanning tree in the complete
bipartite geometric graph with bipartition $(R,B)$. The minimum (respectively
maximum) bichromatic spanning tree problem is the problem of computing a
bichromatic spanning tree of minimum (respectively maximum) total edge length.
  1. We present a simple algorithm that solves the minimum bichromatic spanning
tree problem in $O(n\log^3 n)$ time. This algorithm can easily be extended to
solve the maximum bichromatic spanning tree problem within the same time bound.
It also can easily be generalized to multicolored point sets.
  2. We present $\Theta(n\log n)$-time algorithms that solve the minimum and
the maximum bichromatic spanning tree problems.
  3. We extend the bichromatic spanning tree algorithms and solve the
multicolored version of these problems in $O(n\log n\log k)$ time, where $k$ is
the number of different colors (or the size of the multipartition in a complete
multipartite geometric graph).
