The ACM programming contest problem Color a tree turns out to be equivalent to scheduling with tree precedence constraints.

There is a fast solution to this first worked out (although not analyzed) by Horn in 1972.

I wanted to check my solution, so I modelled this as
an integer program. Unlike Horn's algorithm,
this takes no advantage of the special tree structure of the
constraints. This is both good and bad: more general constraint DAGs
can be modelled, but it is *much* slower to solve the integer
program. Here some example data files, all trees