  We define the parametric closure problem, in which the input is a partially
ordered set whose elements have linearly varying weights and the goal is to
compute the sequence of minimum-weight lower sets of the partial order as the
weights vary. We give polynomial time solutions to many important special cases
of this problem including semiorders, reachability orders of bounded-treewidth
graphs, partial orders of bounded width, and series-parallel partial orders.
Our result for series-parallel orders provides a significant generalization of
a previous result of Carlson and Eppstein on bicriterion subtree problems.
