  We give a 2-approximation algorithm for the Maximum Agreement Forest problem
on two rooted binary trees. This NP-hard problem has been studied extensively
in the past two decades, since it can be used to compute the rooted Subtree
Prune-and-Regraft (rSPR) distance between two phylogenetic trees. Our algorithm
is combinatorial and its running time is quadratic in the input size. To prove
the approximation guarantee, we construct a feasible dual solution for a novel
linear programming formulation. In addition, we show this linear program is
stronger than previously known formulations, and we give a compact formulation,
showing that it can be solved in polynomial time
