A Duality Based 2-Approximation Algorithm for Maximum Agreement Forest
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
Olver, N.K, Schalekamp, F, van der Ster, S.L, Stougie, L, & van Zuylen, A. (2018). A Duality Based 2-Approximation Algorithm for Maximum Agreement Forest.