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 exponential-size linear programming formulation. In addition, we show this linear program has a smaller integrality gap than previously known formulations, and we give an equivalent compact formulation, showing that it can be solved in polynomial time.

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Albert Heijn Online, Zaandam, The Netherlands
Mathematical Programming
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Olver, N., Schalekamp, F., van der Ster, S., Stougie, L., & van Zuylen, A. (2023). A duality based 2-approximation algorithm for maximum agreement forest. Mathematical Programming, 198, 811–853. doi:10.1007/s10107-022-01790-y