A duality based 2-approximation algorithm for maximum agreement forest

Olver, Neil ORCID: 0000-0001-8897-5459, Schalekamp, Frans, van der Ster, Suzanne, Stougie, Leen and van Zuylen, Anke (2023) A duality based 2-approximation algorithm for maximum agreement forest. Mathematical Programming, 198 (1). 811 - 853. ISSN 0025-5610

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Abstract

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.

Item Type:	Article
Official URL:	https://www.springer.com/journal/10107
Additional Information:	© 2022 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	16 Feb 2022 16:15
Last Modified:	15 Apr 2024 07:51
URI:	http://eprints.lse.ac.uk/id/eprint/113761

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