A duality based 2-approximation algorithm for maximum agreement forest

• 成果类型: Article
• 署名作者: Olver, Neil; Schalekamp, Frans; van der Ster, Suzanne; Stougie, Leen; van Zuylen, Anke
• 署名单位: University of London; London School Economics & Political Science; Cornell University; Cornell University; Vrije Universiteit Amsterdam
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-022-01790-y
• 发表日期: 2023
• 页码: 811-853
• 关键词: approximation algorithms; computation

摘要

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.