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A duality based 2-approximation algorithm for maximum agreement forest.

Neil Olver1,2, Frans Schalekamp3, Suzanne van der Ster4

  • 1Department of Mathematics, London School of Economics and Political Science, London, United Kingdom.

Mathematical Programming
|February 27, 2023
PubMed
Summary
This summary is machine-generated.

We developed a 2-approximation algorithm for the Maximum Agreement Forest problem, crucial for calculating the rooted Subtree Prune-and-Regraft (rSPR) distance between phylogenetic trees. This combinatorial approach offers an efficient solution for this NP-hard problem.

Keywords:
Computational biologyMaximum agreement forestPhylogenetic treeSPR distanceSubtree prune-and-regraft distance

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Area of Science:

  • Computational Biology
  • Algorithm Design
  • Phylogenetics

Background:

  • The Maximum Agreement Forest (MAF) problem is NP-hard and central to computing evolutionary distances between phylogenetic trees.
  • The rooted Subtree Prune-and-Regraft (rSPR) distance is a key metric in phylogenetics, often computed via MAF.
  • Existing methods for MAF may lack efficient approximation guarantees or efficient computation.

Purpose of the Study:

  • To present a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees.
  • To provide an efficient combinatorial algorithm for a problem relevant to phylogenetic tree comparison.
  • To improve upon existing computational approaches for MAF.

Main Methods:

  • A combinatorial 2-approximation algorithm with quadratic running time was developed.
  • A novel, exponential-size linear programming formulation was introduced.
  • A feasible dual solution was constructed to prove the approximation guarantee.
  • The integrality gap of the linear program was analyzed and compared to prior formulations.

Main Results:

  • The algorithm achieves a 2-approximation for the Maximum Agreement Forest problem.
  • A new linear programming formulation for MAF was established.
  • The proposed linear program demonstrates a smaller integrality gap.
  • An equivalent compact formulation was derived, solvable in polynomial time.

Conclusions:

  • The study provides an efficient and theoretically sound approximation algorithm for MAF.
  • The work contributes to the computational understanding and tractability of phylogenetic tree comparison.
  • The findings pave the way for more efficient computation of the rSPR distance.