A branch-&-price approach to the unrooted maximum agreement forest problem

Martin Frohn; Steven Kelk; Simona Vychytilova

doi:10.1016/j.orl.2025.107364

A branch-&-price approach to the unrooted maximum agreement forest problem

Martin Frohn^*, Steven Kelk, Simona Vychytilova

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We propose the first branch-&-price algorithm for the maximum agreement forest problem on unrooted binary trees: given two unrooted X-labelled binary trees we seek to partition X into a minimum number of blocks such that the induced subtrees are disjoint and have the same topologies in both trees. We provide a dynamic programming algorithm for the weighted maximum agreement subtree problem to solve the pricing problem. When combined with rigorous polynomial-time pre-processing our branch-&-price algorithm exhibits (beyond) state-of-the-art performance.

Original language	English
Article number	107364
Journal	Operations Research Letters
Volume	63
DOIs	https://doi.org/10.1016/j.orl.2025.107364
Publication status	Published - 1 Nov 2025

Keywords

Branch-&-price
Dynamic programming
Phylogenetics

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10.1016/j.orl.2025.107364Licence: CC BY

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title = "A branch-\&-price approach to the unrooted maximum agreement forest problem",

abstract = "We propose the first branch-\&-price algorithm for the maximum agreement forest problem on unrooted binary trees: given two unrooted X-labelled binary trees we seek to partition X into a minimum number of blocks such that the induced subtrees are disjoint and have the same topologies in both trees. We provide a dynamic programming algorithm for the weighted maximum agreement subtree problem to solve the pricing problem. When combined with rigorous polynomial-time pre-processing our branch-\&-price algorithm exhibits (beyond) state-of-the-art performance.",

keywords = "Branch-\&-price, Dynamic programming, Phylogenetics",

author = "Martin Frohn and Steven Kelk and Simona Vychytilova",

note = "Funding Information: M. Frohn was supported by grant OCENW.M.21.306 from The Dutch Research Council (NWO) . We thank the anonymous reviewer for detailed feedback which helped to improve the article. Publisher Copyright: {\textcopyright} 2025 The Author(s)",

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AU - Frohn, Martin

AU - Kelk, Steven

AU - Vychytilova, Simona

N1 - Funding Information: M. Frohn was supported by grant OCENW.M.21.306 from The Dutch Research Council (NWO) . We thank the anonymous reviewer for detailed feedback which helped to improve the article. Publisher Copyright: © 2025 The Author(s)

PY - 2025/11/1

Y1 - 2025/11/1

N2 - We propose the first branch-&-price algorithm for the maximum agreement forest problem on unrooted binary trees: given two unrooted X-labelled binary trees we seek to partition X into a minimum number of blocks such that the induced subtrees are disjoint and have the same topologies in both trees. We provide a dynamic programming algorithm for the weighted maximum agreement subtree problem to solve the pricing problem. When combined with rigorous polynomial-time pre-processing our branch-&-price algorithm exhibits (beyond) state-of-the-art performance.

AB - We propose the first branch-&-price algorithm for the maximum agreement forest problem on unrooted binary trees: given two unrooted X-labelled binary trees we seek to partition X into a minimum number of blocks such that the induced subtrees are disjoint and have the same topologies in both trees. We provide a dynamic programming algorithm for the weighted maximum agreement subtree problem to solve the pricing problem. When combined with rigorous polynomial-time pre-processing our branch-&-price algorithm exhibits (beyond) state-of-the-art performance.

KW - Branch-&-price

KW - Dynamic programming

KW - Phylogenetics

U2 - 10.1016/j.orl.2025.107364

DO - 10.1016/j.orl.2025.107364

M3 - Article

SN - 0167-6377

VL - 63

JO - Operations Research Letters

JF - Operations Research Letters

M1 - 107364

ER -

A branch-&-price approach to the unrooted maximum agreement forest problem

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Keywords

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