TY - GEN
T1 - Relaxed Agreement Forests
AU - Ardévol Martínez, Virginia
AU - Chaplick, Steven
AU - Kelk, Steven
AU - Meuwese, Ruben
AU - Mihalák, Matúš
AU - Stamoulis, Georgios
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024
Y1 - 2024
N2 - The phylogenetic inference process can produce, for multiple reasons, conflicting hypotheses of the evolutionary history of a set X of biological entities, i.e., phylogenetic trees with the same set of leaf labels X but with distinct topologies. It is natural to wish to quantify the difference between two such trees T1 and T2. We introduce the problem of computing a maximum relaxed agreement forest (MRAF) and use this as a proxy for the dissimilarity of T1 and T2, which in this article we assume to be unrooted and binary. MRAF asks for a partition of the leaf labels X into a minimum number of blocks S1,…,Sk such that the two subtrees induced in T1 and T2 by every Si are isomorphic up to suppression of degree-2 nodes and taking the labels X into account. Unlike the earlier introduced maximum agreement forest (MAF) model, the subtrees induced by the Si are allowed to overlap. We prove that it is NP-hard to compute MRAF, by reducing from the problem of partitioning a permutation into a minimum number of monotonic subsequences (PIMS). We further show that MRAF has a O(logn)-approximation algorithm where n=|X| and permits exact algorithms with single-exponential running time. When one of the trees is a caterpillar, we prove that testing whether a MRAF has size at most k can be answered in polynomial time when k is fixed. We also note that on two caterpillars the approximability of MRAF is related to that of PIMS. Finally, we establish a number of bounds on MRAF, compare its behaviour to MAF both theoretically and experimentally and discuss a number of open problems.
AB - The phylogenetic inference process can produce, for multiple reasons, conflicting hypotheses of the evolutionary history of a set X of biological entities, i.e., phylogenetic trees with the same set of leaf labels X but with distinct topologies. It is natural to wish to quantify the difference between two such trees T1 and T2. We introduce the problem of computing a maximum relaxed agreement forest (MRAF) and use this as a proxy for the dissimilarity of T1 and T2, which in this article we assume to be unrooted and binary. MRAF asks for a partition of the leaf labels X into a minimum number of blocks S1,…,Sk such that the two subtrees induced in T1 and T2 by every Si are isomorphic up to suppression of degree-2 nodes and taking the labels X into account. Unlike the earlier introduced maximum agreement forest (MAF) model, the subtrees induced by the Si are allowed to overlap. We prove that it is NP-hard to compute MRAF, by reducing from the problem of partitioning a permutation into a minimum number of monotonic subsequences (PIMS). We further show that MRAF has a O(logn)-approximation algorithm where n=|X| and permits exact algorithms with single-exponential running time. When one of the trees is a caterpillar, we prove that testing whether a MRAF has size at most k can be answered in polynomial time when k is fixed. We also note that on two caterpillars the approximability of MRAF is related to that of PIMS. Finally, we establish a number of bounds on MRAF, compare its behaviour to MAF both theoretically and experimentally and discuss a number of open problems.
U2 - 10.1007/978-3-031-52113-3_3
DO - 10.1007/978-3-031-52113-3_3
M3 - Conference article in proceeding
SN - 9783031521126
VL - 14519 LNCS
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 40
EP - 54
BT - SOFSEM 2024: Theory and Practice of Computer Science - 49th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2024, Cochem, Germany, February 19–23, 2024, Proceedings
A2 - Fernau, Henning
A2 - Gaspers, Serge
A2 - Klasing, Ralf
PB - Springer Science and Business Media B.V.
T2 - 49th International Conference on Current Trends in Theory and Practice of Computer Science
Y2 - 19 February 2024 through 23 February 2024
ER -