A phylogenetic tree is a graphical representation of an evolutionary history of taxa in which the leaves correspond to the taxa and the non-leaves correspond to speciations. One of important problems in phylogenetic analysis is to assemble a global phylogenetic tree from small phylogenetic trees, particularly, quartet trees. Quartet Compatibility is the problem of deciding whether there is a phylogenetic tree inducing a given collection of quartet trees, and to construct such a phylogenetic tree if it exists. It is known that Quartet Compatibility is NP-hard and that there are only a few results known for polynomial-time solvable subclasses. In this paper, we introduce two novel classes of quartet systems, called complete multipartite quartet system and full multipartite quartet system, and present polynomial time algorithms for Quartet Compatibility for these systems. We also see that complete/full multipartite quartet systems naturally arise from a limited situation of block-restricted measurement. a < l a t e x i t s h a 1 _ b a s e 6 4 = " e w u S P 0 X D U 5 B Q M j D u i I Q L q O I 4 Y k 8 = " > A A A C Z H i c h V H L S s N A F D 2 N r 1 q r r R Z B E E Q s i q t y I 4 L i q u j G Z R + 2 C r W U J I 4 a m i Y h S Q u 1 + A O 6 V V y 4 U h A
As a subsequent work to the present article, Hirai and Iwamasa REF have introduced two novel classes of quartet systems, named complete multipartitite quartet systems and full multipartite quartet systems, and showed that Quartet Compatibility for these quartet systems can be solved in polynomial time.
Reconstructing phylogenetic tree from multipartite quartet system
ISAAC 2018
arXiv: Combinatorics
Mathematics Computer Science