Mauricio Soto Gomez | Searcharxiv

arXiv2025

On recognizing graphs representing Persistent Perfect Phylogenies

The Persistent Perfect phylogeny, also known as Dollo-1, has been introduced as a generalization of the well-known perfect phylogenetic model for binary characters to deal with the potential loss of characters. The problem of deciding the existence of a Persistent Perfect phylogeny can be reduced to the one of recognizing a class of bipartite graphs whose nodes are species and characters. Thus an interesting question is solving directly the problem of recognizing such graphs. We present a polynomial-time algorithm for deciding Persistent Perfect phylogeny existence in maximal graphs, where no character's species set is contained within another character's species set. Our solution, that relies only on graph properties, narrows the gap between the linear-time simple algorithm for Perfect Phylogeny and the NP-hardness results for the Dollo-$k$ phylogeny with $k>1$.

cs.DS↗

arXiv2025

On Computing the Dollo-1 phylogeny in polynomial time

The Dollo model for reconstructing evolutionary trees from binary characters has been proposed as a generalization of the infinite sites model, also known as the Perfect Phylogeny. In particular, the Dollo model is considered more realistic than the Perfect Phylogeny for inferring the evolution of tumor mutations. In the case of binary matrices, the Dollo-$k$ model requires an evolutionary tree in which each character, corresponding to a column in the input matrix, may change from $0$ to $1$ at most once, and from $1$ to $0$ at most $k$ times throughout the entire tree. Given a binary matrix, the problem of deciding whether there exists a Dollo-$k$ tree compatible with the matrix is NP-complete for any fixed $k \geq 2$, while computing a Dollo-$0$ tree corresponds to the Perfect Phylogeny decision problem, which admits a simple linear-time algorithm. The Dollo-$1$ tree problem corresponds to the Persistent Phylogeny problem, whose computational complexity, albeit under an equivalent formulation, was posed as an open question 20 years ago. We solve this problem by presenting a polynomial-time algorithm for the Persistent Phylogeny problem. Our solution relies on efficiently solving a specific class of binary matrices, represented as bipartite graphs called \emph{skeleton graphs}, or simply skeletons. In these graphs, characters are \emph{maximal}, that is their corresponding sets of species are not related by inclusion.

cs.DS↗