Minimum Leaf Removal for Reconciliation: Complexity and Algorithms
Reconciliation is a well-known method for studying the evolution of a gene family through speciation, duplication, and loss. Unfortunately, the inferred history strongly depends on the considered gene tree for the gene family, as a few misplaced leaves can lead to a completely different history, possibly with significantly more duplications and losses. It is therefore essential to develop methods that are able to preprocess and correct gene trees prior to reconciliation. In this paper, we consider a combinatorial problem, known as the Minimum Leaf Removal problem, that has been proposed to remove errors from a gene tree by deleting some of its leaves. We prove that the problem is APX-hard, even in the restricted case of a gene family with at most two copies per genome. On the positive side, we present fixed-parameter algorithms where the parameters are the size of the solution (minimum number of leaf removals) and the number of genomes containing multiple gene copies.
KeywordsSpecies Tree Gene Tree Vertex Cover Leaf Removal Multiple Gene Copy
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