Complexity Insights of the Minimum Duplication Problem

Abstract

The Minimum Duplication problem is a well-known problem in phylogenetics and comparative genomics. Given a set of gene trees, the Minimum Duplication problem asks for a species tree that induces the minimum number of gene duplications in the input gene trees. Recently, a variant of the Minimum Duplication problem, called Minimum Duplication Bipartite, has been introduced, where the goal is to find all pre-duplications, that is duplications that in the evolution precede the first speciation with respect to a species tree. In this paper, we investigate the complexity of both Minimum Duplication and Minimum Duplication Bipartite. First of all, we prove that the Minimum Duplication problem is APX-hard, even when the input consists of five uniquely leaf-labeled gene trees (improving upon known results on the complexity of the problem). Then, we show that the Minimum Duplication Bipartite problem can be solved efficiently with a randomized algorithm when the input gene trees have bounded depth. An extended abstract of this paper appeared in SOFSEM 2012 [1].

Correcting gene tree by removal and modification: Tractability and approximability

“…The comparison of a gene tree and a species tree is known as reconciliation [4,5,6,7,8,9,10,11,12,13,14,15], and has the goal of inferring the macro-evolutionary events (duplications, losses, and in some cases lateral gene transfers) that occurred during evolution. When no species tree is known, then the definition of the problem changes: starting from a set of possibly discordant gene trees, it asks to infer a correct species tree, usually based on a parsimonious evolutionary scenario [16,6,17].…”

Minimum Leaf Removal for Reconciliation: Complexity and Algorithms

“…This concept was pioneered by Goodman [15] and then widely accepted, utilized, and improved [3,6,7,8,10,13,26,28,29,30]. When no preliminary knowledge on the species tree is given, a natural problem, known as the species tree inference problem, is to infer, from a set of gene trees, a species tree leading to a parsimonious evolution scenario [4,8,22].…”