New algorithms for the duplication-loss model
RECOMB '00 Proceedings of the fourth annual international conference on Computational molecular biology
Some APX-completeness results for cubic graphs
Theoretical Computer Science
From Gene Trees to Species Trees
SIAM Journal on Computing
Gene Trees and Species Trees: The Gene-Duplication Problem in Fixed-Parameter Tractable
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Algorithm Design
The Gene-Duplication Problem: Near-Linear Time Algorithms for NNI-Based Local Searches
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
New Perspectives on Gene Family Evolution: Losses in Reconciliation and a Link with Supertrees
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
Heuristics for the gene-duplication problem: a Θ(n) speed-up for the local search
RECOMB'07 Proceedings of the 11th annual international conference on Research in computational molecular biology
New results on optimizing rooted triplets consistency
Discrete Applied Mathematics
RECOMB-CG'10 Proceedings of the 2010 international conference on Comparative genomics
A Note on the Fixed Parameter Tractability of the Gene-Duplication Problem
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Minimum leaf removal for reconciliation: complexity and algorithms
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Gene tree correction for reconciliation and species tree inference: Complexity and algorithms
Journal of Discrete Algorithms
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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. More recently, a variant of the Minimum Duplication problem, called Minimum Duplication Bipartite, has been introduced in [14], where the goal is to find all pre-duplications , that is duplications that precede, in the evolution, the first speciation with respect to a species tree. In this paper, we investigate the complexity of both Minimum Duplication and Minimum Duplication Bipartite problems. First of all, we prove that the Minimum Duplication problem is APX-hard, even when the input consists of five uniquely leaf-labelled gene trees (progressing on the complexity of the problem). Then, we show that the Minimum Duplication Bipartite problem can be solved efficiently by a randomized algorithm when the input gene trees have bounded depth.