Some APX-completeness results for cubic graphs
Theoretical Computer Science
From Gene Trees to Species Trees
SIAM Journal on Computing
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
Reconciling a gene tree to a species tree under the duplication cost model
Theoretical Computer Science
DLS-trees: a model of evolutionary scenarios
Theoretical Computer Science
Maximum agreement and compatible supertrees
Journal of Discrete Algorithms
From Gene Trees to Species Trees through a Supertree Approach
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
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
New results on optimizing rooted triplets consistency
Discrete Applied Mathematics
A linear time algorithm for error-corrected reconciliation of unrooted gene trees
ISBRA'11 Proceedings of the 7th international conference on Bioinformatics research and applications
Removing noise from gene trees
WABI'11 Proceedings of the 11th international conference on Algorithms in bioinformatics
Complexity insights of the minimum duplication problem
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Minimum leaf removal for reconciliation: complexity and algorithms
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
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Reconciliation consists in mapping a gene tree T into a species tree S, and explaining the incongruence between the two as evidence for duplication, loss and other events shaping the gene family represented by the leaves of T. When S is unknown, the Species Tree Inference Problem is to infer, from a set of gene trees, a species tree leading to a minimum reconciliation cost. As reconciliation is very sensitive to errors in T, gene tree correction prior to reconciliation is a fundamental task. In this paper, we investigate the complexity of four different combinatorial approaches for deleting misplaced leaves from T. First, we consider two problems (Minimum Leaf Removal and Minimum Species Removal) related to the reconciliation of T with a known species tree S. In the former (latter respectively) we want to remove the minimum number of leaves (species respectively) so that T is ''MD-consistent'' with S. Second, we consider two problems (Minimum Leaf Removal Inference and Minimum Species Removal Inference) related to species tree inference. In the former (latter respectively) we want to remove the minimum number of leaves (species respectively) from T so that there exists a species tree S such that T is MD-consistent with S. We prove that Minimum Leaf Removal and Minimum Species Removal are APX-hard, even when each label has at most two occurrences in the input gene tree, and we present fixed-parameter algorithms for the two problems. We prove that Minimum Leaf Removal Inference is not only NP-hard, but also W[2]-hard and inapproximable within factor clnn, where n is the number of leaves in the gene tree. Finally, we show that Minimum Species Removal Inference is NP-hard and W[2]-hard, when parameterized by the size of the solution, that is the minimum number of species removals.