Regular Article: Extension Operations on Sets of Leaf-Labeled Trees
Advances in Applied Mathematics
Fixed-parameter tractability of graph modification problems for hereditary properties
Information Processing Letters
Reconstruction of rooted trees from subtrees
Discrete Applied Mathematics
Computing the local consensus of trees
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
A general method to speed up fixed-parameter-tractable algorithms
Information Processing Letters
A supertree method for rooted trees
Discrete Applied Mathematics
Minimum-Flip Supertrees: Complexity and Algorithms
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Parameterized Complexity
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In computational phylogenetics, the problem of constructing a consensus tree for a given set of rooted input trees has frequently been addressed. In this article we study the Minimum-Flip Problem: the input trees are transformed into a binary matrix, and we want to find a perfect phylogeny for this matrix using a minimum number of flips, that is, corrections of single entries in the matrix. The graph-theoretical formulation of the problem is as follows: Given a bipartite graph G = (Vt ∪ Vc, E), the task is to find a minimum set of edge modifications such that the resulting graph has no induced path with four edges that starts and ends in Vt, where Vt corresponds to the taxa set and Vc corresponds to the character set. We present two fixed-parameter algorithms for the Minimum-Flip Problem, one with running time O(4.83k + poly(m, n)) and another one with running time O(4.42k + poly(m, n)) for n taxa, m characters, k flips, and poly(m, n) denotes a polynomial function in m and n. Additionally, we discuss several heuristic improvements. We also report computational results on phylogenetic data.