Generating the maximum spanning trees of a weighted graph
Journal of Algorithms
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Compatibility of unrooted phylogenetic trees is FPT
Theoretical Computer Science - Parameterized and exact computation
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Constructing perfect phylogenies and proper triangulations for three-state characters
WABI'11 Proceedings of the 11th international conference on Algorithms in bioinformatics
Efficiently solvable perfect phylogeny problems on binary and k-state data with missing values
WABI'11 Proceedings of the 11th international conference on Algorithms in bioinformatics
Subexponential parameterized algorithm for minimum fill-in
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
A parameterized algorithm for chordal sandwich
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
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The compatibility problem is the problem of determining if a set of unrooted trees are compatible, i.e. if there is a supertree that represents all of the trees in the set. This fundamental problem in phylogenetics is NP-complete but fixed-parameter tractable in the number of trees. Recently, Vakati and Fernández-Baca showed how to efficiently reduce the compatibility problem to determining if a specific type of constrained triangulation exists for a non-chordal graph derived from the input trees, mirroring a classic result by Buneman for the closely related Perfect-Phylogeny problem. In this paper, we show a different way of efficiently reducing the compatibility problem to that of determining if another type of constrained triangulation exists for a new non-chordal intersection graph. In addition to its conceptual contribution, such reductions are desirable because of the extensive and continuing literature on graph triangulations, which has been exploited to create algorithms that are efficient in practice for a variety of Perfect-Phylogeny problems. Our reduction allows us to frame the compatibility problem as a minimal triangulation problem (in particular, as a chordal graph sandwich problem) and to frame a maximization variant of the compatibility problem as a minimal triangulation problem.