Graphs and algorithms
A few logs suffice to build (almost) all trees (l): part I
Random Structures & Algorithms
A supertree method for rooted trees
Discrete Applied Mathematics
Inferring evolutionary trees with strong combinatorial evidence
Theoretical Computer Science - computing and combinatorics
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
Constructing Big Trees from Short Sequences
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Quartet Cleaning: Improved Algorithms and Simulations
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Orchestrating Quartets: Approximation and Data Correction
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Using Max Cut to Enhance Rooted Trees Consistency
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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Given a collection of rooted phylogenetic trees with overlapping sets of leaves, a compatible supertree $S$ is a single tree whose set of leaves is the union of the input sets of leaves and such that $S$ agrees with each input tree when restricted to the leaves of the input tree. Typically with trees from real data, no compatible supertree exists, and various methods may be utilized to reconcile the incompatibilities in the input trees. This paper focuses on a measure of robustness of a supertree method called its ``radius" $R$. The larger the value of $R$ is, the further the data set can be from a natural correct tree $T$ and yet the method will still output $T$. It is shown that the maximal possible radius for a method is $R = 1/2$. Many familiar methods, both for supertrees and consensus trees, are shown to have $R = 0$, indicating that they need not output a tree $T$ that would seem to be the natural correct answer. A polynomial-time method Normalized Triplet Supertree (NTS) with the maximal possible $R = 1/2$ is defined. A geometric interpretion is given, and NTS is shown to solve an optimization problem. Additional properties of NTS are described.