Unbalanced and Hierarchical Bipartite Matchings with Applications to Labeled Tree Comparison
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Approximating the Maximum Isomorphic Agreement Subtree Is Hard
COM '00 Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching
A Faster and Unifying Algorithm for Comparing Trees
COM '00 Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
An improved algorithm for the maximum agreement subtree problem
Information Processing Letters
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Computing the maximum agreement of phylogenetic networks
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Theoretical Computer Science
Propagation-vectors for trees (PVT): concise yet effective summaries for hierarchical data and trees
Proceedings of the 2008 ACM workshop on Large-Scale distributed systems for information retrieval
An improved algorithm for the maximum agreement subtree problem
Information Processing Letters
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
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Constructing evolutionary trees for species sets is a fundamental problem in biology. Unfortunately, there is no single agreed upon method for this task, and many methods are in use. Current practice dictates that trees be constructed using different methods and that the resulting trees should be compared for consensus. It has become necessary to automate this process as the number of species under consideration has grown. We study one formalization of the problem: the maximum agreement-subtree $($\MAST$)$ problem.The $\MAST$ problem is as follows: given a set $A$ and two rooted trees $\cT_0$ and $\cT_1$ leaf-labeled by the elements of $A$, find a maximum-cardinality subset $B$ of $A$ such that the topological restrictions of $\cT_0$ and $\cT_1$ to $B$ are isomorphic. In this paper, we will show that this problem reduces to unary weighted bipartite matching ($\UWBM$) with an $O(n^{1+o(1)})$ additive overhead. We also show that $\UWBM$ reduces linearly to $\MAST$. Thus our algorithm is optimal unless $\UWBM$ can be solved in near linear time. The overall running time of our algorithm is $O(n^{1.5} \log n)$, improving on the previous best algorithm, which runs in $O(n^2)$. We also derive an $O(n c^{\sqrt{\log n}})$-time algorithm for the case of bounded degrees, whereas the previously best algorithm runs in $O(n^2),$ as in the unbounded case.