Reconstructing the shape of a tree from observed dissimilarity data
Advances in Applied Mathematics
Some open problems in computational molecular biology
Journal of Algorithms
Performance study of phylogenetic methods: (unweighted) quartet methods and neighbor-joining
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Faster exact algorithms for hard problems: a parameterized point of view
Discrete Mathematics
Inferring evolutionary trees with strong combinatorial evidence
Theoretical Computer Science - computing and combinatorics
On Efficient Fixed Parameter Algorithms for WEIGHTED VERTEX COVER
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
From Quartets to Phylogenetic Trees
SOFSEM '98 Proceedings of the 25th Conference on Current Trends in Theory and Practice of Informatics: Theory and Practice of Informatics
An efficient fixed-parameter algorithm for 3-hitting set
Journal of Discrete Algorithms
Parameterized Complexity
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Parameterized enumeration, transversals, and imperfect phylogeny reconstruction
Theoretical Computer Science - Parameterized and exact computation
An Efficient Fixed-Parameter Enumeration Algorithm for Weighted Edge Dominating Set
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Comparing trees via crossing minimization
Journal of Computer and System Sciences
Parameterized top-K algorithms
Theoretical Computer Science
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We study the parameterized complexity of the problem to reconstruct a binary (evolutionary) tree from a complete set of quartet topologies in the case of a limited number of errors. More precisely, we are given n taxa, exactly one topology for every subset of 4 taxa, and a positive integer k (the parameter). Then, the Minimum Quartet Inconsistency (MQI) problem is the question of whether we can find an evolutionary tree inducing a set of quartet topologies that differs from the given set in only k quartet topologies. MQI is NP-complete. However, we can compute the required tree in worst case time O(4k 驴 n + n4)-- the problem is fixed parameter tractable. Our experimental results show that in practice, also based on heuristic improvements proposed by us, even a much smaller exponential growth can be achieved. We extend the fixed parameter tractability result to weighted versions of the problem. In particular, our algorithm can produce all solutions that resolve at most k errors.