Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem

@inproceedings{Guillemot2007FixedParameterTO,
  title={Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem},
  author={Sylvain Guillemot and Vincent Berry},
  booktitle={CPM},
  year={2007}
}
Given a ground set L of labels and a collection of trees whose leaves are bijectively labelled by some elements of L, the Maximum Agreement Supertree problem (SMAST) is the following: find a tree T on a largest label set L′ ⊆ L that homeomorphically contains every input tree restricted to L′. The problem finds applications in several fields, e.g. phylogenetics. In this paper we focus on the parameterized complexity of this NP-hard problem. We consider different combinations of parameters for… 
Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem
  • Sylvain Guillemot, V. Berry
  • Computer Science, Mathematics
    IEEE/ACM Transactions on Computational Biology and Bioinformatics
  • 2010
TLDR
This paper shows that SMAST on k rooted binary trees on a label set of size n can be solved in O((8n)k) time, which is an improvement with respect to the previously known O(n3k2) time algorithm and gives the first fixed-parameter tractable algorithms on a single parameter for this problem.
Kernel and Fast Algorithm for Dense Triplet Inconsistency
TLDR
The results are the first polynomial kernel for this problem, with O(p2) labels, and a subexponential fixed-parameter algorithm running in time $2^{O(p^{1/3} \log p)} + O(n^4)$.
New results on optimizing rooted triplets consistency
TLDR
This paper proves that unless P=NP, MinRTI cannot be approximated within a ratio of c@?lnn for some constant c>0 in polynomial time, and provides a deterministic construction of a triplet set having a similar property which is subsequently used to prove that both MaxRTC and Min RTI are NP-hard even if restricted to minimally dense instances.
Enumerating All Maximal Frequent Subtrees
TLDR
The novel problem of enumerating all MFSTs in collections of phylogenetic trees, a compact non-redundant summary of all FSTs, is tackled and its utility is demonstrated in returning larger consensus trees in comparison to MAST.
Fixed Parameter Polynomial Time Algorithms for Maximum Agreement and Compatible Supertrees
TLDR
This paper gives the first polynomial time algorithms for both MASP and MCSP when both $k$ and the maximum degree $D$ of the trees are constant.
Improved Algorithms for Maximum Agreement and Compatible Supertrees
TLDR
The results imply the first polynomial time algorithms for both MASP and MCSP when both k and the maximum degree D of the input trees are constant.
Conflict Packing yields linear vertex-kernels for Rooted Triplet Inconsistency and other problems
TLDR
It is proved that the Dense Rooted Triplet Inconsistency problem admits a linear vertex-kernel and this result improves the best known bound of O(k) vertices for this problem [19].
EvoMiner: frequent subtree mining in phylogenetic databases
TLDR
EvoMiner is an Apriori-like levelwise method, which uses a novel phylogeny-specific constant-time candidate generation scheme, an efficient fingerprinting-based technique for downward closure, and a lowest-common-ancestor-based support counting step that requires neither costly subtree operations nor database traversal.
Conflict Packing: an unifying technique to obtain polynomial kernels for editing problems on dense instances
TLDR
A technique that is called Conflict Packing is developed, obtaining (and improving) several polynomial kernels for editing problems on dense instances, and it is proved that the Dense Rooted Triplet Inconsistency problem admits a linear vertex-kernel.

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