Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem

  title={Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem},
  author={Sylvain Guillemot and Vincent Berry},
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
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
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
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
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
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
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
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
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
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.


Maximum agreement and compatible supertrees
Kaikoura Tree Theorems: Computing the Maximum Agreement Subtree
Parameterized Complexity Theory
  • J. Flum, Martin Grohe
  • Computer Science
    Texts in Theoretical Computer Science. An EATCS Series
  • 2006
Fixed-Parameter Tractability.- Reductions and Parameterized Intractability.- The Class W[P].- Logic and Complexity.- Two Fundamental Hierarchies.- The First Level of the Hierarchies.- The
Consensus supertrees: The synthesis of rooted trees containing overlapping sets of labeled leaves
An algorithm for obtaining the strict consensus supertree of two consistent sample trees is presented, as are procedures for merging two inconsistent sample trees.
Bounded nondeterminism and alternation in parameterized complexity theory
The focus of the attention is the class W[P], which is characterised as the class of all parameterized problems decidable by a nondeterministic fixed-parameter tractable algorithm, whose use of nondeterminism is bounded in terms of the parameter.
Constructing a Tree from Homeomorphic Subtrees, with Applications to Computational Evolutionary Biology
Two algorithms which test if a given set of trees has a consensus tree and if so, construct one are presented and two applications of these consensus tree algorithms which solve other problems in computational evolutionary biology are presented.
Rooted Maximum Agreement Supertrees
The maximum agreement supertree problem (MASP) is proved to be NP-hard for any fixed k ≥ 3 when D is unrestricted, and also NP- hard forAny fixed D ≥ 2 when k is unrestricted even if each input tree is required to contain at most three leaves.
Mining Closed and Maximal Frequent Subtrees from Databases of Labeled Rooted Trees
CMTreeMiner is presented, a computationally efficient algorithm that discovers only closed and maximal frequent subtrees in a database of labeled rooted trees, where the rooted trees can be either ordered or unordered.
Reconstructing the shape of a tree from observed dissimilarity data