Treewidth distance on phylogenetic trees

@article{Kelk2018TreewidthDO,
  title={Treewidth distance on phylogenetic trees},
  author={Steven M. Kelk and Georgios Stamoulis and Taoyang Wu},
  journal={ArXiv},
  year={2018},
  volume={abs/1703.10840}
}
Treewidth of display graphs: bounds, brambles and applications
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References

SHOWING 1-10 OF 55 REFERENCES
On Low Treewidth Graphs and Supertrees
TLDR
It is shown that whenever the treewidth of an auxiliary structure known as the display graph is strictly larger than the number of input trees, the instance is incompatible and a polynomial-time algorithm is given to construct a supertree in this case.
Subtree Transfer Operations and Their Induced Metrics on Evolutionary Trees
TLDR
The problem of computing the minimum number of TBR operations required to transform one tree to another can be reduced to a problem whose size is a function just of the distance between the trees, and thereby establish that the problem is fixed-parameter tractable.
Phylogenetic incongruence through the lens of Monadic Second Order logic
TLDR
This article uses Monadic Second Order logic (MSOL) to give alternative, compact proofs of fixed parameter tractability for several well-known incongruency measures and introduces a number of "phylogenetics MSOL primitives" which will hopefully be of use to other researchers.
On the fixed parameter tractability of agreement-based phylogenetic distances
TLDR
New analyses are presented showing that the use of the “cluster reduction” rule—already defined for the hybridization number and the rSPR distance and introduced here for the TBR distance—can transform any algorithm for solving three important measures of dissimilarity in phylogenetic trees into an O(f(k)·n)-time one.
Efficient FPT Algorithms for (Strict) Compatibility of Unrooted Phylogenetic Trees
TLDR
This paper gives the first explicit dynamic programming algorithms for solving the compatibility and the strict compatibility problems for unrooted phylogenetic trees, both running in time 2O(k^2)·n, where n is the total size of the input.
Reducing Problems in Unrooted Tree Compatibility to Restricted Triangulations of Intersection Graphs
TLDR
This paper shows a different way of efficiently reducing the compatibility problem to that of determining if another type of constrained triangulation exists for a new non-chordal intersection graph.
On the Complexity of Computing MP Distance Between Binary Phylogenetic Trees
TLDR
This work shows that computation of MP distance on two binary phylogenetic trees is NP-hard, and gives a simple Integer Linear Program (ILP) formulation which is capable of computing the MP distance exactly for small trees and for larger trees when only a small number of character states are available.
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