New Reduction Rules for the Tree Bisection and Reconnection Distance

  title={New Reduction Rules for the Tree Bisection and Reconnection Distance},
  author={Steven M. Kelk and Simone Linz},
  journal={Annals of Combinatorics},
  • S. Kelk, S. Linz
  • Published 4 May 2019
  • Computer Science, Mathematics, Biology
  • Annals of Combinatorics
Recently it was shown that, if the subtree and chain reduction rules have been applied exhaustively to two unrooted phylogenetic trees, the reduced trees will have at most $$15k-9$$ 15 k - 9 taxa where k is the TBR (Tree Bisection and Reconnection) distance between the two trees, and that this bound is tight. Here, we propose five new reduction rules and show that these further reduce the bound to $$11k-9$$ 11 k - 9 . The new rules combine the “unrooted generator” approach introduced in Kelk… 
3 Citations
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A tight kernel for computing the tree bisection and reconnection distance between two phylogenetic trees
  • S. Kelk, S. Linz
  • Mathematics, Computer Science
    SIAM J. Discret. Math.
  • 2019
This work reanalyse Allen and Steel's kernelization algorithm and proves that the reduced instances will in fact have at most 15k-9 taxa, and introduces and uses "unrooted generators" which are analogues of rooted structures that have appeared earlier in the phylogenetic networks literature.
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