Papers › Convex characters, algorithms and matchings
Convex characters, algorithms and matchings
Steven Kelk, Ruben Meuwese, Stephan Wagner
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Phylogenetic trees are used to model evolution: leaves are labelled to represent contemporary species ("taxa") and interior vertices represent extinct ancestors. Informally, convex characters are measurements on the contemporary species in which the subset of species (both contemporary and extinct) that share a given state, form a connected subtree. In \cite{KelkS17} it was shown how to efficiently count, list and sample certain restricted subfamilies of convex characters, and algorithmic applications were given. We continue this work in a number of directions. First, we show how combining the enumeration of convex characters with existing parameterised algorithms can be used to speed up exponential-time algorithms for the \emph{maximum agreement forest problem} in phylogenetics. Second, we re-visit the quantity g₂(T), defined as the number of convex characters on T in which each state appears on at least 2 taxa. We use this to give an algorithm with running time O( ϕⁿ ·poly(n) ), where ϕ≈1.6181 is the golden ratio and n is the number of taxa in the input trees, for computation of \emph{maximum parsimony distance on two state characters}. By further restricting the characters counted by g₂(T) we open an interesting bridge to the literature on enumeration of matchings. By crossing this bridge we improve the running time of the aforementioned parsimony distance algorithm to O( 1.5895ⁿ ·poly(n) ), and obtain a number of new results in themselves relevant to enumeration of matchings on at-most binary trees.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections