Fixed-Parameter and Approximation Algorithms for Maximum Agreement Forests

A Unifying View on Approximation and FPT of Agreement Forests (Extended Abstract⋆)

We provide a unifying view on the structure of maximum (acyclic) agreement forests of rooted and unrooted phylogenies. This enables us to obtain linearor O(n log n)-time 3-approximation and improved fixed-parameter algorithms for the subtree prune and regraft distance between two rooted phylogenies, the tree bisection and reconnection distance between two unrooted phylogenies, and the hybridiza...

A Unifying View on Approximation and FPT of Agreement Forests

We provide a unifying view on the structure of maximum (acyclic) agreement forests of rooted and unrooted phylogenies. This enables us to obtain linearor O(n logn)-time 3-approximation and improved fixed-parameter algorithms for the subtree prune and regraft distance between two rooted phylogenies, the tree bisection and reconnection distance between two unrooted phylogenies, and the hybridizat...

Approximation Algorithms for Nonbinary Agreement Forests

Given two rooted phylogenetic trees on the same set of taxa X, the Maximum Agreement Forest problem (MAF) asks to find a forest that is, in a certain sense, common to both trees and has a minimum number of components. The Maximum Acyclic Agreement Forest problem (MAAF) has the additional restriction that the components of the forest cannot have conflicting ancestral relations in the input trees...

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems

Efficient Approximation Algorithms for Point-set Diameter in Higher Dimensions

We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...