Nela Lekić

Cycle killer... qu'est-ce que c'est? On the comparative approximability of hybridization number and directed feedback vertex set

We show that the problem of computing the hybridization number of two rooted binary phylogenetic trees on the same set of taxa

Approximation Algorithms for Nonbinary Agreement Forests

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Hybridization Number on Three Rooted Binary Trees is EPT

has a constant factor polynomial-time approximation if and only if the problem of computing a minimum-size feedback vertex set in a directed graph (DFVS) has a constant factor polynomial-time approximation. The latter problem, which asks for a minimum number of vertices to be removed from a directed graph to transform it into a directed acyclic graph, is one of the problems in Karps seminal 1972 list of 21 NP-complete problems. Despite considerable attention from the combinatorial optimization community, it remains to this day unknown whether a constant factor polynomial-time approximation exists for DFVS. Our result thus places the (in)approximability of hybridization number in a much broader complexity context, and as a consequence we obtain that it inherits inapproximability results from the problem Vertex Cover. On the positive side, we use results from the DFVS literatur...

A practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees

Given two rooted phylogenetic trees on the same set of taxa

A practical approximation algorithm for solving massive instances of hybridization number

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On Low Treewidth Graphs and Supertrees

, the Maximum Agreement Forest (maf) problem 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 (maaf) problem has the additional restriction that the components of the forest cannot have conflicting ancestral relations in the input trees. There has been considerable interest in the special cases of these problems in which the input trees are required to be binary. However, in practice, phylogenetic trees are rarely binary, due to uncertainty about the precise order of speciation events. Here, we show that the general, nonbinary version of maf has a polynomial-time 4-approximation and a fixed-parameter tractable (exact) algorithm that runs in

Hybridization Number on Three Trees

O(4^k {\rm poly}(n))

Satisfying ternary permutation constraints by multiple linear orders or phylogenetic trees

time, where

A short note on exponential-time algorithms for hybridization number

n=|X|

Computing nonbinary agreement forests

and