Related papers: Additive Approximation for Near-Perfect Phylogeny …
Distance-based phylogenetic algorithms attempt to solve the NP-hard least squares phylogeny problem by mapping an arbitrary dissimilarity map representing biological data to a tree metric. The set of all dissimilarity maps is a Euclidean…
We consider the problem of augmenting an $n$-vertex tree with one shortcut in order to minimize the diameter of the resulting graph. The tree is embedded in an unknown space and we have access to an oracle that, when queried on a pair of…
We present an algorithm for phylogenetic reconstruction using quartets that returns the correct topology for $n$ taxa in $O(n \log n)$ time with high probability, in a probabilistic model where a quartet is not consistent with the true…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
A chief problem in phylogenetics and database theory is the computation of a maximum consistent tree from a set of rooted or unrooted trees. A standard input are triplets, rooted binary trees on three leaves, or quartets, unrooted binary…
Maximum parsimony distance is a measure used to quantify the dissimilarity of two unrooted phylogenetic trees. It is NP-hard to compute, and very few positive algorithmic results are known due to its complex combinatorial structure. Here we…
We consider an incremental variant of the rooted prize-collecting Steiner-tree problem with a growing budget constraint. While no incremental solution exists that simultaneously approximates the optimum for all budgets, we show that a…
The reconstruction of phylogenetic trees from discrete character data typically relies on models that assume the characters evolve under a continuous-time Markov process operating at some overall rate $\lambda$. When $\lambda$ is too high…
The supertree problem asking for a tree displaying a set of consistent input trees has been largely considered for the reconstruction of species trees. Here, we rather explore this framework for the sake of reconstructing a gene tree from a…
The supertree construction problem is about combining several phylogenetic trees with possibly conflicting information into a single tree that has all the leaves of the source trees as its leaves and the relationships between the leaves are…
Given a graph $G = (V, E)$, we wish to compute a spanning tree whose maximum vertex degree, i.e. tree degree, is as small as possible. Computing the exact optimal solution is known to be NP-hard, since it generalizes the Hamiltonian path…
Most of major algorithms for phylogenetic tree reconstruction assume that sequences in the analyzed set either do not have any offspring, or that parent sequences can maximally mutate into just two descendants. The graph resulting from such…
In this experimental study we consider Steiner tree approximations that guarantee a constant approximation of ratio smaller than $2$. The considered greedy algorithms and approaches based on linear programming involve the incorporation of…
We give a randomized O(n polylog n)-time approximation scheme for the Steiner forest problem in the Euclidean plane. For every fixed eps > 0 and given n terminals in the plane with connection requests between some pairs of terminals, our…
Given two sets of points in the plane, $P$ of $n$ terminals and $S$ of $m$ Steiner points, a Steiner tree of $P$ is a tree spanning all points of $P$ and some (or none or all) points of $S$. A Steiner tree with length of longest edge…
Phylogenetic Diversity (PD) is a measure of the overall biodiversity of a set of present-day species (taxa) within a phylogenetic tree. In Maximize Phylogenetic Diversity (MPD) one is asked to find a set of taxa (of bounded size/cost) for…
We consider the problem of embedding the Steiner points of a Steiner tree with given topology into the rectilinear plane. Thereby, the length of the path between a distinguished terminal and each other terminal must not exceed given length…
Finding an optimal assignment between two sets of objects is a fundamental problem arising in many applications, including the matching of `bag-of-words' representations in natural language processing and computer vision. Solving the…
Phylogenetically decisive collections of taxon sets have the property that if trees are chosen for each of their elements, as long as these trees are compatible, the resulting supertree is unique. This means that as long as the trees…
Reconstructing the evolutionary history of a set of species is a central task in computational biology. In real data, it is often the case that some information is missing: the Incomplete Directed Perfect Phylogeny (IDPP) problem asks,…