Related papers: The Complexity of Rooted Phylogeny Problems
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
Given a graph G and an integer k, the objective of the $\Pi$-Contraction problem is to check whether there exists at most k edges in G such that contracting them in G results in a graph satisfying the property $\Pi$. We investigate the…
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…
The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of…
This paper tackles the problem of the existence of solutions for recursive systems of Horn clauses with second-order variables interpreted as integer relations, and harnessed by quantifier-free difference bounds arithmetic. We start by…
The NP-hard general factor problem asks, given a graph and for each vertex a list of integers, whether the graph has a spanning subgraph where each vertex has a degree that belongs to its assigned list. The problem remains NP-hard even if…
As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…
We prove that finding a rooted subtree with at least $k$ leaves in a digraph is a fixed parameter tractable problem. A similar result holds for finding rooted spanning trees with many leaves in digraphs from a wide family $\cal L$ that…
When a computer algebra system fails to solve an Ordinary Differential Equation, is this a limitation of its implementation, or a genuine computational barrier? Three traditions bear on the question. Modern computer algebra algorithms can…
We show that two important problems that have applications in computational biology are ASP-complete, which implies that, given a solution to a problem, it is NP-complete to decide if another solution exists. We show first that a variation…
While every rooted binary phylogenetic tree is determined by its set of displayed rooted triples, such a result does not hold for an arbitrary rooted binary phylogenetic network. In particular, there exist two non-isomorphic rooted binary…
Phylogenetic reconciliation seeks to explain host-symbiont co-evolution by mapping parasite trees onto host trees through events such as cospeciation, duplication, host switching, and loss. Finding an optimal reconciliation that ensures…
Phylogenetic networks are a flexible model of evolution that can represent reticulate evolution and handle complex data. Tree-based networks, which are phylogenetic networks that have a spanning tree with the same root and leaf-set as the…
In the point set embeddability problem, we are given a plane graph $G$ with $n$ vertices and a point set $S$ with $n$ points. Now the goal is to answer the question whether there exists a straight-line drawing of $G$ such that each vertex…
Reconciling a gene tree with a species tree is an important task that reveals much about the evolution of genes, genomes, and species, as well as about the molecular function of genes. A wide array of computational tools have been devised…
We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…
The resilience of a Boolean query is the minimum number of tuples that need to be deleted from the input tables in order to make the query false. A solution to this problem immediately translates into a solution for the more widely known…
We present approximation algorithms for the following NP-hard optimization problems related to bottleneck spanning trees in metric spaces. 1. The disjoint bottleneck spanning tree problem: Given $n$ pairs of points in a metric space, find…
Rooted phylogenetic networks are often constructed by combining trees, clusters, triplets or characters into a single network that in some well-defined sense simultaneously represents them all. We review these four models and investigate…
We study the problem of maximizing a monotone submodular function with viability constraints. This problem originates from computational biology, where we are given a phylogenetic tree over a set of species and a directed graph, the…