26 research outputs found
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 X 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 Karp's seminal 1972
list of 21 NP-complete problems. However, 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 hybridization number
inherits inapproximability results from the problem Vertex Cover. On the
positive side, we use results from the DFVS literature to give an O(log r log
log r) approximation for hybridization number, where r is the value of an
optimal solution to the hybridization number problem
Foundations of Digital Arch{\ae}oludology
Digital Archaeoludology (DAL) is a new field of study involving the analysis
and reconstruction of ancient games from incomplete descriptions and
archaeological evidence using modern computational techniques. The aim is to
provide digital tools and methods to help game historians and other researchers
better understand traditional games, their development throughout recorded
human history, and their relationship to the development of human culture and
mathematical knowledge. This work is being explored in the ERC-funded Digital
Ludeme Project.
The aim of this inaugural international research meeting on DAL is to gather
together leading experts in relevant disciplines - computer science, artificial
intelligence, machine learning, computational phylogenetics, mathematics,
history, archaeology, anthropology, etc. - to discuss the key themes and
establish the foundations for this new field of research, so that it may
continue beyond the lifetime of its initiating project.Comment: Report on Dagstuhl Research Meeting. Authored/edited by all
participants. Appendices by Thierry Depauli
Ancient dispersal of the human fungal pathogen Cryptococcus gattii from the Amazon rainforest.
Over the past two decades, several fungal outbreaks have occurred, including the high-profile 'Vancouver Island' and 'Pacific Northwest' outbreaks, caused by Cryptococcus gattii, which has affected hundreds of otherwise healthy humans and animals. Over the same time period, C. gattii was the cause of several additional case clusters at localities outside of the tropical and subtropical climate zones where the species normally occurs. In every case, the causative agent belongs to a previously rare genotype of C. gattii called AFLP6/VGII, but the origin of the outbreak clades remains enigmatic. Here we used phylogenetic and recombination analyses, based on AFLP and multiple MLST datasets, and coalescence gene genealogy to demonstrate that these outbreaks have arisen from a highly-recombining C. gattii population in the native rainforest of Northern Brazil. Thus the modern virulent C. gattii AFLP6/VGII outbreak lineages derived from mating events in South America and then dispersed to temperate regions where they cause serious infections in humans and animals
On the relative complexity of approximately counting H-colourings
EThOS - Electronic Theses Online ServiceGBUnited Kingdo
A Simple Fixed Parameter Tractable Algorithm for Computing the Hybridization Number of Two (Not Necessarily Binary) Trees
Uniqueness, intractability and exact algorithms: reflections on level-k phylogenetic networks
Phylogenetic networks provide a way to describe and visualize evolutionary histories that have undergone so-called reticulate evolutionary events such as recombination, hybridization or horizontal gene transfer. The level k of a network determines how non-treelike the evolution can be, with level-0 networks being trees. We study the problem of constructing level-k phylogenetic networks from triplets, i.e. phylogenetic trees for three leaves (taxa). We give, for each k, a level-k network that is uniquely defined by its triplets. We demonstrate the applicability of this result by using it to prove that (1) for all k of at least one it is NP-hard to construct a level-k network consistent with all input triplets, and (2) for all k it is NP-hard to construct a level-k network consistent with a maximum number of input triplets, even when the input is dense. As a response to this intractability we give an exact algorithm for constructing level-1 networks consistent with a maximum number of input triplets