Related papers: Listing Conflicting Triples in Optimal Time
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
We give a non-technical introduction to convergence-divergence models, a new modeling approach for phylogenetic data that allows for the usual divergence of species post speciation but also allows for species to converge, i.e. become more…
We present an axiomatic framework for analyzing the algorithmic properties of decision trees. This framework supports the classification of decision tree problems through structural and ancestral constraints within a rigorous mathematical…
The classical paradox of social choice theory asserts that there is no fair way to deterministically select a winner in an election among more than two candidates; the only definite collective preferences are between individual pairs of…
Evolution is a process that is influenced by various environmental factors, e.g. the interactions between different species, genes, and biogeographical properties. Hence, it is interesting to study the combined evolutionary history of…
Phylogenetic reconstruction aims at finding plausible hypotheses of the evolutionary history of genes or species based on genomic sequence information. The distinction of orthologous genes (genes that having a common ancestry and diverged…
Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data is generated by a mixture model has stimulated considerable recent…
Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…
Construction of phylogenetic trees and networks for extant species from their characters represents one of the key problems in phylogenomics. While solution to this problem is not always uniquely defined and there exist multiple methods for…
The rendezvous task calls for two mobile agents, starting from different nodes of a network modeled as a graph to meet at the same node. Agents have different labels which are integers from a set $\{1,\dots,L\}$. They wake up at possibly…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
Evolutionary relationships between species are usually inferred through phylogenetic analysis, which provides phylogenetic trees computed from allelic profiles built by sequencing specific regions of the sequences and abstracting them to…
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…
The 3SUM problem is to decide, given a set of $n$ real numbers, whether any three sum to zero. It is widely conjectured that a trivial $O(n^2)$-time algorithm is optimal and over the years the consequences of this conjecture have been…
In mathematical phylogenetics, evolutionary relationships are often represented by trees and networks. The latter are typically used whenever the relationships cannot be adequately described by a tree, which happens when so-called…
In this paper we propose a family of algorithms combining tree-clustering with conditioning that trade space for time. Such algorithms are useful for reasoning in probabilistic and deterministic networks as well as for accomplishing…
Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if…
Rooted phylogenetic networks allow biologists to represent evolutionary relationships between present-day species by revealing ancestral speciation and hybridization events. A convenient and well-studied class of such networks are…
We develop a technique that we call Conflict Packing in the context of kernelization, obtaining (and improving) several polynomial kernels for editing problems on dense instances. We apply this technique on several well-studied problems:…
Phylogenetic diversity indices such as the Fair Proportion (FP) index are frequently discussed as prioritization criteria in biodiversity conservation. They rank species according to their contribution to overall diversity by taking into…