Related papers: A quadratic kernel for computing the hybridization…
The Minimum Branch Vertices Spanning Tree problem aims to find a spanning tree $T$ in a given graph $G$ with the fewest branch vertices, defined as vertices with a degree three or more in $T$. This problem, known to be NP-hard, has…
Phylogenetic networks are a generalization of evolutionary trees that are used by biologists to represent the evolution of organisms which have undergone reticulate evolution. Essentially, a phylogenetic network is a directed acyclic graph…
In the framework of computational complexity and in an effort to define a more natural reduction for problems of equivalence, we investigate the recently introduced kernel reduction, a reduction that operates on each element of a pair…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
Phylogenetic networks are an extension of phylogenetic trees that allow for the representation of reticulate evolution events. One of the classes of networks that has gained the attention of the scientific community over the last years is…
The Tree of Life is the graphical structure that represents the evolutionary process from single-cell organisms at the origin of life to the vast biodiversity we see today. Reconstructing this tree from genomic sequences is challenging due…
Packing problems are in general NP-hard, even for simple cases. Since now there are no highly efficient algorithms available for solving packing problems. The two-dimensional bin packing problem is about packing all given rectangular items,…
The maximum parsimony phylogenetic tree reconstruction problem is NP-hard, presenting a computational bottleneck for classical computing and motivating the exploration of emerging paradigms like quantum computing. To this end, we design…
Phylogenetic networks have gained prominence over the years due to their ability to represent complex non-treelike evolutionary events such as recombination or hybridization. Popular combinatorial objects used to construct them are triplet…
A method of reducing the problem of the calculation of tree multiparticle cross sections in $\phi^4$ theory to the solution of a singular classical Euclidean boundary value problem is introduced. The solutions are obtained numerically 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…
Applying kernel methods to matchings is challenging due to their discrete, non-Euclidean nature. In this paper, we develop a principled framework for constructing geometric kernels that respect the natural geometry of the space of…
We study the existence of polynomial kernels for the problem of deciding feasibility of integer linear programs (ILPs), and for finding good solutions for covering and packing ILPs. Our main results are as follows: First, we show that the…
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…
We develop a framework for applying treewidth-based dynamic programming on graphs with "hybrid structure", i.e., with parts that may not have small treewidth but instead possess other structural properties. Informally, this is achieved by…
We introduce a new kernelization tool, called rainbow matching technique}, that is appropriate for the design of polynomial kernels for packing problems and their hitting counterparts. Our technique capitalizes on the powerful combinatorial…
The traditional clustering problem of renewable energy profiles is typically formulated as a combinatorial optimization that suffers from the Curse of Dimensionality (CoD) on classical computers. To address this issue, this paper first…
A binary phylogenetic network on a taxon set $X$ is a rooted acyclic digraph in which the degree of each nonleaf node is three and its leaves (i.e.degree-one nodes) are uniquely labeled with the taxa of $X$. It is tree-child if each nonleaf…
Makespan minimization (on parallel identical or unrelated machines) is arguably the most natural and studied scheduling problem. A common approach in practical algorithm design is to reduce the size of a given instance by a fast…
Hierarchical embedding constraints define a set of allowed cyclic orders for the edges incident to the vertices of a graph. These constraints are expressed in terms of FPQ-trees. FPQ-trees are a variant of PQ-trees that includes F-nodes in…