Related papers: Visualizing Multispecies Coalescent Trees: Drawing…

Phylogenetic trees are leaf-labelled trees used to model the evolution of species. Here we explore the practical impact of kernelization (i.e. data reduction) on the NP-hard problem of computing the TBR distance between two unrooted binary…

Symbolic regression (SR) is the process of discovering hidden relationships from data with mathematical expressions, which is considered an effective way to reach interpretable machine learning (ML). Genetic programming (GP) has been the…

Given a connected, undirected graph whose edges are labelled (or coloured), the minimum labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest number of distinct labels (or colours). In recent work, the…

We study the statistics of edges and vertices in the vicinity of a reference vertex (origin) within random planar quadrangulations and Eulerian triangulations. Exact generating functions are obtained for theses graphs with fixed numbers of…

Unraveling the co-expression of genes across studies enhances the understanding of cellular processes. Inferring gene co-expression networks from transcriptome data presents many challenges, including spurious gene correlations, sample…

Planar partial $3$-trees are subgraphs of those planar graphs obtained by repeatedly inserting a vertex of degree $3$ into a face. In this paper, we show that planar partial $3$-trees have $1$-string $B_1$-VPG representations, i.e.,…

The LR-drawing-method is a method of drawing an ordered rooted binary tree based on drawing one root-to-leaf path on a vertical line and attaching recursively obtained drawings of the subtrees on the left and right. In this paper, we study…

A visibility representation is a classical drawing style of planar graphs. It displays the vertices of a graph as horizontal vertex-segments, and each edge is represented by a vertical edge-segment touching the segments of its end vertices;…

We consider the counting problem of the number of \textit{leaf-labeled increasing trees}, where internal nodes may have an arbitrary number of descendants. The set of all such trees is a discrete representation of the genealogies obtained…

In computer-aided design (CAD) systems, 2D line drawings are commonly used to illustrate 3D object designs. To reconstruct the 3D models depicted by a single 2D line drawing, an important key is finding the edge loops in the line drawing…

Given a planar graph $G$ and an integer $b$, OrthogonalPlanarity is the problem of deciding whether $G$ admits an orthogonal drawing with at most $b$ bends in total. We show that OrthogonalPlanarity can be solved in polynomial time if $G$…

A \emph{binary tanglegram} is a drawing of a pair of rooted binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example, in phylogenetics, it is essential…

We consider the irregular strip packing problem of rasterized shapes, where a given set of pieces of irregular shapes represented in pixels should be placed into a rectangular container without overlap. The rasterized shapes provide simple…

We introduce the $k$-Plane Insertion into Plane drawing ($k$-PIP) problem: given a plane drawing of a planar graph $G$ and a set $F$ of edges, insert the edges in $F$ into the drawing such that the resulting drawing is $k$-plane. In this…

Survival analysis studies and predicts the time of death, or other singular unrepeated events, based on historical data, while the true time of death for some instances is unknown. Survival trees enable the discovery of complex nonlinear…

Binary phylogenetic trees inferred from biological data are central to understanding the shared history among evolutionary units. However, inferring the placement of latent nodes in a tree is computationally expensive. State-of-the-art…

The standard formalization of preprocessing in parameterized complexity is given by kernelization. In this work, we depart from this paradigm and study a different type of preprocessing for problems without polynomial kernels, still aiming…

We study the robustness verification problem for tree-based models, including decision trees, random forests (RFs) and gradient boosted decision trees (GBDTs). Formal robustness verification of decision tree ensembles involves finding the…

Reciprocal best match graphs (RBMGs) are vertex colored graphs whose vertices represent genes and the colors the species where the genes reside. Edges identify pairs of genes that are most closely related with respect to an underlying…

We concern the problem of modifying the edge lengths of a tree in minimum total cost so that the prespecified $p$ vertices become the $p$-maxian with respect to the new edge lengths. This problem is called the inverse $p$-maxian problem on…