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Deep neural networks have been proven powerful at processing perceptual data, such as images and audio. However for tabular data, tree-based models are more popular. A nice property of tree-based models is their natural interpretability. In…

Machine Learning · Computer Science 2018-06-20 Yongxin Yang , Irene Garcia Morillo , Timothy M. Hospedales

Generalized Pythagoras trees were developed for visualizing hierarchical data, producing organic, fractal-like representations. However, the drawback of the original layout algorithm is visual overlap of tree branches. To avoid such…

Graphics · Computer Science 2019-07-31 Tanja Munz , Michael Burch , Toon van Benthem , Yoeri Poels , Fabian Beck , Daniel Weiskopf

A metro-line crossing minimization problem is to draw multiple lines on an underlying graph that models stations and rail tracks so that the number of crossings of lines becomes minimum. It has several variations by adding restrictions on…

Data Structures and Algorithms · Computer Science 2013-06-18 Yoshio Okamoto , Yuichi Tatsu , Yushi Uno

Compatibility of unrooted phylogenetic trees is a well studied problem in phylogenetics. It asks to determine whether for a set of k input trees there exists a larger tree (called a supertree) that contains the topologies of all k input…

Discrete Mathematics · Computer Science 2014-03-03 Alexander Grigoriev , Steven Kelk , Nela Lekic

The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees.…

Data Structures and Algorithms · Computer Science 2021-05-26 Svein Høgemo , Benjamin Bergougnoux , Ulrik Brandes , Christophe Paul , Jan Arne Telle

Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…

Machine Learning · Computer Science 2025-01-15 Catalin E. Brita , Jacobus G. M. van der Linden , Emir Demirović

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…

Data Structures and Algorithms · Computer Science 2025-07-16 Luisa Gargano , Adele A. Rescigno

Order diagrams allow human analysts to understand and analyze structural properties of ordered data. While an experienced expert can create easily readable order diagrams, the automatic generation of those remains a hard task. In this work,…

Computational Geometry · Computer Science 2021-02-05 Dominik Dürrschnabel , Gerd Stumme

In this paper, we study the complexity of the periodic temporal graph realization problem with respect to upper bounds on the fastest path durations among its vertices. This constraint with respect to upper bounds appears naturally in…

Data Structures and Algorithms · Computer Science 2025-04-22 George B. Mertzios , Hendrik Molter , Nils Morawietz , Paul G. Spirakis

While the algorithmic drawing of static trees is well-understood and well-supported by software tools, creating animations depicting how a tree changes over time is currently difficult: software support, if available at all, is not…

Computational Geometry · Computer Science 2016-08-31 Malte Skambath , Till Tantau

Linear model trees are regression trees that incorporate linear models in the leaf nodes. This preserves the intuitive interpretation of decision trees and at the same time enables them to better capture linear relationships, which is hard…

Machine Learning · Statistics 2024-07-10 Jakob Raymaekers , Peter J. Rousseeuw , Tim Verdonck , Ruicong Yao

We study the problem of connecting the parts of a multipartite graph using a minimum number of edges under a matching constraint. We introduce interconnection trees, defined as matchings whose projections onto the quotient graph form a…

Computational Complexity · Computer Science 2026-05-19 Noé Demange , Yann Strozecki

Decision Trees are prominent prediction models for interpretable Machine Learning. They have been thoroughly researched, mostly in the batch setting with a fixed labelled dataset, leading to popular algorithms such as C4.5, ID3 and CART.…

Machine Learning · Computer Science 2024-06-24 Ayman Chaouki , Jesse Read , Albert Bifet

Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and…

Machine Learning · Statistics 2021-10-25 Rafael Blanquero , Emilio Carrizosa , Cristina Molero-Río , Dolores Romero Morales

Bipartite graphs model the relationships between two disjoint sets of entities in several applications and are naturally drawn as 2-layer graph drawings. In such drawings, the two sets of entities (vertices) are placed on two parallel lines…

We consider upward-planar layered drawings of directed graphs, i.e., crossing-free drawings in which each edge is drawn as a y-monotone curve going upward from its tail to its head, and the y-coordinates of the vertices are integers. The…

Computational Geometry · Computer Science 2026-05-04 Patrizio Angelini , Sabine Cornelsen , Giordano Da Lozzo , Fabrizio Frati , Philipp Kindermann , Ignaz Rutter , Johannes Zink

Let $T$ be a weighted tree. The weight of a subtree $T_1$ of $T$ is defined as the product of weights of vertices and edges of $T_1$. We obtain a linear-time algorithm to count the sum of weights of subtrees of $T$. As applications, we…

Combinatorics · Mathematics 2007-05-23 Weigen Yan , Yeong-Nan Yeh

Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split:…

Data Structures and Algorithms · Computer Science 2013-04-17 Ryan R. Curtin , William B. March , Parikshit Ram , David V. Anderson , Alexander G. Gray , Charles L. Isbell

Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…

Machine Learning · Computer Science 2025-11-19 Varun Babbar , Hayden McTavish , Cynthia Rudin , Margo Seltzer

We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph $G$ and a constraint function $D$, we ask for a (minimum-cost) spanning tree $T$ such that for each vertex $v$, $T$…

Data Structures and Algorithms · Computer Science 2026-05-05 Narek Bojikian , Alexander Firbas , Robert Ganian , Hung P. Hoang , Krisztina Szilágyi