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In this paper, we introduce a new approach for drawing diagrams that have applications in software visualization. Our approach is to use a technique we call confluent drawing for visualizing non-planar diagrams in a planar way. This…

Computational Geometry · Computer Science 2007-05-23 Matthew Dickerson , David Eppstein , Michael T. Goodrich , Jeremy Meng

Planar drawings of graphs tend to be favored over non-planar drawings. Testing planarity and creating a planar layout of a planar graph can be done in linear time. However, creating readable drawings of nearly planar graphs remains a…

Computational Geometry · Computer Science 2023-04-18 Simon van Wageningen , Tamara Mchedlidze , Alexandru Telea

A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show the surprising fact that it is NP-hard to compute the crossing number of near-planar graphs. A graph is 1-planar if it has a drawing where every…

Computational Geometry · Computer Science 2012-03-28 Sergio Cabello , Bojan Mohar

Bach et al. [1] recently presented an algorithm for constructing confluent drawings, by leveraging power graph decomposition to generate an auxiliary routing graph. We identify two issues with their method which we call the node split and…

Computational Geometry · Computer Science 2019-09-04 Jonathan X. Zheng , Samraat Pawar , Dan F. M. Goodman

Many problems can be presented in an abstract form through a wide range of binary objects and relations which are defined over problem domain. In these problems, graphical demonstration of defined binary objects and solutions is the most…

Graphics · Computer Science 2016-03-24 Mohammadreza Ashouri , Ali Golshani , Dara Moazzmi , Mandana Ghasemi

One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…

Data Analysis, Statistics and Probability · Physics 2009-09-29 Hristo Djidjev

In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…

Data Structures and Algorithms · Computer Science 2016-06-13 Christian Komusiewicz , André Nichterlein , Rolf Niedermeier

We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to…

Discrete Mathematics · Computer Science 2024-02-29 Julia Katheder , Stephen G. Kobourov , Axel Kuckuk , Maximilian Pfister , Johannes Zink

The study of nonplanar drawings of graphs with restricted crossing configurations is a well-established topic in graph drawing, often referred to as beyond-planar graph drawing. One of the most studied types of drawings in this area are the…

Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…

Social and Information Networks · Computer Science 2020-02-19 Ilya Amburg , Nate Veldt , Austin R. Benson

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…

Data Structures and Algorithms · Computer Science 2019-04-12 He Sun , Luca Zanetti

Edge bundling techniques cluster edges with similar attributes (i.e. similarity in direction and proximity) together to reduce the visual clutter. All edge bundling techniques to date implicitly or explicitly cluster groups of individual…

Graphics · Computer Science 2021-10-29 Markus Wallinger , Daniel Archambault , David Auber , Martin Nöllenburg , Jaakko Peltonen

We investigate the problem of constructing planar drawings with few bends for two related problems, the partially embedded graph problem---to extend a straight-line planar drawing of a subgraph to a planar drawing of the whole graph---and…

Computational Geometry · Computer Science 2014-10-31 Timothy M. Chan , Fabrizio Frati , Carsten Gutwenger , Anna Lubiw , Petra Mutzel , Marcus Schaefer

Inspired by artistic practices such as beadwork and himmeli, we study the problem of threading a single string through a set of tubes, so that pulling the string forms a desired graph. More precisely, given a connected graph (where edges…

Data Structures and Algorithms · Computer Science 2024-05-29 Erik D. Demaine , Yael Kirkpatrick , Rebecca Lin

Correlation clustering provides a method for separating the vertices of a signed graph into the optimum number of clusters without specifying that number in advance. The main goal in this type of clustering is to minimize the number of…

Combinatorics · Mathematics 2025-07-15 Leila Parsaei-Majd

Graph Crossing Number is a fundamental problem with various applications. In this problem, the goal is to draw an input graph $G$ in the plane so as to minimize the number of crossings between the images of its edges. Despite extensive…

Data Structures and Algorithms · Computer Science 2021-01-12 Julia Chuzhoy , Sepideh Mahabadi , Zihan Tan

The crossing number of a graph $G$ is the least number of crossings over all possible drawings of $G$. We present a structural characterization of graphs with crossing number one.

Combinatorics · Mathematics 2021-08-24 André C. Silva , Alan Arroyo , R. Bruce Richter , Orlando Lee

Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…

Machine Learning · Statistics 2013-02-06 Brian Baingana , Georgios B. Giannakis

We consider the minimization of edge-crossings in geometric drawings of graphs $G=(V, E)$, i.e., in drawings where each edge is depicted as a line segment. The respective decision problem is NP-hard [Bienstock, '91]. In contrast to theory…

Computational Geometry · Computer Science 2019-07-03 Marcel Radermacher , Ignaz Rutter

When processing a batch of graphs in machine learning models such as Graph Neural Networks (GNN), it is common to combine several small graphs into one overall graph to accelerate processing and remove or reduce the overhead of padding.…

Machine Learning · Computer Science 2022-09-20 Mario Michael Krell , Manuel Lopez , Sreenidhi Anand , Hatem Helal , Andrew William Fitzgibbon