arXiv subjects

Seok-Hee Hong

Publications and source records attributed to Seok-Hee Hong.

At least 19 recordsLinked to original sources

arXiv2026

Beyond Degree Four: Near-Orthogonal Planar Drawings

Orthogonal planar drawings constitute a classical and mainstream research topic in graph drawing due to their clarity and wide applicability. In an orthogonal planar drawing of a graph, each face is represented as an orthogonal polygon, that is, a polygon whose edges are either horizontal or vertical. Yet a planar graph admits such a representation if and only if its maximum degree is at most four. In this paper, we consider planar polyline drawings of graphs with unrestricted maximum degree. We focus on drawings that are ``close to orthogonal'', where closeness is measured by the number of faces that are not orthogonal polygons. We show that, even when the input graph is triconnected and thus has a unique planar embedding, the problem of testing whether there exists a planar polyline drawing with at most $h$ non-orthogonal faces is NP-complete. Motivated by this computational hardness, we study parameterized and approximation algorithms. In the fixed-embedding setting, we prove that the problem admits linear-time FPT algorithms parameterized by (i) the outerplanarity index and (ii) the natural parameter $h$. In addition, we provide an FPT algorithm parameterized by the treewidth and a polynomial-time approximation scheme. In the variable-embedding setting, we give an FPT algorithm parameterized by treewidth for biconnected graphs.

cs.CG↗

arXiv2026

Fast and Faithful Edge Bundling using Spectral Sparsification

Edge bundling reduces the visual complexity of drawings of large and complex graphs by clustering "compatible" edges. However, it often introduces distortion by bundling "unrelated" edges, resulting in misleading, ambiguous drawings. Moreover, existing edge bundling methods often have high computational complexity. We present new edge bundling methods and faithfulness metrics for edge bundling using spectral sparsification, which sparsifies a graph G into a subgraph G' with O(n log n) edges, based on the effective resistance values of edges, preserving the spectrum of G, closely related to important structural properties of G, such as connectivity, clustering, and the commute distance. We first present a new edge bundling method SEB (Spectral Edge Bundling), introducing effective resistance-based compatibility for spectral-faithful bundling, improving distortion and ambiguity. Then, we present a general framework FEB (Fast Edge Bundling) utilizing spectral sparsification to improve the efficiency of existing bundling methods while maintaining a similar quality. We also present FBQ (Fast Bundling Quality) framework for proxy bundle faithfulness metrics, for measuring how FEB faithfully preserves the ground truth structure in the original edge bundling, with two variants, FBQ_JS (utilizing Jaccard Similarity) and FBQ_SQ (utilizing sampling quality metrics). Extensive experiments using various real-world and synthetic graphs demonstrate the effectiveness of SEB for edge bundling, outperforming state-of-art bundling methods on quality metrics, with 46% and 17% average improvement in distortion and ambiguity respectively for SEB2. Furthermore, experiments successfully demonstrate the efficiency of the FEB framework, with 61% runtime improvement over the original edge bundling methods without sparsification, while maintaining a similar quality, with 74% similarity based on FBQ_SQ.

cs.DS↗

arXiv2025

SS-GUMAP, SL-GUMAP, SSSL-GUMAP: Fast UMAP Algorithms for Large Graph Drawing

UMAP is a popular neighborhood-preserving dimension reduction (DR) algorithm. However, its application for graph drawing has not been evaluated. Moreover, a naive application of UMAP to graph drawing would include O(nm) time all-pair shortest path computation, which is not scalable to visualizing large graphs. In this paper, we present fast UMAP-based for graph drawing. Specifically, we present three fast UMAP-based algorithms for graph drawing: (1) The SS-GUMAP algorithm utilizes spectral sparsification to compute a subgraph G' preserving important properties of a graph G, reducing the O(nm) component of the runtime to O(n^2 log n) runtime; (2) The SSL-GUMAP algorithm reduces the kNN (k-Nearest Neighbors) graph computation from $O(n \log n)$ time to linear time using partial BFS (Breadth First Search), and the cost optimization runtime from O(n) time to sublinear time using edge sampling; (3) The SSSL-GUMAP algorithm combines both approaches, for an overall O(n) runtime. Experiments demonstrate that SS-GUMAP runs 28% faster than GUMAP, a naive application of UMAP to graph drawing, with similar quality metrics, while SL-GUMAP and SSSL-GUMAP run over 80% faster than GUMAP with less than 15% difference on average for all quality metrics. We also present an evaluation of GUMAP to tsNET, a graph layout based on the popular DR algorithm t-SNE. GUMAP runs 90% faster than tsNET with similar neighborhood preservation and, on average, 10% better on quality metrics such as stress, edge crossing, and shape-based metrics, validating the effectiveness of UMAP for graph drawing.

cs.DS↗

arXiv2025

BH-tsNET, FIt-tsNET, L-tsNET: Fast tsNET Algorithms for Large Graph Drawing

The tsNET algorithm utilizes t-SNE to compute high-quality graph drawings, preserving the neighborhood and clustering structure. We present three fast algorithms for reducing the time complexity of tsNET algorithm from O(nm) time to O(n log n) time and O(n) time. To reduce the runtime of tsNET, there are three components that need to be reduced: (C0) computation of high-dimensional probabilities, (C1) computation of KL divergence gradient, and (C2) entropy computation. Specifically, we reduce the overall runtime of tsNET, integrating our new fast approaches for C0 and C2 with fast t-SNE algorithms for C1. We first present O(n log n)-time BH-tsNET, based on (C0) new O(n)-time partial BFS-based high-dimensional probability computation and (C2) new O(n log n)-time quadtree-based entropy computation, integrated with (C1) O(n log n)-time quadtree-based KL divergence computation of BH-SNE. We next present faster O(n log n)-time FIt-tsNET, using (C0) O(n)-time partial BFS-based high-dimensional probability computation and (C2) quadtree-based O(n log n)-time entropy computation, integrated with (C1) O(n)-time interpolation-based KL divergence computation of FIt-SNE. Finally, we present the O(n)-time L-tsNET, integrating (C2) new O(n)-time FFT-accelerated interpolation-based entropy computation with (C0) O(n)-time partial BFS-based high-dimensional probability computation, and (C1) O(n)-time interpolation-based KL divergence computation of FIt-SNE. Extensive experiments using benchmark data sets confirm that BH-tsNET, FIt-tsNET, and L-tsNET outperform tsNET, running 93.5%, 96%, and 98.6% faster while computing similar quality drawings in terms of quality metrics (neighborhood preservation, stress, edge crossing, and shape-based metrics) and visual comparison. We also present a comparison between our algorithms and DRGraph, another dimension reduction-based graph drawing algorithm.

cs.DS↗

arXiv2025

Planar Stories of Graph Drawings: Algorithms and Experiments

We address the problem of computing a dynamic visualization of a geometric graph $G$ as a sequence of frames. Each frame shows only a portion of the graph but their union covers $G$ entirely. The two main requirements of our dynamic visualization are: $(i)$ guaranteeing drawing stability, so to preserve the user's mental map; $(ii)$ keeping the visual complexity of each frame low. To satisfy the first requirement, we never change the position of the vertices. Regarding the second requirement, we avoid edge crossings in each frame. More precisely, in the first frame we visualize a suitable subset of non-crossing edges; in each subsequent frame, exactly one new edge enters the visualization and all the edges that cross with it are deleted. We call such a sequence of frames a planar story of $G$. Our goal is to find a planar story whose minimum number of edges contemporarily displayed is maximized (i.e., a planar story that maximizes the minimum frame size). Besides studying our model from a theoretical point of view, we also design and experimentally compare different algorithms, both exact techniques and heuristics. These algorithms provide an array of alternative trade-offs between efficiency and effectiveness, also depending on the structure of the input graph.

cs.CG↗

arXiv2024

GraphTrials: Visual Proofs of Graph Properties

Graph and network visualization supports exploration, analysis and communication of relational data arising in many domains: from biological and social networks, to transportation and powergrid systems. With the arrival of AI-based question-answering tools, issues of trustworthiness and explainability of generated answers motivate a greater role for visualization. In the context of graphs, we see the need for visualizations that can convince a critical audience that an assertion about the graph under analysis is valid. The requirements for such representations that convey precisely one specific graph property are quite different from standard network visualization criteria which optimize general aesthetics and readability. In this paper, we aim to provide a comprehensive introduction to visual proofs of graph properties and a foundation for further research in the area. We present a framework that defines what it means to visually prove a graph property. In the process, we introduce the notion of a visual certificate, that is, a specialized faithful graph visualization that leverages the viewer's perception, in particular, pre-attentive processing (e.g. via pop-out effects), to verify a given assertion about the represented graph. We also discuss the relationships between visual complexity, cognitive load and complexity theory, and propose a classification based on visual proof complexity. Finally, we provide examples of visual certificates for problems in different visual proof complexity classes.

cs.HC↗

arXiv2024

The Price of Upwardness

Not every directed acyclic graph (DAG) whose underlying undirected graph is planar admits an upward planar drawing. We are interested in pushing the notion of upward drawings beyond planarity by considering upward $k$-planar drawings of DAGs in which the edges are monotonically increasing in a common direction and every edge is crossed at most $k$ times for some integer $k \ge 1$. We show that the number of crossings per edge in a monotone drawing is in general unbounded for the class of bipartite outerplanar, cubic, or bounded pathwidth DAGs. However, it is at most two for outerpaths and it is at most quadratic in the bandwidth in general. From the computational point of view, we prove that testing upward-$k$-planarity is NP-complete already for $k=1$ and even for restricted instances for which upward planarity testing is polynomial. On the positive side, we can decide in linear time whether a single-source DAG admits an upward 1-planar drawing in which all vertices are incident to the outer face.

cs.CG↗

arXiv2024

Min-$k$-planar Drawings of Graphs

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 $k$-planar drawings $(k \geq 1)$, where each edge cannot cross more than $k$ times. We generalize $k$-planar drawings, by introducing the new family of min-$k$-planar drawings. In a min-$k$-planar drawing edges can cross an arbitrary number of times, but for any two crossing edges, one of the two must have no more than $k$ crossings. We prove a general upper bound on the number of edges of min-$k$-planar drawings, a finer upper bound for $k=3$, and tight upper bounds for $k=1,2$. Also, we study the inclusion relations between min-$k$-planar graphs (i.e., graphs admitting min-$k$-planar drawings) and $k$-planar graphs. In our setting we only allow simple drawings, that is, any two edges cross at most once, no two adjacent edges cross, and no three edges intersect at a common crossing point.

cs.CG↗

arXiv2022

Mask Off: Analytic-based Malware Detection By Transfer Learning and Model Personalization

The vulnerability of smartphones to cyberattacks has been a severe concern to users arising from the integrity of installed applications (\textit{apps}). Although applications are to provide legitimate and diversified on-the-go services, harmful and dangerous ones have also uncovered the feasible way to penetrate smartphones for malicious behaviors. Thorough application analysis is key to revealing malicious intent and providing more insights into the application behavior for security risk assessments. Such in-depth analysis motivates employing deep neural networks (DNNs) for a set of features and patterns extracted from applications to facilitate detecting potentially dangerous applications independently. This paper presents an Analytic-based deep neural network, Android Malware detection (ADAM), that employs a fine-grained set of features to train feature-specific DNNs to have consensus on the application labels when their ground truth is unknown. In addition, ADAM leverages the transfer learning technique to obtain its adjustability to new applications across smartphones for recycling the pre-trained model(s) and making them more adaptable by model personalization and federated learning techniques. This adjustability is also assisted by federated learning guards, which protect ADAM against poisoning attacks through model analysis. ADAM relies on a diverse dataset containing more than 153000 applications with over 41000 extracted features for DNNs training. The ADAM's feature-specific DNNs, on average, achieved more than 98% accuracy, resulting in an outstanding performance against data manipulation attacks.

cs.CR↗

arXiv2022

Shape-Faithful Graph Drawings

Shape-based metrics measure how faithfully a drawing D represents the structure of a graph G, using the proximity graph S of D. While some limited graph classes admit proximity drawings (i.e., optimally shape-faithful drawings, where S = G), algorithms for shape-faithful drawings of general graphs have not been investigated. In this paper, we present the first study for shape-faithful drawings of general graphs. First, we conduct extensive comparison experiments for popular graph layouts using the shape-based metrics, and examine the properties of highly shape-faithful drawings. Then, we present ShFR and ShSM, algorithms for shape-faithful drawings based on force-directed and stress-based algorithms, by introducing new proximity forces/stress. Experiments show that ShFR and ShSM obtain significant improvement over FR (Fruchterman-Reingold) and SM (Stress Majorization), on average 12% and 35% respectively, on shape-based metrics.

cs.DS↗

arXiv2021

A Machine Learning Approach for Predicting Human Preference for Graph Layouts

Understanding what graph layout human prefer and why they prefer is significant and challenging due to the highly complex visual perception and cognition system in human brain. In this paper, we present the first machine learning approach for predicting human preference for graph layouts. In general, the data sets with human preference labels are limited and insufficient for training deep networks. To address this, we train our deep learning model by employing the transfer learning method, e.g., exploiting the quality metrics, such as shape-based metrics, edge crossing and stress, which are shown to be correlated to human preference on graph layouts. Experimental results using the ground truth human preference data sets show that our model can successfully predict human preference for graph layouts. To our best knowledge, this is the first approach for predicting qualitative evaluation of graph layouts using human preference experiment data.

cs.HC↗

arXiv2020

New Quality Metrics for Dynamic Graph Drawing

In this paper, we present new quality metrics for dynamic graph drawings. Namely, we present a new framework for change faithfulness metrics for dynamic graph drawings, which compare the ground truth change in dynamic graphs and the geometric change in drawings. More specifically, we present two specific instances, cluster change faithfulness metrics and distance change faithfulness metrics. We first validate the effectiveness of our new metrics using deformation experiments. Then we compare various graph drawing algorithms using our metrics. Our experiments confirm that the best cluster (resp. distance) faithful graph drawing algorithms are also cluster (resp. distance) change faithful.

cs.DS↗

arXiv2019

Packing Trees into 1-planar Graphs

We introduce and study the 1-planar packing problem: Given $k$ graphs with $n$ vertices $G_1, \dots, G_k$, find a 1-planar graph that contains the given graphs as edge-disjoint spanning subgraphs. We mainly focus on the case when each $G_i$ is a tree and $k=3$. We prove that a triple consisting of three caterpillars or of two caterpillars and a path may not admit a 1-planar packing, while two paths and a special type of caterpillar always have one. We then study 1-planar packings with few crossings and prove that three paths (resp. cycles) admit a 1-planar packing with at most seven (resp. fourteen) crossings. We finally show that a quadruple consisting of three paths and a perfect matching with $n \geq 12$ vertices admits a 1-planar packing, while such a packing does not exist if $n \leq 10$.

cs.CG↗

arXiv2019

A Quality Metric for Symmetric Graph Drawings

Symmetry is an important aesthetic criteria in graph drawing and network visualisation. Symmetric graph drawings aim to faithfully represent automorphisms of graphs as geometric symmetries in a drawing. In this paper, we design and implement a framework for quality metrics that measure symmetry, that is, how faithfully a drawing of a graph displays automorphisms as geometric symmetries. The quality metrics are based on geometry (i.e. Euclidean distance) as well as mathematical group theory (i.e. orbits of automorphisms). More specifically, we define two varieties of symmetry quality metrics: (1) for displaying a single automorphism as a symmetry (axial or rotational) and (2) for displaying a group of automorphisms (cyclic or dihedral). We also present algorithms to compute the symmetric quality metrics in O(n log n) time for rotational symmetry and axial symmetry. We validate our symmetry quality metrics using deformation experiments. We then use the metrics to evaluate a number of established graph drawing layouts to compare how faithfully they display automorphisms of a graph as geometric symmetries.

cs.DS↗

arXiv2019

Multi-level Graph Drawing using Infomap Clustering

Infomap clustering finds the community structures that minimize the expected description length of a random walk trajectory; algorithms for infomap clustering run fast in practice for large graphs. In this paper we leverage the effectiveness of Infomap clustering combined with the multi-level graph drawing paradigm. Experiments show that our new Infomap based multi-level algorithm produces good visualization of large and complex networks, with significant improvement in quality metrics.

cs.DS↗

arXiv2019

A Quality Metric for Visualization of Clusters in Graphs

Traditionally, graph quality metrics focus on readability, but recent studies show the need for metrics which are more specific to the discovery of patterns in graphs. Cluster analysis is a popular task within graph analysis, yet there is no metric yet explicitly quantifying how well a drawing of a graph represents its cluster structure. We define a clustering quality metric measuring how well a node-link drawing of a graph represents the clusters contained in the graph. Experiments with deforming graph drawings verify that our metric effectively captures variations in the visual cluster quality of graph drawings. We then use our metric to examine how well different graph drawing algorithms visualize cluster structures in various graphs; the results con-firm that some algorithms which have been specifically designed to show cluster structures perform better than other algorithms.

cs.DS↗

arXiv2019

Gap-planar Graphs

We introduce the family of $k$-gap-planar graphs for $k \geq 0$, i.e., graphs that have a drawing in which each crossing is assigned to one of the two involved edges and each edge is assigned at most $k$ of its crossings. This definition is motivated by applications in edge casing, as a $k$-gap-planar graph can be drawn crossing-free after introducing at most $k$ local gaps per edge. We present results on the maximum density of $k$-gap-planar graphs, their relationship to other classes of beyond-planar graphs, characterization of $k$-gap-planar complete graphs, and the computational complexity of recognizing $k$-gap-planar graphs.

cs.CG↗

arXiv2018

Turning Cliques into Paths to Achieve Planarity

Motivated by hybrid graph representations, we introduce and study the following beyond-planarity problem, which we call $h$-Clique2Path Planarity: Given a graph $G$, whose vertices are partitioned into subsets of size at most $h$, each inducing a clique, remove edges from each clique so that the subgraph induced by each subset is a path, in such a way that the resulting subgraph of $G$ is planar. We study this problem when $G$ is a simple topological graph, and establish its complexity in relation to $k$-planarity. We prove that $h$-Clique2Path Planarity is NP-complete even when $h=4$ and $G$ is a simple $3$-plane graph, while it can be solved in linear time, for any $h$, when $G$ is $1$-plane.

cs.DS↗