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Related papers: Simultaneous Embedding of Planar Graphs

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In this paper, we introduce a method called graph fusion embedding, designed for multi-graph embedding with shared vertex sets. Under the framework of supervised learning, our method exhibits a remarkable and highly desirable synergistic…

Social and Information Networks · Computer Science 2024-06-27 Cencheng Shen , Carey E. Priebe , Jonathan Larson , Ha Trinh

Mining graph data has become a popular research topic in computer science and has been widely studied in both academia and industry given the increasing amount of network data in the recent years. However, the huge amount of network data…

Machine Learning · Computer Science 2020-01-03 Wenwu Zhu , Xin Wang , Peng Cui

Simultaneous Embedding with Fixed Edges (SEFE) is a problem where given $k$ planar graphs we ask whether they can be simultaneously embedded so that the embedding of each graph is planar and common edges are drawn the same. Problems of SEFE…

Discrete Mathematics · Computer Science 2017-12-04 Matěj Konečný , Stanislav Kučera , Jana Novotná , Jakub Pekárek , Martin Smolík , Jakub Tětek , Martin Töpfer

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 2014-01-20 Brian Baingana , Georgios B. Giannakis

One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a graph…

Combinatorics · Mathematics 2019-11-19 A. Arul Shantrinal , R. Sundara Rajan , A. Ramesh Babu , S. Anil , Mohammed Ali Ahmed

Graph representation learning plays an important role in many graph mining applications, but learning embeddings of large-scale graphs remains a problem. Recent works try to improve scalability via graph summarization -- i.e., they learn…

Machine Learning · Computer Science 2022-07-05 Houquan Zhou , Shenghua Liu , Danai Koutra , Huawei Shen , Xueqi Cheng

In this paper, we introduce and study "geometric simultaneous RAC drawing problems", i.e., a combination of problems on geometric RAC drawings and geometric simultaneous graph drawings. To the best of our knowledge, this is the first time…

Data Structures and Algorithms · Computer Science 2011-06-15 Evmorfia N. Argyriou , Michael A. Bekos , Michael Kaufmann , Antonios Symvonis

Heterogeneous graphs (HGs) also known as heterogeneous information networks have become ubiquitous in real-world scenarios; therefore, HG embedding, which aims to learn representations in a lower-dimension space while preserving the…

Social and Information Networks · Computer Science 2020-12-02 Xiao Wang , Deyu Bo , Chuan Shi , Shaohua Fan , Yanfang Ye , Philip S. Yu

Graph drawing research traditionally focuses on producing geometric embeddings of graphs satisfying various aesthetic constraints. After the geometric embedding is specified, there is an additional step that is often overlooked or ignored:…

Computational Geometry · Computer Science 2007-05-23 Michael B. Dillencourt , David Eppstein , Michael T. Goodrich

A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. Almost embeddings (more precisely, their higher-dimensional analogues) naturally appear in…

Geometric Topology · Mathematics 2026-03-10 E. Alkin , A. Miroshnikov , A. Skopenkov

A (possibly denerate) drawing of a graph $G$ in the plane is approximable by an embedding if it can be turned into an embedding by an arbitrarily small perturbation. We show that testing, whether a straight-line drawing of a planar graph…

Computational Geometry · Computer Science 2017-05-09 Radoslav Fulek

We discuss problems of simultaneous tiling. This means that we have an object (set, function) which tiles space with two or more different sets of translations. The most famous problem of this type is the Steinhaus problem which asks for a…

Classical Analysis and ODEs · Mathematics 2022-08-05 Mihail N. Kolountzakis

Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…

Social and Information Networks · Computer Science 2021-12-02 Bogumił Kamiński , Łukasz Kraiński , Paweł Prałat , François Théberge

Neural embedding approaches have become a staple in the fields of computer vision, natural language processing, and more recently, graph analytics. Given the pervasive nature of these algorithms, the natural question becomes how to exploit…

Computation and Language · Computer Science 2020-10-27 Alexander Kalinowski , Yuan An

We study monotone simultaneous embeddings of upward planar digraphs, which are simultaneous embeddings where the drawing of each digraph is upward planar, and the directions of the upwardness of different graphs can differ. We first…

Computational Geometry · Computer Science 2014-03-03 Oswin Aichholzer , Thomas Hackl , Sarah Lutteropp , Tamara Mchedlidze , Alexander Pilz , Birgit Vogtenhuber

Graph embedding techniques have attracted growing interest since they convert the graph data into continuous and low-dimensional space. Effective graph analytic provides users a deeper understanding of what is behind the data and thus can…

Machine Learning · Computer Science 2022-01-21 Azita Nouri , Philip E. Davis , Pradeep Subedi , Manish Parashar

Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…

Machine Learning · Statistics 2022-02-03 Francesco Di Giovanni , Giulia Luise , Michael Bronstein

This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…

Combinatorics · Mathematics 2007-05-23 Sostenes Lins

Graphs are a useful abstraction of image content. Not only can graphs represent details about individual objects in a scene but they can capture the interactions between pairs of objects. We present a method for training a convolutional…

Computer Vision and Pattern Recognition · Computer Science 2018-03-28 Alejandro Newell , Jia Deng

Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. The quality of the embeddings is usually determined by how well the geometry…

Machine Learning · Computer Science 2021-05-13 Federico López , Beatrice Pozzetti , Steve Trettel , Anna Wienhard