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In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match to the given sequence. This realization problem is known to be polynomial-time solvable when the…

Computational Complexity · Computer Science 2012-01-18 Sepp Hartung , André Nichterlein

Due to data compression or low resolution, nearby vertices and edges of a graph drawing may be bundled to a common node or arc. We model such a `compromised' drawing by a piecewise linear map $\varphi:G\rightarrow \mathbb{R}^2$. We wish to…

Computational Geometry · Computer Science 2018-08-24 Radoslav Fulek , Csaba D. Tóth

Algorithmic extension problems of partial graph representations such as planar graph drawings or geometric intersection representations are of growing interest in topological graph theory and graph drawing. In such an extension problem, we…

Data Structures and Algorithms · Computer Science 2020-04-28 Eduard Eiben , Robert Ganian , Thekla Hamm , Fabian Klute , Martin Nöllenburg

Graphs provide a natural representation of relational structure that arises across diverse domains. Despite this ubiquity, graph structure is typically learned in a modality- and task-isolated manner, where graph representations are…

Machine Learning · Computer Science 2026-05-27 Ziming Li , Xiaoming Wu , Zehong Wang , Jiazheng Li , Yijun Tian , Jinhe Bi , Yunpu Ma , Yanfang Ye , Chuxu Zhang

Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…

Computational Geometry · Computer Science 2009-08-28 David Eppstein

The adoption of "human-in-the-loop" paradigms in computer vision and machine learning is leading to various applications where the actual data acquisition (e.g., human supervision) and the underlying inference algorithms are closely…

Computer Vision and Pattern Recognition · Computer Science 2020-08-13 Won Hwa Kim , Mona Jalal , Seongjae Hwang , Sterling C. Johnson , Vikas Singh

Given a map $\mathcal M$ on a connected and closed orientable surface, the delta-matroid of $\mathcal M$ is a combinatorial object associated to $\mathcal M$ which captures some topological information of the embedding. We explore how…

Combinatorics · Mathematics 2015-08-31 Goran Malić

In this paper, we study linear programming based approaches to the maximum matching problem in the semi-streaming model. The semi-streaming model has gained attention as a model for processing massive graphs as the importance of such graphs…

Data Structures and Algorithms · Computer Science 2015-03-19 Kook Jin Ahn , Sudipto Guha

In this paper, we introduce and study the multilevel-planarity testing problem, which is a generalization of upward planarity and level planarity. Let $G = (V, E)$ be a directed graph and let $\ell: V \to \mathcal P(\mathbb Z)$ be a…

Data Structures and Algorithms · Computer Science 2018-11-01 Lukas Barth , Guido Brückner , Paul Jungeblut , Marcel Radermacher

Deep Recurrent Neural Network architectures, though remarkably capable at modeling sequences, lack an intuitive high-level spatio-temporal structure. That is while many problems in computer vision inherently have an underlying high-level…

Computer Vision and Pattern Recognition · Computer Science 2016-04-12 Ashesh Jain , Amir R. Zamir , Silvio Savarese , Ashutosh Saxena

Graphs are mathematical tools that can be used to represent complex real-world systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently. However, it has…

Machine Learning · Computer Science 2023-03-22 O. Deniz Kose , Yanning Shen , Gonzalo Mateos

Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…

Machine Learning · Computer Science 2019-03-08 Qi Liu , Miltiadis Allamanis , Marc Brockschmidt , Alexander L. Gaunt

Using graphs to model irregular information domains is an effective approach to deal with some of the intricacies of contemporary (network) data. A key aspect is how the data, represented as graph signals, depend on the topology of the…

Signal Processing · Electrical Eng. & Systems 2023-05-02 Fernando J. Iglesias Garcia , Santiago Segarra , Antonio G. Marques

In this paper, we define and study the new problem Simultaneous PQ-Ordering. Its input consists of a set of PQ-trees, which represent sets of circular orders of their leaves, together with a set of child-parent relations between these…

Data Structures and Algorithms · Computer Science 2011-12-02 Thomas Bläsius , Ignaz Rutter

A recent line of research has concentrated on exploring the links between analytic and combinatorial theories of submodularity, uncovering several key connections between them. In this context, Lov\'asz initiated the study of matroids from…

Combinatorics · Mathematics 2024-10-16 Kristóf Bérczi , Márton Borbényi , László Lovász , László Márton Tóth

Graphs serve as fundamental descriptors for systems composed of interacting elements, capturing a wide array of data types, from molecular interactions to social networks and knowledge graphs. In this paper, we present an exhaustive review…

Machine Learning · Computer Science 2024-11-13 Chenqing Hua

Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…

Computer Vision and Pattern Recognition · Computer Science 2020-12-01 Runzhong Wang , Junchi Yan , Xiaokang Yang

We introduce a new class of matroids, called graph curve matroids. A graph curve matroid is associated to a graph and defined on the vertices of the graph as a ground set. We prove that these matroids provide a combinatorial description of…

Combinatorics · Mathematics 2024-08-06 Alheydis Geiger , Kevin Kuehn , Raluca Vlad

Graph-based semi-supervised learning usually involves two separate stages, constructing an affinity graph and then propagating labels for transductive inference on the graph. It is suboptimal to solve them independently, as the correlation…

Computer Vision and Pattern Recognition · Computer Science 2019-02-19 Qilin Li , Senjian An , Ling Li , Wanquan Liu

Molecular graphs generally contain subgraphs (known as groups) that are identifiable and significant in composition, functionality, geometry, etc. Flat latent representations (node embeddings or graph embeddings) fail to represent, and…

Machine Learning · Computer Science 2019-04-05 Daniel T. Chang