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Graph embeddings deal with injective maps from a given simple, undirected graph $G=(V,E)$ into a metric space, such as $\mathbb{R}^n$ with the Euclidean metric. This concept is widely studied in computer science, see \cite{ge1}, but also…

Combinatorics · Mathematics 2022-05-04 Dominic van der Zypen

We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-02-09 Matteo Ceccarello , Andrea Pietracaprina , Geppino Pucci , Eli Upfal

Recent studies have experimentally shown that we can achieve in non-Euclidean metric space effective and efficient graph embedding, which aims to obtain the vertices' representations reflecting the graph's structure in the metric space.…

Machine Learning · Statistics 2023-05-16 Atsushi Suzuki , Atsushi Nitanda , Taiji Suzuki , Jing Wang , Feng Tian , Kenji Yamanishi

Unit disk graphs are the set of graphs which represent the intersection of disk graphs and interval graphs. These graphs are of great importance due to their structural similarity with wireless communication networks. Firefighter problem on…

Data Structures and Algorithms · Computer Science 2022-03-30 Diptendu Chatterjee , Rishiraj Bhattacharyya

In the area of beyond-planar graphs, i.e. graphs that can be drawn with some local restrictions on the edge crossings, the recognition problem is prominent next to the density question for the different graph classes. For 1-planar graphs,…

Data Structures and Algorithms · Computer Science 2021-08-04 Henry Förster , Michael Kaufmann , Chrysanthi N. Raftopoulou

Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…

Computational Complexity · Computer Science 2025-12-01 Michal Čertík , Andreas Emil Feldmann , Jaroslav Nešetřil , Paweł Rzążewski

In 1999, Heath, Pemmaraju, and Trenk [SIAM J. Comput. 28(4), 1999] extended the classic notion of book embeddings to digraphs, introducing the concept of upward book embeddings, in which the vertices must appear along the spine in a…

Data Structures and Algorithms · Computer Science 2026-03-19 Giordano Da Lozzo , Fabrizio Frati , Ignaz Rutter

An undirected graph is Eulerian if it is connected and all its vertices are of even degree. Similarly, a directed graph is Eulerian, if for each vertex its in-degree is equal to its out-degree. It is well known that Eulerian graphs can be…

Data Structures and Algorithms · Computer Science 2013-04-23 Fedor V. Fomin , Petr A. Golovach

An \emph{s-graph} is a graph with two kinds of edges: \emph{subdivisible} edges and \emph{real} edges. A \emph{realisation} of an s-graph $B$ is any graph obtained by subdividing subdivisible edges of $B$ into paths of arbitrary length (at…

Discrete Mathematics · Computer Science 2013-09-05 Benjamin Lévêque , David Y. Lin , Frédéric Maffray , Nicolas Trotignon

The unit distance embeddability of a graph, like planarity, involves a mix of constraints that are combinatorial and geometric. We construct a unit distance embedding for $H-e$ in the hope that it will lead to an embedding for $H$. We then…

Combinatorics · Mathematics 2007-11-08 Mitchell A. Harris

In the 70s, Berge introduced 1-extendable graphs (also called B-graphs), which are graphs where every vertex belongs to a maximum independent set. Motivated by an application in the design of wireless networks, we study the computational…

Computational Complexity · Computer Science 2022-04-13 Pierre Bergé , Anthony Busson , Carl Feghali , Rémi Watrigant

A disk graph is an intersection graph of disks in the Euclidean plane, where the disks correspond to the vertices of the graph and a pair of vertices are adjacent if and only if their corresponding disks intersect. The problem of…

Computational Geometry · Computer Science 2023-03-15 Jared Espenant , J. Mark Keil , Debajyoti Mondal

Subgraph matching is the problem of determining the presence and location(s) of a given query graph in a large target graph. Despite being an NP-complete problem, the subgraph matching problem is crucial in domains ranging from network…

Machine Learning · Computer Science 2020-10-28 Rex , Ying , Zhaoyu Lou , Jiaxuan You , Chengtao Wen , Arquimedes Canedo , Jure Leskovec

We investigate a fundamental vertex-deletion problem called (Induced) Subgraph Hitting: given a graph $G$ and a set $\mathcal{F}$ of forbidden graphs, the goal is to compute a minimum-sized set $S$ of vertices of $G$ such that $G-S$ does…

Data Structures and Algorithms · Computer Science 2023-12-05 Zdeněk Dvořák , Daniel Lokshtanov , Fahad Panolan , Saket Saurabh , Jie Xue , Meirav Zehavi

Fan-planar graphs were recently introduced as a generalization of 1-planar graphs. A graph is fan-planar if it can be embedded in the plane, such that each edge that is crossed more than once, is crossed by a bundle of two or more edges…

Computational Geometry · Computer Science 2014-09-02 Michael A. Bekos , Sabine Cornelsen , Luca Grilli , Seok-Hee Hong , Michael Kaufmann

Although there are very algorithms for embedding graphs on unbounded grids, only few results on embedding or drawing graphs on restricted grids has been published. In this work, we consider the problem of embedding paths and cycles on grid…

Discrete Mathematics · Computer Science 2014-10-10 Asghar Asgharian Sardroud , Alireza Bagheri

Given a set of $n$ points in the plane, the Unit Disk Cover (UDC) problem asks to compute the minimum number of unit disks required to cover the points, along with a placement of the disks. The problem is NP-hard and several approximation…

Computational Geometry · Computer Science 2022-05-05 Rachel Friederich , Matthew Graham , Anirban Ghosh , Brian Hicks , Ronald Shevchenko

In recent years several compressed indexes based on variants of the Burrows-Wheeler transformation have been introduced. Some of these index structures far more complex than a single string, as was originally done with the FM-index…

Computational Complexity · Computer Science 2019-02-27 Daniel Gibney , Sharma V. Thankachan

Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…

Machine Learning · Computer Science 2023-11-30 Andrea Marinoni , Pietro Lio' , Alessandro Barp , Christian Jutten , Mark Girolami

Graph similarity computation is one of the core operations in many graph-based applications, such as graph similarity search, graph database analysis, graph clustering, etc. Since computing the exact distance/similarity between two graphs…

Machine Learning · Computer Science 2021-05-18 Yunsheng Bai , Hao Ding , Yizhou Sun , Wei Wang