Related papers: Approximation Algorithms for Graph Burning
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…
We study spreading processes in temporal graphs, i. e., graphs whose connections change over time. These processes naturally model real-world phenomena such as infectious diseases or information flows. More precisely, we investigate how…
The burning number of a graph can be used to measure the spreading speed of contagion in a network. The burning number conjecture is arguably the main unresolved conjecture related to this graph parameter, which can be settled by showing…
The burning number of a graph $G$ is the smallest positive integer $k$ such that the vertex set of $G$ can be covered with balls of radii $0, 1, \dots, k-1$. A well-known conjecture by Bonato, Janssen and Roshabin states that any connected…
Fake news on social media is increasingly regarded as one of the most concerning issues. Low cost, simple accessibility via social platforms, and a plethora of low-budget online news sources are some of the factors that contribute to the…
The Firefighter problem is to place firefighters on the vertices of a graph to prevent a fire with known starting point from lighting up the entire graph. In each time step, a firefighter may be permanently placed on an unburned vertex and…
This work introduces two techniques for the design and analysis of branching algorithms, illustrated through the case study of the Vertex Cover problem. First, we present a method for automatically generating branching rules through a…
Graph similarity search is among the most important graph-based applications, e.g. finding the chemical compounds that are most similar to a query compound. Graph similarity computation, such as Graph Edit Distance (GED) and Maximum Common…
Wildfire forecasting is notoriously hard due to the complex interplay of different factors such as weather conditions, vegetation types and human activities. Deep learning models show promise in dealing with this complexity by learning…
Let $G$ be any connected graph on $n$ vertices, $n \ge 2.$ Let $k$ be any positive integer. Suppose that a fire breaks out on some vertex of $G.$ Then in each turn $k$ firefighters can protect vertices of $G$ --- each can protect one vertex…
In this paper, we study a graph parameter that was recently introduced, the burning number, focusing on a few probabilistic aspects of the problem. The original burning number is revisited and analyzed for binomial random graphs G(n,p),…
The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, information retrieval and many other areas related to the World Wide Web. There exist several algorithms for the problem with…
Graph coloring is a fundamental problem in combinatorics with many applications in practice. In this problem, the vertices in a given graph must be colored by using the least number of colors in such a way that a vertex has a different…
The shortest path problem is among the most fundamental combinatorial optimization problems to answer reachability queries. It is hard to deter-mine which vertices or edges are visited during shortest path traversals. In this paper, we…
Exploring unknown environments is a fundamental task in many domains, e.g., robot navigation, network security, and internet search. We initiate the study of a learning-augmented variant of the classical, notoriously hard online graph…
The study of networks has received increased attention recently not only from the social sciences and statistics but also from physicists, computer scientists and mathematicians. One of the principal problem in networks is community…
Graph neural networks (GNNs) are widely used for learning node embeddings in graphs, typically adopting a message-passing scheme. This approach, however, leads to the neighbor explosion problem, with exponentially growing computational and…
Analyzing large graph data is an essential part of many modern applications, such as social networks. Due to its large computational complexity, distributed processing is frequently employed. This requires graph data to be divided across…
Graph coloring, also known as vertex coloring, considers the problem of assigning colors to the nodes of a graph such that adjacent nodes do not share the same color. The optimization version of the problem concerns the minimization of the…
Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks.…