Related papers: Approximation Algorithms for Graph Burning
Spreading processes on graphs are a natural model for a wide variety of real-world phenomena, including information spread over social networks and biological diseases spreading over contact networks. Often, the networks over which these…
Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…
We consider the problem of covering a graph with a given number of induced subgraphs so that the maximum number of vertices in each subgraph is minimized. We prove NP-completeness of the problem, prove lower bounds, and give approximation…
The asynchronous rumor algorithm spreading propagates a piece of information, the so-called rumor, in a network. Starting with a single informed node, each node is associated with an exponential time clock with rate $1$ and calls a random…
The firefighter problem is a monotone dynamic process in graphs that can be viewed as modeling the use of a limited supply of vaccinations to stop the spread of an epidemic. In more detail, a fire spreads through a graph, from burning…
The popularity of online social networks has enabled rapid dissemination of information. People now can share and consume information much more rapidly than ever before. However, low-quality and/or accidentally/deliberately fake information…
Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the…
Guiding users to actively expanding their online social circles is one of the primary strategies for enhancing user participation and growing online social networks. In this paper, we study the active friending problem which aims at…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class…
Combinatorial optimization problems near algorithmic phase transitions represent a fundamental challenge for both classical algorithms and machine learning approaches. Among them, graph coloring stands as a prototypical constraint…
We consider the propagation of a contagion process (epidemic) on a network and study the problem of dynamically allocating a fixed curing budget to the nodes of the graph, at each time instant. For bounded degree graphs, we provide a lower…
Given a social network represented by a graph $G$, we consider the problem of finding a bounded cardinality set of nodes $S$ with the property that the influence spreading from $S$ in $G$ is as large as possible. The dynamics that govern…
The problem of diffusion control on networks has been extensively studied, with applications ranging from marketing to controlling infectious disease. However, in many applications, such as cybersecurity, an attacker may want to attack a…
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The…
Given a directed graph $G = (V, E)$, the $k$-path partition problem is to find a minimum collection of vertex-disjoint directed paths each of order at most $k$ to cover all the vertices of $V$. The problem has various applications in…
Graph sparsification is a technique that approximates a given graph by a sparse graph with a subset of vertices and/or edges. The goal of an effective sparsification algorithm is to maintain specific graph properties relevant to the…
Graph coloring is fundamental to distributed computing. We give the first general treatment of the coloring of virtual graphs, where the graph $H$ to be colored is locally embedded within the communication graph $G$. Besides generalizing…
An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…
In the last decade, wildfires have become wider and more destructive. The climate change and the growth of urban areas may further increase the probability of incidence of large-scale fires. The risk of fire can be lowered with preventive…