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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…
Climate change is intensifying wildfire risks globally, making reliable forecasting critical for adaptation strategies. While machine learning shows promise for wildfire prediction from Earth observation data, current approaches lack…
One of the most elementary spreading models on graphs can be described by a fire spreading from a burning vertex in discrete time steps. At each step, all neighbors of burning vertices catch fire. A well-studied extension to model fire…
This paper examines the use of risk models to predict the timing and location of wildfires caused by electricity infrastructure. Our data include historical ignition and wire-down points triggered by grid infrastructure collected between…
We consider a deterministic discrete-time model of fire spread introduced by Hartnell [1995] and the problem of minimizing the number of burnt vertices when deploying a limited number of firefighters per timestep. We consider the process…
We study the problem of evacuation planning for natural disasters, focusing on wildfire evacuations. By creating pre-planned evacuation routes that can be updated based on real-time data, we provide an easily adjustable approach to…
Graph burning is a discrete-time process on graphs, where vertices are sequentially burned, and burned vertices cause their neighbours to burn over time. We consider extremal properties of this process in the new setting where the…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
Graph burning studies how fast a contagion, modeled as a set of fires, spreads in a graph. The burning process takes place in synchronous, discrete rounds. In each round, a fire breaks out at a vertex, and the fire spreads to all vertices…
We study a large family of graph covering problems, whose definitions rely on distances, for graphs of bounded cyclomatic number (that is, the minimum number of edges that need to be removed from the graph to destroy all cycles). These…
We consider straight line drawings of a planar graph $G$ with possible edge crossings. The \emph{untangling problem} is to eliminate all edge crossings by moving as few vertices as possible to new positions. Let $fix(G)$ denote the maximum…
Graph burning is a process of information spreading through the network by an agent in discrete steps. The problem is to find an optimal sequence of nodes which have to be given information so that the network is covered in least number of…
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…
The problem of inferring unknown graph edges from numerical data at a graph's nodes appears in many forms across machine learning. We study a version of this problem that arises in the field of \emph{landscape genetics}, where genetic…
Electric utilities are struggling to manage increasing wildfire risk in a hotter and drier climate. Utility transmission and distribution lines regularly ignite destructive fires when they make contact with surrounding vegetation. Trimming…
The Burning Number Conjecture, that a graph on $n$ vertices can be burned in at most $\lceil \sqrt{n} \ \rceil$ rounds, has been of central interest for the past several years. Much of the literature toward its resolution focuses on two…
In 2016, Bonato, Janssen, and Roshanbin introduced graph burning as a discrete process that models the spread of social contagion. Although the burning process is a simple algorithm, the problem of determining the least number of rounds…
Convolutional Neural Networks (CNNs) have proven instrumental across various computer science domains, enabling advancements in object detection, classification, and anomaly detection. This paper explores the application of CNNs to analyze…
The paper studies a dynamic blocking problem, motivated by a model of optimal fire confinement. While the fire can expand with unit speed in all directions, barriers are constructed in real time. An optimal strategy is sought, minimizing…
With climate change intensifying fire weather conditions globally, accurate seasonal wildfire forecasting has become critical for disaster preparedness and ecosystem management. We introduce FireCastNet, a novel deep learning architecture…