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In this paper, we consider the following \emph{$k$-many firefighter problem} on a finite graph $G=(V,E)$. Suppose that a fire breaks out at a given vertex $v \in V$. In each subsequent time unit, a firefighter protects $k$ vertices which…
Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods,…
We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A \subseteq…
We propose the conjecture that every graph $G$ of order $n$ with less than $3n-6$ edges has a vertex cut that induces a forest. Maximal planar graphs do not have such vertex cuts and show that the density condition would be best possible.…
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…
Graph-modification problems, where we modify a graph by adding or deleting vertices or edges or contracting edges to obtain a graph in a {\it simpler} class, is a well-studied optimization problem in all algorithmic paradigms including…
Predicting the extent of massive wildfires once ignited is essential to reduce the subsequent socioeconomic losses and environmental damage, but challenging because of the complexity of fire behaviour. Existing physics-based models are…
Can we efficiently compute optimal solutions to instances of a hard problem from optimal solutions to neighboring (i.e., locally modified) instances? For example, can we efficiently compute an optimal coloring for a graph from optimal…
Wildfire forecasting problems usually rely on complex grid-based mathematical models, mostly involving Computational fluid dynamics(CFD) and Celluar Automata, but these methods have always been computationally expensive and difficult to…
The increasing frequency and severity of wildfires highlight the need for accurate fire and plume spread models. We introduce an approach that effectively isolates and tracks fire and plume behavior across various spatial and temporal…
We study the problem of aggregating polygons by covering them with disjoint representative regions, thereby inducing a clustering of the polygons. Our objective is to minimize a weighted sum of the total area and the total perimeter of the…
Wildfire risk poses a growing challenge for electric utilities, as powerline failures can ignite wildfires while large fires can disrupt grid operations. Utilities increasingly rely on operational interventions such as Public Safety Power…
Graph burning models the spread of information or contagion in a graph. At each time step, two events occur: neighbours of already burned vertices become burned, and a new vertex is chosen to be burned. The big conjecture is known as the…
The complexity of a reasoning task over a graphical model is tied to the induced width of the underlying graph. It is well-known that the conditioning (assigning values) on a subset of variables yields a subproblem of the reduced complexity…
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…
Wildfires can severely damage electricity grids leading to long periods of power interruption. Climate change will exacerbate this threat by increasing the frequency of dry climate conditions. Under these climate conditions, human-related…
The concept of graph burning and burning number ($bn(G)$) of a graph G was introduced recently [1]. Graph burning models the spread of contagion (fire) in a graph in discrete time steps. $bn(G)$ is the minimum time needed to burn a graph…
Successful development of wind farms relies on the optimal siting of wind turbines to maximize the power capacity under stochastic wind conditions and wake losses caused by neighboring turbines. This paper presents a novel method to quickly…
Experimental data on the propagation of wildfires show that its short-time spread has a double semi-elliptical shape. Our main goal is to show that this shape can be accurately approximated in polar coordinates by choosing suitable…
We combine two methods for the lossless compression of unlabeled graphs - entropy compressing adjacency lists and computing canonical names for vertices - and solve an ensuing novel optimisation problem: Minimum-Entropy Tree-Extraction…