Related papers: About the Infinite Windy Firebreak Location proble…
Given a graph $G = (V,E)$ with vertex weights $w(v)$ and a desired number of parts $k$, the goal in graph partitioning problems is to partition the vertex set V into parts $V_1,\ldots,V_k$. Metrics for compactness, contiguity, and balance…
Motivated by applications in network epidemiology, we consider the problem of determining whether it is possible to delete at most $k$ edges from a given input graph (of small treewidth) so that the resulting graph avoids a set…
Recent wildfires in Australia have led to considerable economic loss and property destruction, and there is increasing concern that climate change may exacerbate their intensity, duration, and frequency. Hazard quantification for extreme…
We study the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem aims at locating p facilities on the vertices (of the network) so as to maximise coverage, considering that the…
One of the impacts of climate change is the difficulty of tree regrowth after wildfires over areas that traditionally were covered by certain tree species. Here a deep learning model is customized to classify land covers from four-band…
The graph burning problem is an NP-hard combinatorial optimization problem that helps quantify the vulnerability of a graph to contagion. This paper introduces a simple farthest-first traversal-based approximation algorithm for this problem…
We consider random dynamics on the edges of a uniform Cayley tree with $n$ vertices, in which edges are either inflammable, fireproof, or burt. Every inflammable edge is replaced by a fireproof edge at unit rate, while fires start at…
In this paper, we introduce the problem of finding an orientation of a given undirected graph that maximizes the burning number of the resulting directed graph. We show that the problem is polynomial-time solvable on K\H{o}nig-Egerv\'{a}ry…
Over 8,024 wildfire incidents have been documented in 2024 alone, affecting thousands of fatalities and significant damage to infrastructure and ecosystems. Wildfires in the United States have inflicted devastating losses. Wildfires are…
In recent years, wildfires have posed a significant challenge due to their increasing frequency and severity. For this reason, accurate delineation of burned areas is crucial for environmental monitoring and post-fire assessment. However,…
Unmanned Aerial Vehicle (UAV) path planning algorithms often assume a knowledge reward function or priority map, indicating the most important areas to visit. In this paper we propose a method to create priority maps for monitoring or…
Given a graph $G=(V,E)$, the problem of \gb{} is to find a sequence of nodes from $V$, called burning sequence, in order to burn the whole graph. This is a discrete-step process, in each step an unburned vertex is selected as an agent to…
A two-dimensional model of wildfire spread and merger is presented. Three features affect the fire propagation: (i) a constant basic rate of spread term accounting for radiative and convective heat transfer, (ii) the unidirectional,…
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of…
This paper presents the development of a new continuous forest fire model implemented as a weighted local small-world network approach. This new approach was designed to simulate fire patterns in real, heterogeneous landscapes. The wildland…
In the matching interdiction problem, we are given an undirected graph with weights and interdiction costs on the edges and seek to remove a subset of the edges constrained to some budget, such that the weight of a maximum weight matching…
In recent years, the frequency and intensity of grid-ignited wildfires have increased significantly, leading to an elevated level of risk exposure to public safety and financial repercussions for electric utilities threatening their…
Due to recent climate changes, we have seen more frequent and severe wildfires in the United States. Predicting wildfires is critical for natural disaster prevention and mitigation. Advances in technologies in data processing and…
We define a range of new coarse geometric invariants based on various graph-theoretic measures of complexity for finite graphs, including: treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these…
We consider the problem of adding a fixed number of new edges to an undirected graph in order to minimize the diameter of the augmented graph, and under the constraint that the number of edges added for each vertex is bounded by an integer.…