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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…
The minimal dominating set for a digraph(directed graph)is a prototypical hard combinatorial optimization problem. In a previous paper, we studied this problem using the cavity method. Although we found a solution for a given graph that…
We study a network design problem motivated by the challenge of placing wildlife crossings to reconnect fragmented habitats of animal species, which is among the 17 goals towards sustainable development by the UN: Given a graph, whose…
In wildfires, burning pieces of ember-firebrands-are carried downstream by wind. At the time of landing, these firebrands can start secondary fires far away from the main burning unit. This phenomenon is called spotting and the secondary…
Given a graph $G=(V,E)$, a set $\mathcal{F}$ of forbidden subgraphs, we study $\mathcal{F}$-Free Edge Deletion, where the goal is to remove minimum number of edges such that the resulting graph does not contain any $F\in \mathcal{F}$ as a…
Wildfires are one of the costliest and deadliest natural disasters in the US, causing damage to millions of hectares of forest resources and threatening the lives of people and animals. Of particular importance are risks to firefighters and…
Gathering is a fundamental coordination problem in swarm robotics, where the objective is to bring robots together at a point not known to them at the beginning. While most research focuses on continuous domains, some studies also examine…
We study the problem of distance-preserving graph compression for weighted paths and trees. The problem entails a weighted graph $G = (V, E)$ with non-negative weights, and a subset of edges $E^{\prime} \subset E$ which needs to be removed…
Identifying regions that have high likelihood for wildfires is a key component of land and forestry management and disaster preparedness. We create a data set by aggregating nearly a decade of remote-sensing data and historical fire records…
In [1], whether a target binary string s can be represented from a boolean formula with operands chosen from a set of binary strings W was studied. In this paper, we first examine selecting a maximum subset X from W, so that for any string…
Choosing the placement of wildlife crossings (i.e., green bridges) to reconnect animal species' fragmented habitats is among the 17 goals towards sustainable development by the UN. We consider the following established model: Given a graph…
The objective of the present study is twofold. First, the last developments and validation results of a hybrid model designed to simulate fire patterns in heterogeneous landscapes are presented. The model combines the features of a…
In this paper, we introduce the Fixed Topology Minimum-Length Tree with Neighborhood Problem, which aims to embed a rooted tree-shaped graph into a $d$-dimensional metric space while minimizing its total length provided that the nodes must…
Reducing the fuel load in fire-prone landscapes is aimed at mitigating the risk of catastrophic wildfires but there are ecological consequences. Maintaining habitat for fauna of both sufficient extent and connectivity while fragmenting…
In the \emph{dynamic edge coloring} problem, one has to maintain a graph of maximum degree $\Delta$ with at most $\Delta+c$ colors, given updates to the edges of the graph. An important objective is to minimize the \emph{recourse}, which is…
A sequence of vertices in a graph is called a legal dominating sequence if every vertex in the sequence dominates at least one vertex not dominated by those that precede it, and at the end all vertices of the graph are dominated. The Grundy…
Vertex splitting replaces a vertex by two copies and partitions its incident edges amongst the copies. This problem has been studied as a graph editing operation to achieve desired properties with as few splits as possible, most often…
The irrelevant vertex technique provides a powerful tool for the design of parameterized algorithms for a wide variety of problems on graphs. A common characteristic of these problems, permitting the application of this technique on…
We study the parameterized complexity of interdiction problems in graphs. For an optimization problem on graphs, one can formulate an interdiction problem as a game consisting of two players, namely, an interdictor and an evader, who…
The burning and forcing processes are both instances of propagation processes on graphs that are commonly used to model real-world spreading phenomena. The contribution of this paper is two-fold. We first establish a connection between…