Related papers: Online Firefighting on Grids
Firefighting is a dynamic activity, in which numerous operations occur simultaneously. Maintaining situational awareness (i.e., knowledge of current conditions and activities at the scene) is critical to the accurate decision-making…
The problem of dispatching emergency responders to service traffic accidents, fire, distress calls and crimes plagues urban areas across the globe. While such problems have been extensively looked at, most approaches are offline. Such…
Several classical combinatorial problems have been considered and analysed on temporal graphs. Recently, a variant of Vertex Cover on temporal graphs, called MinTimelineCover, has been introduced to summarize timeline activities in social…
The proliferation of peer-to-peer (P2P) file sharing protocols is due to their efficient and scalable methods for data dissemination to numerous users. But many of these networks have no provisions to provide users with long term access to…
In this paper, we explicitly study the online vertex cover problem, which is a natural generalization of the well-studied ski-rental problem. In the online vertex cover problem, we are required to maintain a monotone vertex cover in a graph…
Intelligent detection and processing capabilities can be instrumental to improving the safety, efficiency, and successful completion of rescue missions conducted by firefighters in emergency first response settings. The objective of this…
Graph burning is a discrete-time process that models the spread of influence in a network. Vertices are either burning or unburned, and in each round, a burning vertex causes all of its neighbours to become burning before a new fire source…
A procedure called \textit{graph burning} was introduced to facilitate the modelling of spread of an alarm, a social contagion, or a social influence or emotion on graphs and networks. Graph burning runs on discrete time-steps (or rounds).…
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…
We analyze the problem of packing squares in an online fashion: Given a semi-infinite strip of width 1 and an unknown sequence of squares of side length in [0,1] that arrive from above, one at a time. The objective is to pack these items as…
In the eternal vertex cover problem, mobile guards on the vertices of a graph are used to defend it against an infinite sequence of attacks on its edges by moving to neighbor vertices. The eternal vertex cover problem consists in…
We consider a perimeter defense problem in a rooted full tree graph environment in which a single defending vehicle seeks to defend a set of specified vertices, termed as the perimeter from mobile intruders that enter the environment…
Graph burning is one model for the spread of memes and contagion in social networks. The corresponding graph parameter is the burning number of a graph $G$, written $b(G)$, which measures the speed of the social contagion. While it is…
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…
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…
Based on complex network theory, we propose a computational methodology that addresses the spatial distribution of fuel breaks for the inhibition of the spread and size of wildland fires on heterogeneous landscapes. This is a two-tire…
Consider the following forest-fire process on a connected graph. Each site of the graph can be either occupied or vacant. A vacant site becomes occupied with rate 1. A site is ignited with rate lambda, and its whole occupied cluster burns…
The Burning Number Problem (BNP) models the spread of information or contagion in a network through a discrete-time process on a graph. At each step, one new vertex is selected as a burning source, while fire simultaneously spreads from…
Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In…
We study a model for the destruction of a random network by fire. Suppose that we are given a multigraph of minimum degree at least 2 having real-valued edge-lengths. We pick a uniform point from along the length and set it alight; the…