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Recent years have seen increased interest in the design and deployment of smart grid devices and control algorithms. Each of these smart communicating devices represents a potential access point for an intruder spurring research into…

Computer Science and Game Theory · Computer Science 2016-11-18 Scott Backhaus , Russell Bent , James Bono , Ritchie Lee , Brendan Tracey , David Wolpert , Dongping Xie , Yildiray Yildiz

We use Hartnell's model for virus spread on a graph, also known as firefighting. For rooted trees, we propose an Unburning Algorithm, a type of greedy algorithm starting from the leaves and working back towards the root. We show that the…

Combinatorics · Mathematics 2024-09-24 Andrea Barnett , Robert Bond , Anthony Macias , Thomas W. Mattman , Bill Parnell , Ely Schoenfield

Graph burning is a deterministic, discrete-time process that models how influence or contagion spreads in a graph. Associated to each graph is its burning number, which is a parameter that quantifies how quickly the influence spreads. We…

Combinatorics · Mathematics 2020-09-23 Anthony Bonato

This paper considers a game-theoretic formulation of the covert communications problem with finite blocklength, where the transmitter (Alice) can randomly vary her transmit power in different blocks, while the warden (Willie) can randomly…

Information Theory · Computer Science 2020-05-28 Alex S. Leong , Daniel E. Quevedo , Subhrakanti Dey

The future smart grid is envisioned as a large-scale cyber-physical system encompassing advanced power, communications, control, and computing technologies. In order to accommodate these technologies, it will have to build on solid…

Information Theory · Computer Science 2012-02-03 Walid Saad , Zhu Han , H. Vincent Poor , Tamer Başar

We introduce and study coverage games - a novel framework for multi-agent planning in settings in which a system operates several agents but does not have full control on them, or interacts with an environment that consists of several…

Computer Science and Game Theory · Computer Science 2026-03-24 Orna Kupferman , Noam Shenwald

Given a graph $G$, the optimization version of the graph burning problem seeks for a sequence of vertices, $(u_1,u_2,...,u_p) \in V(G)^p$, with minimum $p$ and such that every $v \in V(G)$ has distance at most $p-i$ to some vertex $u_i$.…

Discrete Mathematics · Computer Science 2025-03-07 Jesús García-Díaz , José Alejandro Cornejo-Acosta , Joel Trejo Sánchez

Evolution of cooperation in the prisoner's dilemma game is studied where initially all players are linked via a regular graph, having four neighbors each. Simultaneously with the strategy evolution, players are allowed to make new…

Physics and Society · Physics 2009-03-27 Attila Szolnoki , Matjaz Perc , Zsuzsa Danku

In this work the single server model with counteraction is considered. We extend the classic fluid model using results from the theory of conflict controlled processes. Our new model describes conflict processes in neworks. For this model…

Optimization and Control · Mathematics 2009-09-30 Oleksii Ignatenko

Chip-firing on a directed graph is a game in which chips, a discrete commodity, are placed on the vertices of the graph and are transferred between vertices. In this paper, we study a chip-firing game on the Hasse diagram of the lattice of…

Combinatorics · Mathematics 2026-01-15 Ryota Inagaki , Tanya Khovanova , Austin Luo

Chip-firing is a combinatorial game on a graph, in which chips are placed and dispersed among its vertices until a stable configuration is achieved. We specifically study a chip-firing variant on an infinite, rooted, directed $k$-ary tree…

Combinatorics · Mathematics 2026-01-14 Ryota Inagaki , Tanya Khovanova , Austin Luo

The Cops and Robber game is played on undirected finite graphs. $k$ cops and one robber are positioned on vertices and take turn in moving along edges. The cops win if, after a move, a cop and the robber are on the same vertex. A graph is…

Combinatorics · Mathematics 2011-11-10 Dirk Oliver Theis

While game-theoretic models and algorithms have been developed to combat illegal activities, such as poaching and over-fishing, in green security domains, none of the existing work considers the crucial aspect of community engagement:…

Computer Science and Game Theory · Computer Science 2020-02-24 Taoan Huang , Weiran Shen , David Zeng , Tianyu Gu , Rohit Singh , Fei Fang

We introduce the game of Surrounding Cops and Robbers on a graph, as a variant of the original game of Cops and Robbers. In contrast to the original game in which the cops win by occupying the same vertex as the robber, they now win by…

Graph burning runs on discrete time steps. The aim is to burn all the vertices in a given graph in the least number of time steps. This number is known to be the burning number of the graph. The spread of social influence, an alarm, or a…

Data Structures and Algorithms · Computer Science 2021-02-02 Arya Tanmay Gupta , Swapnil A. Lokhande , Kaushik Mondal

This paper proposes a game-theoretic approach to address the problem of optimal sensor placement for detecting cyber-attacks in networked control systems. The problem is formulated as a zero-sum game with two players, namely a malicious…

Optimization and Control · Mathematics 2022-05-30 Anh Tung Nguyen , André M. H. Teixeira , Alexander Medvedev

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…

Atmospheric and Oceanic Physics · Physics 2013-07-02 F. Aguayo , A. Fuentes , J. -P. Clerc , B. Porterie

Interdicting a criminal with limited police resources is a challenging task as the criminal changes location over time. The size of the large transportation network further adds to the difficulty of this scenario. To tackle this issue, we…

Artificial Intelligence · Computer Science 2026-04-08 Sukanya Samanta , Kei Kimura , Makoto Yokoo , Palash Dey

The aim of this paper is to solve the "gift exchange" problem: you are one of n players, and there are n wrapped gifts on display; when your turn comes, you can either choose any of the remaining wrapped gifts, or you can "steal" a gift…

Combinatorics · Mathematics 2009-07-06 David Applegate , N. J. A. Sloane

A new model of population dynamics on lattices is proposed. The model consists of players on lattice points, each of which plays the RSP game with neighboring players. Each player copies the next hand from the hand of the neighbouring…

Statistical Mechanics · Physics 2008-02-01 Hiroyuki Nishiuchi , Naomichi Hatano , Kenn Kubo
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