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We study the entanglement game, which is a version of cops and robbers, on sparse graphs. While the minimum degree of a graph G is a lower bound for the number of cops needed to catch a robber in G, we show that the required number of cops…

离散数学 · 计算机科学 2018-01-23 Anders Martinsson , Florian Meier , Patrick Schnider , Angelika Steger

We consider a variant of the target defense problem where a single defender is tasked to capture a sequence of incoming intruders. The intruders' objective is to breach the target boundary without being captured by the defender. As soon as…

机器人学 · 计算机科学 2022-12-14 Arman Pourghorban , Michael Dorothy , Daigo Shishika , Alexander Von Moll , Dipankar Maity

In this paper an N-pursuer vs. M-evader team conflict is studied. The differential game of border defense is addressed and we focus on the game of degree in the region of the state space where the pursuers are able to win. This work extends…

最优化与控制 · 数学 2019-11-12 Eloy Garcia , David W. Casbeer , Alexander Von Moll , Meir Pachter

The localization game is a variant of the game of Cops and Robber in which the robber is invisible and moves between adjacent vertices, but the cops can probe any $k$ vertices of the graph to obtain the distance between probed vertices and…

组合数学 · 数学 2026-02-10 Vesna Iršič Chenoweth , Matija Skrt

We present a method for pursuit/evasion that is highly efficient and and scales to large teams of aircraft. The underlying algorithm is an efficient algorithm for solving Markov Decision Processes (MDPs) that supports fully continuous state…

人工智能 · 计算机科学 2019-09-11 Joshua R. Bertram , Peng Wei

In the game of Cops and Robbers, a team of cops attempts to capture a robber on a graph $G$. All players occupy vertices of $G$. The game operates in rounds; in each round the cops move to neighboring vertices, after which the robber does…

组合数学 · 数学 2018-06-20 William B. Kinnersley

This paper studies a planar multiplayer Homicidal Chauffeur reach-avoid differential game, where each pursuer is a Dubins car and each evader has simple motion. The pursuers aim to protect a goal region cooperatively from the evaders. Due…

计算机科学与博弈论 · 计算机科学 2021-07-13 Rui Yan , Ruiliang Deng , Haowen Lai , Weixian Zhang , Zongying Shi , Yisheng Zhong

Surveillance-Evasion (SE) games form an important class of adversarial trajectory-planning problems. We consider time-dependent SE games, in which an Evader is trying to reach its target while minimizing the cumulative exposure to a moving…

最优化与控制 · 数学 2019-09-09 Elliot Cartee , Lexiao Lai , Qianli Song , Alexander Vladimirsky

We consider "Containment": a variation of the graph pursuit game of Cops and Robber in which cops move from edge to adjacent edge, the robber moves from vertex to adjacent vertex (but cannot move along an edge occupied by a cop), and the…

组合数学 · 数学 2019-03-19 Danny Crytser , Natasha Komarov , John Mackey

We study the survival of a prey that is hunted by N predators. The predators perform independent random walks on a square lattice with V sites and start a direct chase whenever the prey appears within their sighting range. The prey is…

统计力学 · 物理学 2022-06-08 G. Oshanin , O. Vasilyev , P. L. Krapivsky , J. Klafter

The problem of searching a polygonal region for an unpredictably moving intruder by a set of stationary guards, each carrying an orientable laser, is known as the Searchlight Scheduling Problem. Determining the computational complexity of…

计算几何 · 计算机科学 2015-03-20 Giovanni Viglietta

Pursuit-evasion is the problem of capturing mobile targets with one or more pursuers. We use deep reinforcement learning for pursuing an omni-directional target with multiple, homogeneous agents that are subject to unicycle kinematic…

多智能体系统 · 计算机科学 2021-08-10 Cristino de Souza , Rhys Newbury , Akansel Cosgun , Pedro Castillo , Boris Vidolov , Dana Kulic

Cops and robbers is a vertex-pursuit game played on graphs. In the classical cops-and-robbers game, a set of cops and a robber occupy the vertices of the graph and move alternately along the graph's edges with perfect information about each…

离散数学 · 计算机科学 2018-06-12 Ziyuan Gao , Boting Yang

In this paper, a time-optimal feedback solution to the game of two cars, for the case where the pursuer is faster and more agile than the evader, is presented. The concept of continuous subsets of the reachable set is introduced to…

系统与控制 · 电气工程与系统科学 2021-06-01 Aditya Chaudhari , Debraj Chakraborty

The Meeting problem for $k\geq 2$ searchers in a polygon $P$ (possibly with holes) consists in making the searchers move within $P$, according to a distributed algorithm, in such a way that at least two of them eventually come to see each…

分布式、并行与集群计算 · 计算机科学 2019-07-09 Giuseppe A. Di Luna , Paola Flocchini , Nicola Santoro , Giovanni Viglietta , Masafumi Yamashita

We consider a pursuit-evasion problem with a heterogeneous team of multiple pursuers and multiple evaders. Although both the pursuers (robots) and the evaders are aware of each others' control and assignment strategies, they do not have…

机器人学 · 计算机科学 2021-03-30 Leiming Zhang , Amanda Prorok , Subhrajit Bhattacharya

We show that the expected time for a smart "cop" to catch a drunk "robber" on an $n$-vertex graph is at most $n + {\rm o}(n)$. More precisely, let $G$ be a simple, connected, undirected graph with distinguished points $u$ and $v$ among its…

组合数学 · 数学 2014-11-05 Natasha Komarov , Peter Winkler

This paper introduces a new family of pursuit strategies for multi-pursuer single-evader games in a planar environment. They leverage conditions under which the minimum-time solution of the game becomes equivalent to that of a suitable…

系统与控制 · 电气工程与系统科学 2024-10-11 Marco Casini , Andrea Garulli

We consider "surrounding" versions of the classic Cops and Robber game. The game is played on a connected graph in which two players, one controlling a number of cops and the other controlling a robber, take alternating turns. In a turn,…

组合数学 · 数学 2024-10-14 Paul Jungeblut , Samuel Schneider , Torsten Ueckerdt

Most tracking-by-detection methods employ a local search window around the predicted object location in the current frame assuming the previous location is accurate, the trajectory is smooth, and the computational capacity permits a search…

计算机视觉与模式识别 · 计算机科学 2015-12-01 Gao Zhu , Fatih Porikli , Hongdong Li