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We consider a Cops-and-Robber game played on the subsets of an $n$-set. The robber starts at the full set; the cops start at the empty set. On each turn, the robber moves down one level by discarding an element, and each cop moves up one…

Combinatorics · Mathematics 2016-02-24 William B. Kinnersley , Paweł Prałat , Douglas B. West

We study the zero-visibility cops and robbers game, where the robber is invisible to the cops until they are caught. This differs from the classic game where full information about the robber's location is known at any time. A previously…

Discrete Mathematics · Computer Science 2025-09-08 Igor Potapov , Tymofii Prokopenko , John Sylvester

The game of Cat Herding is one in which cat and herder players alternate turns, with the evasive cat moving along non-trivial paths between vertices, and the herder deleting single edges from the graph. Eventually the cat cannot move, and…

Combinatorics · Mathematics 2025-05-13 Rylo Ashmore , Danny Dyer , Rebecca Milley

With the advent of autonomous robots with two- and three-dimensional scanning capabilities, classical visibility-based exploration methods from computational geometry have gained in practical importance. However, real-life laser scanning of…

Computational Geometry · Computer Science 2010-09-28 Sandor P. Fekete , Christiane Schmidt

We introduce a pursuit game played between a team of a sensor and an attacker and a mobile target in the unbounded Euclidean plane. The target is faster than the sensor, but slower than the attacker. The sensor's objective is to keep the…

Systems and Control · Electrical Eng. & Systems 2025-09-09 Prajakta Surve , Shaunak D. Bopardikar , Alexander Von Moll , Isaac Weintraub , David W. Casbeer

In this short paper we study the game of cops and robbers, which is played on the vertices of some fixed graph $G$. Cops and a robber are allowed to move along the edges of $G$ and the goal of cops is to capture the robber. The cop number…

Combinatorics · Mathematics 2010-04-13 Alex Scott , Benny Sudakov

Suppose in a given planar region, there are smart mobile evaders and we want to detect them using sweeping agents. We assume that the agents have line sensors of equal length. We propose procedures for designing cooperative sweeping…

Multiagent Systems · Computer Science 2022-05-17 Roee M. Francos , Alfred M. Bruckstein

A sliding camera inside an orthogonal polygon $P$ is a point guard that travels back and forth along an orthogonal line segment $\gamma$ in $P$. The sliding camera $g$ can see a point $p$ in $P$ if the perpendicular from $p$ onto $\gamma$…

Computational Geometry · Computer Science 2016-04-26 Therese Biedl , Timothy M. Chan , Stephanie Lee , Saeed Mehrabi , Fabrizio Montecchiani , Hamideh Vosoughpour

We consider a game in which a cop searches for a moving robber on a graph using distance probes, studied by Carragher, Choi, Delcourt, Erickson and West, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt,…

Combinatorics · Mathematics 2020-08-12 John Haslegrave , Richard A. B. Johnson , Sebastian Koch

We investigate extremal graphs related to the game of Cops and Robbers. We focus on graphs where a single cop can catch the robber; such graphs are called cop-win. The capture time of a cop-win graph is the minimum number of moves the cop…

Combinatorics · Mathematics 2019-03-21 David Offner , Kerry Ojakian

Learning motion planners to move robot from one point to another within an obstacle-occupied space in a collision-free manner requires either an extensive amount of data or high-quality demonstrations. This requirement is caused by the fact…

Robotics · Computer Science 2020-10-20 Xuesu Xiao , Bo Liu , Peter Stone

This paper introduces a nonlinear optimal guidance framework for guiding a pursuer to intercept a moving target, with an emphasis on real-time generation of optimal feedback control for a nonlinear optimal control problem. Initially,…

Optimization and Control · Mathematics 2025-04-11 Han Wang , Zheng Chen

Cops and Robbers games have been studied for the last few decades in computer science and mathematics. As in general pursuit evasion games, pursuers (cops) seek to capture evaders (robbers); however, players move in turn and are constrained…

Discrete Mathematics · Computer Science 2020-04-27 Frédéric Simard , Josée Desharnais , François Laviolette

Suppose that a polygon $P$ is given as an array containing the vertices in counterclockwise order. We analyze how many vertices (including the index of each of these vertices) we need to know before we can bound $P$, i.e., report a bounded…

Computational Geometry · Computer Science 2025-09-05 Mikkel Abrahamsen , Jack Stade , Shuyi Yan , Hanwen Zhang

In the robot follow-ahead task, a mobile robot is tasked to maintain its relative position in front of a moving human actor while keeping the actor in sight. To accomplish this task, it is important that the robot understand the full 3D…

Robotics · Computer Science 2024-03-21 Qingyuan Jiang , Burak Susam , Jun-Jee Chao , Volkan Isler

Cops and Robbers is a type of pursuit-evasion game played on a graph where a set of cops try to capture a single robber. The cops first choose their initial vertex positions, and later the robber chooses a vertex. The cops and robbers make…

Discrete Mathematics · Computer Science 2024-09-25 Prosenjit Bose , Jean-Lou De Carufel , Anil Maheshwari , Karthik Murali

We propose a bio-inspired, agent-based approach to describe the natural phenomenon of group chasing in both two and three dimensions. Using a set of local interaction rules we created a continuous-space and discrete-time model with time…

Biological Physics · Physics 2017-05-24 Milán Janosov , Csaba Virágh , Gábor Vásárhelyi , Tamás Vicsek

We propose and study a strategic model of hiding in a network, where the network designer chooses the links and his position in the network facing the seeker who inspects and disrupts the network. We characterize optimal networks for the…

Theoretical Economics · Economics 2020-01-10 Francis Bloch , Bhaskar Dutta , Marcin Dziubinski

Current state-of-the-art trackers only rely on a target appearance model in order to localize the object in each frame. Such approaches are however prone to fail in case of e.g. fast appearance changes or presence of distractor objects,…

Computer Vision and Pattern Recognition · Computer Science 2020-05-04 Goutam Bhat , Martin Danelljan , Luc Van Gool , Radu Timofte

The Cops and Robber game is played on undirected finite graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if they can catch the robber. The minimum number of cops needed…

Combinatorics · Mathematics 2013-12-30 Nancy E. Clarke , Samuel Fiorini , Gwenaël Joret , Dirk Oliver Theis