English
Related papers

Related papers: Characterizations and algorithms for generalized C…

200 papers

In this paper we study the two-player generalized Cops and Robber (GCR) games introduced by Bonato and MacGillivray. Our main goal is to present a full, self-contained game theoretic analysis of such games.

Combinatorics · Mathematics 2020-11-20 Athanasios Kehagias , Georgios Konstantinidis

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…

Combinatorics · Mathematics 2026-02-10 Vesna Iršič Chenoweth , Matija Skrt

In this paper we study the concurrent cops and robber (CCCR) game. CCCR follows the same rules as the classical, turn-based game, except for the fact that the players move simultaneously. The cops' goal is to capture the robber and the…

Discrete Mathematics · Computer Science 2015-06-12 Georgios Konstantinidis , Athanasios Kehagias

The game of cops and robber is a turn based vertex pursuit game played on a connected graph between a team of cops and a single robber. The cops and the robber move alternately along the edges of the graph. We say the team of cops win the…

Combinatorics · Mathematics 2022-11-30 Uttam K. Gupta , Suchismita Mishra , Dinabandhu Pradhan

Shmuel Gal and Jerome Casas have recently introduced a game theoretic model that combines search and pursuit by a predator for a prey animal. The prey (hider) can hide in a finite number of locations. The predator (searcher) can inspect any…

Computer Science and Game Theory · Computer Science 2019-12-10 Steve Alpern , Viciano Lee

Cops and Robbers is a well-studied pursuit-evasion game in which a set of cops seeks to catch a robber in a graph G, where cops and robber move along edges of G. The cop number of G is the minimum number of cops that is sufficient to catch…

This paper considers a game in which a single cop and a single robber take turns moving along the edges of a given graph $G$. If there exists a strategy for the cop which enables it to be positioned at the same vertex as the robber…

Data Structures and Algorithms · Computer Science 2019-08-20 Thomas Erlebach , Jakob T. Spooner

The deduction game is a variation of the game of cops and robber on graphs in which searchers must capture an invisible evader in at most one move. Searchers know each others' initial locations, but can only communicate if they are on the…

Combinatorics · Mathematics 2024-12-24 Andrea Burgess , Danny Dyer , Mozhgan Farahani

The localization game is a two player combinatorial game played on a graph $G=(V,E)$. The cops choose a set of vertices $S_1 \subseteq V$ with $|S_1|=k$. The robber then chooses a vertex $v \in V$ whose location is hidden from the cops, but…

Combinatorics · Mathematics 2022-09-07 Lyuben Lichev , Dieter Mitsche , Pawel Pralat

The localization game is a pursuit-evasion game analogous to Cops and Robbers, where the robber is invisible and the cops send distance probes in an attempt to identify the location of the robber. We present a novel graph parameter called…

Combinatorics · Mathematics 2021-05-21 Natalie C. Behague , Anthony Bonato , Melissa A. Huggan , Trent G. Marbach , Brittany Pittman

We compare two kinds of pursuit-evasion games played on graphs. In Cops and Robbers, the cops can move strategically to adjacent vertices as they please, while in a new variant, called deterministic Zombies and Survivors, the zombies (the…

Combinatorics · Mathematics 2018-09-11 David Offner , Kerry Ojakian

We theoretically analyze the Cops and Robber Game for the first time in a multidimensional grid. It is shown that for an $n$-dimensional grid, at least $n$ cops are necessary to ensure capture of the robber. We also present a set of cop…

Discrete Mathematics · Computer Science 2015-06-12 Sayan Bhattacharya , Goutam Paul , Swagato Sanyal

The cops-and-robber (CR) game has been used in mobile robotics as a discretized model (played on a graph G) of pursuit/evasion problems. The "classic" CR version is a perfect information game: the cops' (pursuer's) location is always known…

Discrete Mathematics · Computer Science 2014-02-26 Athanasios Kehagias , Dieter Mitsche , Pawel Pralat

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…

Combinatorics · Mathematics 2018-06-20 William B. Kinnersley

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

We discuss winning possibilities of players in various variants of cops and robber game played on large random graphs, a testbed for various kinds of network queries, search problems in particular. We explore the use of logic frameworks to…

Logic in Computer Science · Computer Science 2025-12-01 Sourav Chakraborty , Sujata Ghosh , Smiha Samanta

We consider the effect on the length of the game of Cops and Robbers when more cops are added to the game play. In Overprescribed Cops and Robbers, as more cops are added, the capture time (the minimum length of the game assuming optimal…

Combinatorics · Mathematics 2016-11-24 Anthony Bonato , Xavier Pérez-Giménez , Paweł Prałat , Benjamin Reiniger

We consider a variant of Cops and Robbers in which both the cops and the robber are allowed to traverse up to $s$ edges on each of their turns, where $s \ge 2$. We give several general for this new model as well as establish bounds for the…

Combinatorics · Mathematics 2025-06-27 William B. Kinnersley , Nikolas Townsend

We study pursuit-evasion in a polygonal environment with polygonal obstacles. In this turn based game, an evader $e$ is chased by pursuers $p_1, p_2, ..., p_{\ell}$. The players have full information about the environment and the location…

Computational Geometry · Computer Science 2014-10-21 Brendan Ames , Andrew Beveridge , Rosalie Carlson , Claire Djang , Volkan Isler , Stephen Ragain , Maxray Savage

We propose a decentralized solution for a pursuit-evasion game involving a heterogeneous group of rational (selfish) pursuers and a single evader based on the framework of potential games. In the proposed game, the evader aims to delay (or,…

Systems and Control · Electrical Eng. & Systems 2021-08-19 Yoonjae Lee , Efstathios Bakolas