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Offline variants of the "lion and man" problem

Adrian Dumitrescu, Ichiro Suzuki, Paweł Żyliński
2008 Theoretical Computer Science  
We call this variant the continuous model of the safe path planning problem.  ...  In the final part of our paper, we consider other related offline questions, such as the maximum number of men problem and the spy problem.  ...  Acknowledgments The authors thank Joseph Mitchell for inspiring conversations on the topic, and the anonymous referees for their helpful comments.  ... 
doi:10.1016/j.tcs.2008.02.039 fatcat:yb47lyztozftnly3gpwjdh3m7y

Escaping offline searchers and isoperimetric theorems

Peter Brass, Kyue D. Kim, Hyeon-Suk Na, Chan-Su Shin
2009 Computational geometry  
Zylinski, Offline variants of the "lion and man" problem, in: SoCG 2007, Proc. 23rd Annual Symposium on Computational Geometry, ACM Press, 2007, pp. 102-111] in the simultaneous-move-model where at each  ...  In the proof, we use new isoperimetric theorems for subsets of the n × n grid and the n × n square, which is of independent interest.  ...  Introduction Pursuit-evasion problems have been studied in many models, and under many names, like lion and man [19] , cop and robber [3, 14] or hunter and rabbit [1] .  ... 
doi:10.1016/j.comgeo.2008.08.001 fatcat:ogx5begjize3bmnpv25n5ae664

How Many Lions Are Needed to Clear a Grid?

Florian Berger, Alexander Gilbers, Ansgar Grüne, Rolf Klein
2009 Algorithms  
Furthermore, we analyze a problem variant where the lions are also allowed to jump from grid vertices to non-adjacent grid vertices.  ...  In this paper, we consider the same problem in dimension d > 2 and prove that Θ(n d−1 / √ d) lions are necessary and sufficient to clear the n d -grid.  ...  However, we prefer to take the lion and man notation used by Dumitrescu. The second approach to the problem above even makes the man unnecessary.  ... 
doi:10.3390/a2031069 fatcat:otu4bmwpmbbwzf52mcpjh5bwza

A local strategy for cleaning expanding cellular domains by simple robots [article]

Rolf Klein, David Kriesel, Elmar Langetepe
2015 arXiv   pre-print
Initially, the contaminated area is of height h and width w. It may be bounded by four monotonic chains, and contain rectangular holes.  ...  It moves from cell to cell, d times faster than the contamination spreads, and is able to clean its current cell. A speed of d<√(2)(h+w) is in general not sufficient to contain the contamination.  ...  A good example for this is the family of pursuit-evasion problems (for an overview, see [9] ), also known as intruder search, cops and robbers, or lion and man problems [6, 8] .  ... 
arXiv:1502.03985v1 fatcat:zzaox3t4qbbl5pj7mmnbkpmroe

Visibility Optimization for Surveillance-Evasion Games [article]

Louis Ly, Yen-Hsi Richard Tsai
2022 arXiv   pre-print
We consider a discrete variant of the surveillance-game.  ...  We use an upwind scheme to compute the feedback value function, corresponding to the end-game time of the differential game.  ...  Variants include the lion and man [18, 30] , where both players have the same maneuverability, and the homicidal chauffeur [23] , where one player drives a vehicle, which is faster, but has constrained  ... 
arXiv:2010.09001v2 fatcat:ensedsoxzvc7hmsgnwuxc5urim

Multi-robot target detection and tracking: taxonomy and survey

Cyril Robin, Simon Lacroix
2015 Autonomous Robots  
In this article, our objective is to go beyond the frontiers of specific communities and specific problems, and to enlarge the scope of prior surveys.  ...  We review various work related to each class of problems identified in the taxonomy, highlighting the different approaches, models and results.  ...  Acknowledgements: The authors are thankful to Wheeler Ruml for his helpful remarks.  ... 
doi:10.1007/s10514-015-9491-7 fatcat:yqq75fwdkzdipelxpgtiz3ffba

Visibility optimization for autonomous exploration and surveillance-evasion games [article]

Long Louis Ly, Austin, The University Of Texas At, Yen-Hsi R. Tsai
This dissertation considers problems involving line-of-sight visibility.  ...  In the exploration problem, the agent must efficiently map out a previously unknown environment, using as few sensor measurements as possible.  ...  Variants include the lion and man [45, 87] , where both players have the same maneuverability, and the homicidal chauffeur [69] , where one player drives a vehicle, which is faster, but has constrained  ... 
doi:10.26153/tsw/10147 fatcat:hakf3xedlnhs5o3zdkib2fk6ra