The Pursuit-Evasion Game on the 1-Skeleton Graph of a Regular Polyhedron. II

Part II of the paper considers a game between a group of n pursuers and one evader that move along the 1-Skeleton graph M of regular polyhedrons of three types in the spaces ℝ d , d ≥ 3. Like in Part I, the goal is to find an integer N ( M ) with the following property: if n ≥ N ( M ), then the grou...

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Bibliographic Details
Published in:Automation and remote control 2019, Vol.80 (1), p.164-170
Main Authors: Azamov, A. A., Kuchkarov, A. Sh, Holboyev, A. G.
Format: Article
Language:English
Subjects:
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Computer-Aided Engineering (CAD
Control
Mathematical Game Theory and Applications
Mathematics
Mathematics and Statistics
Mechanical Engineering
Mechatronics
Polyhedra
Pursuit-evasion games
Robotics
Systems Theory
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Summary:Part II of the paper considers a game between a group of n pursuers and one evader that move along the 1-Skeleton graph M of regular polyhedrons of three types in the spaces ℝ d , d ≥ 3. Like in Part I, the goal is to find an integer N ( M ) with the following property: if n ≥ N ( M ), then the group of pursuers wins the game; if n < N ( M ), the evader wins. It is shown that N ( M ) = 2 for the d -dimensional simplex or cocube (a multidimensional analog of octahedron) and N ( M ) = [ d /2] + 1 for the d -dimensional cube.
ISSN:0005-1179
1608-3032
DOI:10.1134/S0005117919010144