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Topological Network-Control Games

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Computing and Combinatorics (COCOON 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14423))

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Abstract

The paper introduces new combinatorial games, called topological network-control games, played on graphs. These games model the influence of competing two parties aiming to control a given network. In a such game given the network, the players move alternatively. At each turn, a player selects an unclaimed vertex and its unclaimed neighbours within distance t. The players obey the topological condition that all claimed vertices stay connected. The goal is to decide which player claims the majority of the vertices at the end of the play. We study greedy, symmetric and optimal strategies. We solve the topological network-control games on various classes of graphs. This progresses our understanding of combinatorial games played on graphs. We prove that finding an optimal winning strategy is a PSPACE-complete problem.

B. Khoussainov—Acknowledges the National Science Foundation of China under Grant No. 62172077.

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Notes

  1. 1.

    The code is at https://github.com/ZihuiLiang/Topological-Network-Control-Game..

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Authors and Affiliations

  1. University of Electronic Science and Technology of China, Chengdu, China

    Zihui Liang, Bakh Khoussainov & Haidong Yang

Authors
  1. Zihui Liang
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  2. Bakh Khoussainov
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  3. Haidong Yang
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Corresponding author

Correspondence to Zihui Liang .

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Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

  2. University of Delaware, Newark, DE, USA

    Guangmo Tong

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Liang, Z., Khoussainov, B., Yang, H. (2024). Topological Network-Control Games. In: Wu, W., Tong, G. (eds) Computing and Combinatorics. COCOON 2023. Lecture Notes in Computer Science, vol 14423. Springer, Cham. https://doi.org/10.1007/978-3-031-49193-1_11

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  • DOI: https://doi.org/10.1007/978-3-031-49193-1_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-49192-4

  • Online ISBN: 978-3-031-49193-1

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