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International Conference on Algorithms and Complexity

CIAC 2017: Algorithms and Complexity pp 393–404Cite as

Perpetually Dominating Large Grids

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10236))

Abstract

In the Eternal Domination game, a team of guard tokens initially occupies a dominating set on a graph G. A rioter then picks a node without a guard on it and attacks it. The guards defend against the attack: one of them has to move to the attacked node, while each remaining one can choose to move to one of his neighboring nodes. The new guards’ placement must again be dominating. This attack-defend procedure continues perpetually. The guards win if they can eternally maintain a dominating set against any sequence of attacks, otherwise the rioter wins.

We study rectangular grids and provide the first known general upper bound for these graphs. Our novel strategy implements a square rotation principle and eternally dominates \(m \times n\) grids by using approximately \(\frac{mn}{5}\) guards, which is asymptotically optimal even for ordinary domination.

Work partially supported by EPSRC grant EP/M027287/1 (Energy Efficient Control).

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Authors and Affiliations

  1. Department of Computer Science, University of Liverpool, Liverpool, UK

    Ioannis Lamprou, Russell Martin & Sven Schewe

Authors
  1. Ioannis Lamprou
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  2. Russell Martin
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  3. Sven Schewe
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Correspondence to Ioannis Lamprou .

Editor information

Editors and Affiliations

  1. National Technical University of Athens, Zografou, Athens, Greece

    Dimitris Fotakis

  2. National Technical University of Athens, Zografou, Athens, Greece

    Aris Pagourtzis

  3. Université Paris-Dauphine, Paris, France

    Vangelis Th. Paschos

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Lamprou, I., Martin, R., Schewe, S. (2017). Perpetually Dominating Large Grids. In: Fotakis, D., Pagourtzis, A., Paschos, V. (eds) Algorithms and Complexity. CIAC 2017. Lecture Notes in Computer Science(), vol 10236. Springer, Cham. https://doi.org/10.1007/978-3-319-57586-5_33

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  • DOI: https://doi.org/10.1007/978-3-319-57586-5_33

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57585-8

  • Online ISBN: 978-3-319-57586-5

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