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    Advantage in the discrete Voronoi game

    Gerbner, D. and Mészáros, V. and Pálvölgyi, D. and Pokrovskiy, Alexey and Rote, G. (2014) Advantage in the discrete Voronoi game. Journal of Graph Algorithms and Applications 18 (3), pp. 439-457. ISSN 1526-1719.

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    We study the discrete Voronoi game, where two players alternately claim vertices of a graph for t rounds. In the end, the remaining vertices are divided such that each player receives the vertices that are closer to his or her claimed vertices. We prove that there are graphs for which the second player gets almost all vertices in this game, but this is not possible for bounded-degree graphs. For trees, the first player can get at least one quarter of the vertices, and we give examples where she can get only little more than one third of them. We make some general observations, relating the result with many rounds to the result for the one-round game on the same graph.


    Item Type: Article
    School: Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School
    Depositing User: Alexey Pokrovskiy
    Date Deposited: 21 Jan 2019 14:40
    Last Modified: 02 Aug 2023 17:47


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