On the facility location problem: One-round weighted Voronoi game
نویسندگان
چکیده
منابع مشابه
Competitive facility location: the Voronoi game
We consider a competitive facility location problem with two players. Players alternate placing points, one at a time, into the playing arena, until each of them has placed n points. The arena is then subdivided according to the nearest-neighbor rule, and the player whose points control the larger area wins. We present a winning strategy for the second player, where the arena is a circle or a l...
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We consider the one-round Voronoi game, where the first player (“White”, called “Wilma”) places a set of n points in a rectangular area of aspect ratio ρ ≤ 1, followed by the second player (“Black”, called “Barney”), who places the same number of points. Each player wins the fraction of A closest to one of his points, and the goal is to win more than half of the total area. This problem has bee...
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Let S be a set of n points in the plane, and let each point p of S have a positive weight w(p). We consider the problem of positioning a point x inside a compact region R ⊆ R such that min{ w(p)−1 · d(x, p) ; p ∈ S } is maximized. Based on the parametric search paradigm, we give the first subquadratic algorithms for this problem, with running time O(n log n). Furthermore, we shall introduce the...
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The one-round discrete Voronoi game, with respect to a n-point user set U , consists of two players Player 1 (P1) and Player 2 (P2). At first, P1 chooses a set F1 of m facilities following which P2 chooses another set F2 of m facilities, disjoint from F1, where m(= O(1)) is a positive constant. The payoff of P2 is defined as the cardinality of the set of points in U which are closer to a facili...
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ژورنال
عنوان ژورنال: SSRN Electronic Journal
سال: 2020
ISSN: 1556-5068
DOI: 10.2139/ssrn.3862132