Existence theory for spatially competitive network facility location models
Annals of Operations Research
Competitive facility location: the Voronoi game
Theoretical Computer Science
Finding a Guard that Sees Most and a Shop that Sells Most
Discrete & Computational Geometry
(r,p)-centroid problems on paths and trees
Theoretical Computer Science
The one-round Voronoi game replayed
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
Journal of Mathematical Modelling and Algorithms
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The one-round discrete Voronoi game, with respect to a npoint 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 a player i is defined as the cardinality of the set of points in U which are closer to a point in Fi than to every point in Fj, for i ≠ j. The objective of both the players in the game is to maximize their respective payoffs. In this paper, we address the case where the points in U are located along a line. We show that if the sorted order of the points in U along the line is known, then the optimal strategy of P2, given any placement of facilities by P1, can be computed in O(n) time. We then prove that for m ≥ 2 the optimal strategy of P1 in the one-round discrete Voronoi game, with the users on a line, can be computed in O(nm-λm) time, where 0 m m.