Abstract
The two-round discrete Voronoi game on a line consists of a finite user set U (with |U | = n), placed along a line ℓ, and two players Player 1 (P1) and Player 2 (P2). We assume that the sorted order of users in U along the line ℓ is known, and P1 and P2 each has two facilities. P1 places one facility followed by which P2 places another facility and this continues for two rounds. The payoff of P2 is defined as the cardinality of the set of points in U which are closer to a facility owned by P2 than to every facility owned by P1. The payoff of P1 is the number of users in U minus the payoff of P2. The objective of both the players is to maximize their respective payoffs. In this paper we show that, P2 always gets at least n/2 users, i.e., P2 always wins the game and the bound is tight. We also present efficient algorithms to find the optimal strategies of the players in both the rounds.
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Banik, A., Bhattacharya, B.B., Das, S., Das, S. (2013). Two-Round Discrete Voronoi Game along a Line. In: Fellows, M., Tan, X., Zhu, B. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7924. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38756-2_22
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DOI: https://doi.org/10.1007/978-3-642-38756-2_22
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