Abstract
Recently several researchers have studied the competitive facility location problem in the form of Voronoi games, where each of the two players places n points with the target of maximizing total Voronoi area of its sites in the Voronoi diagram of 2n points. In this paper we address this problem by introducing Voronoi games by neighbours where the basic objective of an optimal playing strategy is to acquire more neighbors than the opponent. We consider several variations of this game, and for each variation we either give a winning strategy, if it exists, or show how the game ends in a tie.
This research was carried out in the Department of CSE, BUET as part of the M.Sc. Engg. thesis of the first author.
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References
Ahn, H.-K., Cheng, S.-W., Cheong, O., Golin, M., van Oostrum, R.: Competitive facility location: the Voronoi game. Theor. Comput. Sci. 310(1-3), 457–467 (2004)
Ahn, H.-K., Cheng, S.-W., Cheong, O., Golin, M.J., van Oostrum, R.: Competitive facility location along a highway. In: Wang, J. (ed.) COCOON 2001. LNCS, vol. 2108, pp. 237–246. Springer, Heidelberg (2001)
Aurenhammer, F., Klein, R.: Voronoi diagrams. In: Sack, J.-R., Urrutia, J. (eds.) Handbook of Computational Geometry, pp. 201–290. North-Holland, Amsterdam (2000)
Biedl, T., Demaine, E.D., Duncan, C.A., Fleischer, R., Kobourov, S.G.: Tight bounds on maximal and maximum matchings. In: Eades, P., Takaoka, T. (eds.) ISAAC 2001. LNCS, vol. 2223, pp. 308–319. Springer, Heidelberg (2001)
Cheong, O., Efrat, A., Har-Peled, S.: Finding a guard that sees most and a shop that sells most. Discrete Comput. Geom. 37(4), 545–563 (2007)
Cheong, O., Har-Peled, S., Linial, N., Matoušek, J.: The one-round Voronoi game. In: SCG 2002: Proceedings of the 18th Annual Symposium on Computational Geometry, pp. 97–101. ACM, New York (2002)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry: Algorithms and Applications, 2nd edn. Springer, Heidelberg (2000)
Dehne, F.K.H.A., Klein, R., Seidel, R.: Maximizing a voronoi region: The convex case. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 624–634. Springer, Heidelberg (2002)
Fekete, S.P., Meijer, H.: The one-round Voronoi game replayed. Comput. Geom. Theory Appl. 30(2), 81–94 (2005)
Rasheed, M.M.: Voronoi neighbors: Optimization, Variation and Games, MSc Thesis, Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh (2008)
West, D.B.: Introduction to Graph Theory, 2nd edn. Pearson Education, London (2002)
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Rasheed, M.M., Hasan, M., Rahman, M.S. (2009). Maximum Neighbour Voronoi Games. In: Das, S., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2009. Lecture Notes in Computer Science, vol 5431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00202-1_9
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DOI: https://doi.org/10.1007/978-3-642-00202-1_9
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