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The Discrete Voronoi Game in a Simple Polygon

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Computing and Combinatorics (COCOON 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7936))

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Abstract

Let P be a simple polygon with m vertices and let \(\mathcal{U}\) be a set of n points in P. We consider the points of \(\mathcal{U}\) to be “users”. We consider a game with two players \(\mathcal{P}_1\) and \(\mathcal{P}_2\). In this game, \(\mathcal{P}_1\) places a point facility inside P, after which \(\mathcal{P}_2\) places another point facility inside P. We say that a user \(u \in \mathcal{U}\) is served by its nearest facility, where distances are measured by the geodesic distance in P. The objective of each player is to maximize the number of users they serve. We show that for any given placement of a facility by \(\mathcal{P}_1\), an optimal placement for \(\mathcal{P}_2\) can be computed in O(m + n(logn + logm)) time. We also provide a polynomial-time algorithm for computing an optimal placement for \(\mathcal{P}_1\).

Research supported by NSERC and DFAIT Commonwealth Scholarship.

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Banik, A., Das, S., Maheshwari, A., Smid, M. (2013). The Discrete Voronoi Game in a Simple Polygon. In: Du, DZ., Zhang, G. (eds) Computing and Combinatorics. COCOON 2013. Lecture Notes in Computer Science, vol 7936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38768-5_19

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  • DOI: https://doi.org/10.1007/978-3-642-38768-5_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38767-8

  • Online ISBN: 978-3-642-38768-5

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