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Voronoi Game on Graphs
, 2014
"... Voronoi game is a geometric model of competitive facility location problem played between two players. Users are generally modeled as points uniformly distributed on a given underlying space. Each player chooses a set of points in the underlying space to place their facilities. Each user avails serv ..."
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Cited by 5 (1 self)
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. In this paper we consider the two players Voronoi game where the underlying space is a road network modeled by a graph. In this framework we consider the problem of finding k optimal facility locations of Player 2 given any placement of m facilities by Player 1. Our main result is a dynamic programming based
Nash Equilibria in Voronoi Games on Graphs
 In Proceedings of the 15th European Symposium on Algorithms (ESA
, 2007
"... In this paper we study a game where every player is to choose a vertex (facility) in a given undirected graph. All vertices (customers) are then assigned to closest facilities and a player’s payoff is the number of customers assigned to it. We show that deciding the existence of a Nash equilibrium f ..."
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Cited by 10 (1 self)
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In this paper we study a game where every player is to choose a vertex (facility) in a given undirected graph. All vertices (customers) are then assigned to closest facilities and a player’s payoff is the number of customers assigned to it. We show that deciding the existence of a Nash equilibrium
Voronoi game on graphs and its complexity
, 2006
"... The Voronoi game is a twoperson game which is a model for a competitive facility location. The game is played on a continuous domain, and only two special cases (onedimensional case and oneround case) are well investigated. We introduce the discrete Voronoi game in which the game arena is given a ..."
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Cited by 5 (0 self)
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as a graph. We first analyze the game when the arena is a large complete kary tree, and give an optimal strategy. When both players play optimally, the first player wins when k is odd, and the game ends in a tie for even k. Next we show that the discrete Voronoi game is intractable in general. Even
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 543 (11 self)
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The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms
Surface Reconstruction by Voronoi Filtering
 Discrete and Computational Geometry
, 1998
"... We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled ..."
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Cited by 418 (15 self)
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We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Predicting How People Play Games: Reinforcement Learning . . .
 AMERICAN ECONOMIC REVIEW
, 1998
"... ..."
A New VoronoiBased Surface Reconstruction Algorithm
, 2002
"... We describe our experience with a new algorithm for the reconstruction of surfaces from unorganized sample points in R³. The algorithm is the first for this problem with provable guarantees. Given a “good sample” from a smooth surface, the output is guaranteed to be topologically correct and converg ..."
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Cited by 422 (9 self)
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, rather than approximates, the input points. Our algorithm is based on the threedimensional Voronoi diagram. Given a good program for this fundamental subroutine, the algorithm is quite easy to implement.
Results 1  10
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