Nearest Neighbour Graph Realizability is NP-hard
نویسندگان
چکیده
1 I n t r o d u c t i o n This paper investigates the problem of realizing a given graph G as a "nearest neighbour graph" of a set P of points in the plane. Roughly speaking, a "nearest neighbour graph" is a geometric graph formed from a set of points in the plane by joining two points if one is the nearest neighbour of the other. Fig. 1. A mutual nearest neighbour graph One specific kind of nearest neighbour graph is the mutual nearest neighbour graph (defined in detail later). Given a planar point set P , this geometric graph has a vertex-point for each point in P , and an edge-segment between vertexpoints p and q E P if and only if p is as close or closer to q as any other point
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