# Nearest neighbour graph realizability is NP-hard

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## Abstract

Nearest neighbour graphs are geometric graphs defined on point sets. They express certain proximity relations. This paper gives several ways to define these graphs (weak, strong, mutual and general nearest neighbour graphs) and shows, for each definition, that the problem of determining whether a given combinatorial graph can be realized as such a nearest neighbour graph is NP-hard.

## keywords

complexity theory NP-hard proximity graphs nearest neighbour graphs geometric graphs computational geometry graph drawing pattern recognition## Preview

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© Springer-Verlag Berlin Heidelberg 1995