Nearest neighbour graph realizability is NP-hard

  • Peter Eades
  • Sue Whitesides
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 911)


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.


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


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Peter Eades
    • 1
  • Sue Whitesides
    • 2
  1. 1.Department of Computer ScienceUniversity of NewcastleCallaghanAustralia
  2. 2.School of Computer ScienceMcGill UniversityMontrealCanada

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