The Euclidean degree-4 minimum spanning tree problem is NP-hard

  • Authors:
  • Andrea Francke;Michael Hoffmann

  • Affiliations:
  • ETH Zürich, Zürich, Switzerland;ETH Zürich, Zürich, Switzerland

  • Venue:
  • Proceedings of the twenty-fifth annual symposium on Computational geometry
  • Year:
  • 2009

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Abstract

We show that it is an NP-hard problem to decide for a given set P of n points in the Euclidean plane and a given parameter k∈R, whether P admits a spanning tree of maximum vertex degree four whose sum of edge lengths does not exceed k.