On the Area Requirements of Euclidean Minimum Spanning Trees

  • Patrizio Angelini
  • Till Bruckdorfer
  • Marco Chiesa
  • Fabrizio Frati
  • Michael Kaufmann
  • Claudio Squarcella
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6844)


In their seminal paper on Euclidean minimum spanning trees [Discrete & Computational Geometry, 1992], Monma and Suri proved that any tree of maximum degree 5 admits a planar embedding as a Euclidean minimum spanning tree. Their algorithm constructs embeddings with exponential area; however, the authors conjectured that c n ×c n area is sometimes required to embed an n-vertex tree of maximum degree 5 as a Euclidean minimum spanning tree, for some constant c > 1. In this paper, we prove the first exponential lower bound on the area requirements for embedding trees as Euclidean minimum spanning trees.


Maximum Degree Minimum Span Tree Edge Incident Area Requirement Clockwise Order 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Till Bruckdorfer
    • 2
  • Marco Chiesa
    • 1
  • Fabrizio Frati
    • 1
    • 3
  • Michael Kaufmann
    • 2
  • Claudio Squarcella
    • 1
  1. 1.Dipartimento di Informatica e AutomazioneUniversità Roma TreItaly
  2. 2.Wilhelm-Schickard-Institut für InformatikUniversität TübingenGermany
  3. 3.School of Basic SciencesÉcole Polytechnique Fédérale de LausanneSwitzerland

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