Polynomial Area Bounds for MST Embeddings of Trees

  • Michael Kaufmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4875)


In their seminal paper on geometric minimum spanning trees, Monma and Suri [6] gave a method to embed any tree of maximal degree 5 as a minimum spanning tree in the Euclidean plane. They derived area bounds of \(O(2^{k^2} \times 2^{k^2})\) for trees of height k and conjectured that an improvement below c n ×c n is not possible for some constant c > 0. We partially disprove this conjecture by giving polynomial area bounds for arbitrary trees of maximal degree 3 and 4.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Michael Kaufmann
    • 1
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenGermany

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