Proximity drawings in polynomial area and volume

  • Authors:
  • Paolo Penna;Paola Vocca

  • Affiliations:
  • University of Rome "Tor Vergata", Math. Department and Institut für Teoretische Informatik, ETH Zentrum, Clausiusstrasse 49, CH-8092 Zurich, Switzerland;Dipartimento di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, I-00133 Rome, Italy

  • Venue:
  • Computational Geometry: Theory and Applications
  • Year:
  • 2004

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Abstract

We introduce a novel technique for drawing proximity graphs in polynomial area and volume. Previously known algorithms produce representations whose size increases exponentially with the size of the graph. This holds even when we restrict ourselves to binary trees. Our method is quite general and yields the first algorithms to construct (a) polynomial area weak Gabriel drawings of ternary trees, (b) polynomial area weak β-proximity drawing of binary trees for any 0 ≤ β