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Constant-Level Greedy Triangulations Approximate the MWT Well

Author

Listed:
  • Oswin Aichholzer

    (Graz University of Technology)

  • Franz Aurenhammer

    (Graz University of Technology)

  • Günter Rote

    (Graz University of Technology)

  • Yin-Feng Xu

    (Xi'an Jiaotong University)

Abstract

The well-known greedy triangulation GT(S) of a finite point set S is obtained by inserting compatible edges in increasing length order, where an edge is compatible if it does not cross previously inserted ones. Exploiting the concept of so-called light edges, we introduce a definition of GT(S) that does not rely on the length ordering of the edges. Rather, it provides a decomposition of GT(S) into levels, and the number of levels allows us to bound the total edge length of GT(S). In particular, we show |GT(S)| ≤ 3 · 2k + 1|MWT(S)|, where k is the number of levels and MWT(S) is the minimum-weight triangulation of S.

Suggested Citation

  • Oswin Aichholzer & Franz Aurenhammer & Günter Rote & Yin-Feng Xu, 1998. "Constant-Level Greedy Triangulations Approximate the MWT Well," Journal of Combinatorial Optimization, Springer, vol. 2(4), pages 361-369, December.
    • Handle: RePEc:spr:jcomop:v:2:y:1998:i:4:d:10.1023_a:1009776619164
    DOI: 10.1023/A:1009776619164
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