On Steiner minimal trees withL p distance

@article{Liu1992OnSM,
  title={On Steiner minimal trees withL p distance},
  author={Zi-Cheng Liu and Dingzhu Du},
  journal={Algorithmica},
  year={1992},
  volume={7},
  pages={179-191}
}
LetL p be the plane with the distanced p (A 1 ,A 2 ) = (¦x 1 −x 2¦ p + ¦y1 −y 2¦p)/1p wherex i andy i are the cartesian coordinates of the pointA i . LetP be a finite set of points inL p . We consider Steiner minimal trees onP. It is proved that, for 1 <p < ∞, each Steiner point is of degree exactly three. Define the Steiner ratio ϱ p to be inf{L s (P)/L m (P)¦P⊂L p } whereL s (P) andL m (P) are lengths of the Steiner minimal tree and the minimal spanning tree onP, respectively. Hwang showed ϱ1… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.
9 Citations
7 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-7 of 7 references

A new bound for euclidean Steiner minimal trees

  • R. L. Graham
  • Ann . N . Y . Acad . Sci .
  • 1985

A new bound for the Steiner ratio

  • D. Z. Du, F. K. Hwang
  • Trans . Amer . Math . Soc .
  • 1983

Steiner minimal trees and urban service networks , 3 "

  • D. Thomas
  • Soc . Econ . Plann .
  • 1982

Remarks on Steiner minimal trees , Bull

  • F. K. Hwang
  • Inst . Math . Acad . Sinica
  • 1976

Similar Papers

Loading similar papers…