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Brazil, M.; Rubinstein, J. H.; Thomas, D. A.; Weng, J. F.; Wormald, N. C.

Full minimal Steiner trees on lattice sets. (English) Zbl 0874.05018

J. Comb. Theory, Ser. A 78, No. 1, 51-91 (1997).
Given a finite set of points in Euclidean plane, the Steiner tree problem is to find a shortest network interconnecting the points in the set. The authors determine the Steiner minimum tree for \(n\times n\) integer lattice points. This solves an open problem posed by F. Chung, M. Gardner and R. Graham [Math. Mag. 62, No. 2, 83-96 (1989; Zbl 0681.05018)].
Reviewer: Du Ding-Zhu (Minneapolis)

Cited in 1 Review
Cited in 4 Documents

MSC:

05C05 Trees

Keywords:

Steiner tree; lattice points

Citations:

Zbl 0681.05018
Cite Review PDF
Full Text: DOI

References:

[1] Brazil, M.; Cole, T.; Rubinstein, J. H.; Thomas, D. A.; Weng, J. F.; Wormald, N. C., Minimal Steiner trees for \(2^k\)×\(2^k\) square lattices, J. Combin. Theory Ser. A, 73, 91-110 (1996) · Zbl 0844.05036
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