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

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)].

MSC:

05C05 Trees

Citations:

Zbl 0681.05018
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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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