OFFSET
1,1
COMMENTS
The 1994 Bridge's paper entitled "Minimal Steiner Trees for Three Dimensional Networks" (see Links) suggested an optimal strategy to solve the minimum Steiner tree problem for the unit cube {0,1}^3, and the total length of the provided Steiner Tree is 1 + 3*sqrt(3).
LINKS
R. Bridges, Minimal Steiner Trees for Three Dimensional Networks, Math. Gaz., 78 (1994), 157-162.
Math Overflow, Joining the 2^k points of {0,1}^k with the shortest tree.
Mathematics Stack Exchange,, Steiner tree problem in 3D.
J. M. Smith, R. Weiss, and M. Patel, An O(N2) Heuristic for Steiner Minimal Trees in E3, Networks 26 (1995), 273-289.
B. Toppur and J. M. A. Smith, A Sausage Heuristic for Steiner Minimal Trees in Three-Dimensional Euclidean Space, J. Math. Modelling and Algorithms, 4 (2005), 199-217.
EXAMPLE
6.1961524227066318805823390245176171008284157614311418841674209383...
MATHEMATICA
RealDigits[3Sqrt[3]+1, 10, 87][[1]] (* Stefano Spezia, Jul 25 2024 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Marco Ripà, Jul 24 2024
STATUS
approved