A374948 Decimal expansion of the Euclidean length of the minimum Steiner tree joining all the vertices of a unit cube.

6, 1, 9, 6, 1, 5, 2, 4, 2, 2, 7, 0, 6, 6, 3, 1, 8, 8, 0, 5, 8, 2, 3, 3, 9, 0, 2, 4, 5, 1, 7, 6, 1, 7, 1, 0, 0, 8, 2, 8, 4, 1, 5, 7, 6, 1, 4, 3, 1, 1, 4, 1, 8, 8, 4, 1, 6, 7, 4, 2, 0, 9, 3, 8, 3, 5, 5, 7, 9, 9, 0, 5, 0, 7, 2, 6, 4, 0, 0, 1, 1, 1, 2, 4, 3, 4, 3

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 lenght of the provided Steiner Tree is 1 + 3*sqrt(3).

Links

Table of n, a(n) for n=1..87.

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.

Formula

Equals 3*sqrt(3) + 1.

Equals A010482(n) for any n >= 2 and a(1) = A010482(1) + 1.

Example

6.1961524227066318805823390245176171008284157614311418841674209383...

Mathematica

RealDigits[3Sqrt[3]+1, 10, 87][[1]] (* Stefano Spezia, Jul 25 2024 *)

Crossrefs

Cf. A002194, A010482, A374148, A374260.

Essentially the same as A178809, A176532 and A010482.

Sequence in context: A245724 A021908 A093358 * A155079 A153608 A364618

Adjacent sequences: A374945 A374946 A374947 * A374949 A374950 A374951

Keyword

nonn,cons,new

Author

Marco Ripà, Jul 24 2024

Status

approved