A minimum spanning tree is a feasible but not usually optimal solution to the Steiner tree problem. The Steiner ratio is the largest possible ratio between the total length of a minimum spanning tree and the total length of a minimum Steiner tree.
In the metric Steiner tree problems, the Steiner ratio is 2. Therefore an algorithm that finds a minimum spanning tree is a polynomial-time factor-2 approximation algorithm for the metric Steiner tree problem.
In the Euclidean Steiner tree problem, the Steiner ratio is conjectured to be . Despite earlier claims of a proof, the conjecture is still open.
Read more about this topic: Steiner Tree Problem
Famous quotes containing the words steiner and/or ratio:
“To shoot a man because one disagrees with his interpretation of Darwin or Hegel is a sinister tribute to the supremacy of ideas in human affairs—but a tribute nevertheless.”
—George Steiner (b. 1929)
“People are lucky and unlucky not according to what they get absolutely, but according to the ratio between what they get and what they have been led to expect.”
—Samuel Butler (1835–1902)