Abstract
A Steiner tree is a tree interconnecting a given set of points in a metric space such that all leaves are given points. A (full) component of a Steiner tree is a subtree which results from splitting the Steiner tree at some given points. A k-size Steiner tree is a Steiner tree in which every component has at most k given points. The k-Steiner ratio is the largest lower bound for the ratio between lengths of a minimum Steiner tree and a minimum k-size Steiner tree for the same set of points. In this paper, we determine the 3-Steiner ratio in weighted graphs.
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