Abstract
We examine the problem of determining a spanning tree of a given graph such that the number of internal nodes is maximum. The best approximation algorithm known so far for this problem is due to Prieto and Sloper and has a ratio of 2. For graphs without pendant nodes, Salamon has lowered this factor to $\frac{7}{4}$ by means of local search. However, the approximative behaviour of his algorithm on general graphs has remained open. In this paper we show that a simplified and faster version of Salamon's algorithm yields a $\frac{5}{3}$ -approximation even on general graphs. In addition to this, we investigate a node weighted variant of the problem for which Salamon achieved a ratio of 2?Δ(G)?3. Extending Salamon's approach we obtain a factor of 3+∈ for any ∈>0. We complement our results with worst case instances showing that our analyses are tight.
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