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 \(\frac74\) 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 \(\frac53\)-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. Modifying Salamon’s approach we obtain a factor of 3 + ε for any ε> 0. We complement our results with worst case instances showing that our bounds are tight.
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Knauer, M., Spoerhase, J. (2009). Better Approximation Algorithms for the Maximum Internal Spanning Tree Problem. In: Dehne, F., Gavrilova, M., Sack, JR., Tóth , C.D. (eds) Algorithms and Data Structures. WADS 2009. Lecture Notes in Computer Science, vol 5664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03367-4_40
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DOI: https://doi.org/10.1007/978-3-642-03367-4_40
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