Abstract
We consider the MaximumInternalSpanningTree problem which is to find a spanning tree of a given graph with a maximum number of non-leaf nodes. From an optimization point of view, this problem is equivalent to the MinimumLeafSpanningTree problem, and is NP-hard as being a generalization of the HamiltonianPath problem. Although there is no constant factor approximation for the MinimumLeafSpanningTree problem [1], MaximumInternalSpanningTree can be approximated within a factor of 2 [2].
In this paper we improve this factor by giving a \(\frac{7}{4}\)-approximation algorithm. We also investigate the node-weighted case, when the weighted sum of the internal nodes is to be maximized. For this problem, we give a (2Δ− 3)-approximation for general graphs, and a 2-approximation for claw-free graphs. All our algorithms are based on local improvement steps.
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References
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Salamon, G. (2007). Approximation Algorithms for the Maximum Internal Spanning Tree Problem. In: Kučera, L., Kučera, A. (eds) Mathematical Foundations of Computer Science 2007. MFCS 2007. Lecture Notes in Computer Science, vol 4708. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74456-6_10
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DOI: https://doi.org/10.1007/978-3-540-74456-6_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74455-9
Online ISBN: 978-3-540-74456-6
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