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Approximation Algorithms for the Maximum Internal Spanning Tree Problem

  • Gábor Salamon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4708)

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.

Keywords

Approximation algorithm Spanning tree leaves Hamiltonian path 

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References

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    Salamon, G., Wiener, G.: Leaves of spanning trees and vulnerability. In: The 5th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications, pp. 225–235 (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Gábor Salamon
    • 1
  1. 1.Department of Computer Science and Information Theory, Budapest University of Technology and Economics, 1117 Budapest, Magyar tudósok körútja 2Hungary

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