The Power of Local Optimizations: Approximation Algorithms for Maximun-leaf Spanning Tree (DRAFT)*
The Power of Local Optimizations: Approximation Algorithms for Maximun-leaf Spanning Tree (DRAFT)*
Approximate Local Search in Combinatorial Optimization
SIAM Journal on Computing
Reducing to independent set structure: the case of k-internal spanning tree
Nordic Journal of Computing
On finding spanning trees with few leaves
Information Processing Letters
Approximating the Maximum Internal Spanning Tree problem
Theoretical Computer Science
Approximation algorithms for the maximum internal spanning tree problem
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
A linear vertex kernel for maximum internal spanning tree
Journal of Computer and System Sciences
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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 + *** for any *** 0. We complement our results with worst case instances showing that our bounds are tight.