2-Approximation Algorithm for Finding a Spanning Tree with Maximum Number of Leaves
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
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)*
On finding spanning trees with few leaves
Information Processing Letters
Better Approximation Algorithms for the Maximum Internal Spanning Tree Problem
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
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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 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.