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
Spanning trees with many leaves in regular bipartite graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Approximation algorithms for the maximum internal spanning tree problem
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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Given an undirected graph $G$, finding a spanning tree of $G$ with maximum number of leaves is NP-complete. We use the simple technique of local optimization to provide the first approximation algorithms for this problem. Our algorithms run in polynomial time to produce locally optimal solutions. We prove that locally optimal solutions to this problem are globally near-optimal. In particular, we prove that two such algorithms have performance ratios of 5 and 3. The latter algorithm employs more powerful local-improvement steps than the former and hence has higher running time. This may indicate an interesting trade-off between the performance ratios and the running times of the series of algorithms we describe.