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This paper studies a 4-approximation algorithm for k-prize collecting Steinertree problems. This problem generalizes both k-minimum spanning tree problemsand prize collecting Steiner tree problems. Our proposed algorithm employs two2-approximation algorithms for k-minimum spanning tree problems and prizecollecting Steiner tree problems. Also our algorithm framework can be appliedto a special case of k-prize collecting traveling salesman problems.

A 4-Approximation Algorithm for k-Prize Collecting Steiner Tree Problems