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

Abstract: This paper studies a 4-approximation algorithm for k-prize collecting Steiner tree problems. This problem generalizes both k-minimum spanning tree problems and prize collecting Steiner tree problems. Our proposed algorithm employs two 2-approximation algorithms for k-minimum spanning tree problems and prize collecting Steiner tree problems. Also our algorithm framework can be applied to a special case of k-prize collecting traveling salesman problems.