Optimization Letters

, Volume 13, Issue 2, pp 341–348 | Cite as

A 4-approximation algorithm for k-prize collecting Steiner tree problems

  • Yusa Matsuda
  • Satoshi TakahashiEmail author
Original Paper


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.


Approximation algorithm Primal-dual algorithm k-prize collecting Steiner tree problems k-prize collecting traveling salesman problems 



We thank one anonymous reviewer for very valuable feedback. This research was partially supported by the Ministry of Education, Science, Sports and Culture through Grants-in-Aid for Scientific Research (C) 26330025, (B) 15H02972, and through Grants-in-Aid for Young Scientists (B) 26870200.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.The University of Electro-CommunicationsChofuJapan

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