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

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.

[1]  Naveen Garg,et al.  Saving an epsilon: a 2-approximation for the k-MST problem in graphs , 2005, STOC '05.

[2]  Santosh S. Vempala,et al.  New Approximation Guarantees for Minimum-Weight k-Trees and Prize-Collecting Salesmen , 1999, SIAM J. Comput..

[3]  Egon Balas,et al.  The prize collecting traveling salesman problem , 1989, Networks.

[4]  Sanjeev Arora,et al.  A 2 + ɛ approximation algorithm for the k-MST problem , 2000, SODA '00.

[5]  Giorgio Ausiello,et al.  Prize Collecting Traveling Salesman and Related Problems , 2018, Handbook of Approximation Algorithms and Metaheuristics.

[6]  Santosh S. Vempala,et al.  A Constant-Factor Approximation Algorithm for the k-MST Problem , 1999, J. Comput. Syst. Sci..

[7]  Santosh S. Vempala,et al.  A constant-factor approximation for the k-MST problem in the plane , 1995, STOC '95.

[8]  Jens Vygen,et al.  The Book Review Column1 , 2020, SIGACT News.

[9]  David P. Williamson,et al.  A general approximation technique for constrained forest problems , 1992, SODA '92.

[10]  Mohammad Taghi Hajiaghayi,et al.  Improved Approximation Algorithms for PRIZE-COLLECTING STEINER TREE and TSP , 2009, 2009 50th Annual IEEE Symposium on Foundations of Computer Science.

[11]  Naveen Garg,et al.  A 3-approximation for the minimum tree spanning k vertices , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[12]  Dachuan Xu,et al.  A 5-approximation algorithm for the k-prize-collecting Steiner tree problem , 2019, Optim. Lett..

[13]  R. Ravi,et al.  Spanning trees short or small , 1994, SODA '94.

[14]  Sanjeev Arora,et al.  A 2+epsilon approximation algorithm for the k-MST problem , 2000, SODA.

[15]  Matteo Fischetti,et al.  Weighted k-cardinality trees: Complexity and polyhedral structure , 1994, Networks.