no. 3
Constrained Steiner trees in Halin graphs
RAIRO - Operations Research - Recherche Opérationnelle, Tome 37 (2003) no. 3, pp. 179-194

In this paper, we study the problem of computing a minimum cost Steiner tree subject to a weight constraint in a Halin graph where each edge has a nonnegative integer cost and a nonnegative integer weight. We prove the NP-hardness of this problem and present a fully polynomial time approximation scheme for this NP-hard problem.

DOI : 10.1051/ro:2003020
Keywords: Steiner trees, Halin graph, approximation scheme 
@article{RO_2003__37_3_179_0,
     author = {Chen, Guangting and Burkard, Rainer E.},
     title = {Constrained {Steiner} trees in {Halin} graphs},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {179--194},
     year = {2003},
     publisher = {EDP Sciences},
     volume = {37},
     number = {3},
     doi = {10.1051/ro:2003020},
     mrnumber = {2034538},
     zbl = {1039.05058},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ro:2003020/}
}
TY  - JOUR
AU  - Chen, Guangting
AU  - Burkard, Rainer E.
TI  - Constrained Steiner trees in Halin graphs
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2003
SP  - 179
EP  - 194
VL  - 37
IS  - 3
PB  - EDP Sciences
UR  - https://www.numdam.org/articles/10.1051/ro:2003020/
DO  - 10.1051/ro:2003020
LA  - en
ID  - RO_2003__37_3_179_0
ER  - 
%0 Journal Article
%A Chen, Guangting
%A Burkard, Rainer E.
%T Constrained Steiner trees in Halin graphs
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2003
%P 179-194
%V 37
%N 3
%I EDP Sciences
%U https://www.numdam.org/articles/10.1051/ro:2003020/
%R 10.1051/ro:2003020
%G en
%F RO_2003__37_3_179_0
Chen, Guangting; Burkard, Rainer E. Constrained Steiner trees in Halin graphs. RAIRO - Operations Research - Recherche Opérationnelle, Tome 37 (2003) no. 3, pp. 179-194. doi: 10.1051/ro:2003020

[1] G. Chen and G. Xue, A PTAS for weight constrained Steiner trees in series-parallel graphs. Springer-verlag, Lecture Notes in Comput. Sci. 2108 (2001) 519-528. | Zbl | MR

[2] G. Chen and G. Xue, K-pair delay constrained minimum cost routing in undirected networks. Proc. of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (2001) 230-231. | Zbl | MR

[3] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of P-Completeness. San Francisco, W.H. Freeman and Company (1979). | Zbl | MR

[4] R. Hassin, Approximation schemes for the restricted shortest path problem. Math. Oper. Res. 17 (1992) 36-42. | Zbl | MR

[5] F.K. Hwang and D.S. Richards, Steiner tree problems. Networks 22 (1992) 55-89. | Zbl | MR

[6] F.K. Hwang, D.S. Richards and P. Winter, The Steiner tree problem. Ann. Discrete Math. 53 (1992) 68-71. | Zbl | MR

[7] T. Jiang and L. Wang, Computing shortest networks under a fixed topology, in Advances in Steiner Trees, edited by D.-Z. Du, J.M. Smith and J. H. Rubinstein. Kluwer Academic Publishers (2000) 39-62. | Zbl | MR

[8] D.H. Lorenz and D. Raz, A simple efficient approximation scheme for the restricted shortest path problem. Oper. Res. Lett. 28 (2001) 213-219. | Zbl | MR

[9] P. Winter, Steiner problem in Halin networks. Discrete Appl. Math. 17 (1987) 281-294. | Zbl | MR

[10] P. Winter, Steiner problem in networks - a survey. Networks 17 (1987) 129-167. | Zbl | MR

Cité par Sources :