Approximation algorithm for the group Steiner network problem

Networks

Volumn 49, Issue 2, 2007, Pages 160-167

  Penn, Michal ^a   Rozenfeld, Stas ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Approximation algorithm; Group Steiner network; Integer and linear programming

Indexed keywords

COST FUNCTIONS; GRAPHIC METHODS; INTEGER PROGRAMMING; LINEAR PROGRAMMING; PARAMETER ESTIMATION; PROBLEM SOLVING;

APPROXIMATION RATIOS; GROUP STEINER NETWORKS;

APPROXIMATION ALGORITHMS;

EID: 34250630517     PISSN: 00283045     EISSN: 10970037     Source Type: Journal    
DOI: 10.1002/net.20151     Document Type: Article

References (25)

1. R.H. Cardwell, C.L. Monma, and T.H. Wu, Computer-aided design procedures for survivable fiber optic networks, IEEE J Selected Areas Commun 7 (1989), 1188-1197.
2. C. Chekuri, G. Even, and G. Kortsarz, A combinatorial approximation algorithm for the group Steiner problem, Discrete Appl Math 154 (2006), 15-34.
3. M. Dror and M. Haouari, Generalized Steiner problem and other variants. J Combin Optimizat 4 (2000), 415-436.
4. M. Dror, M. Haouari, and J. Chaouachi, Generalized spanning trees. E J Oper Res 120 (2000), 583-592.
5. C. Feremans, M. Labbe, and G. Laporte, Generalized network design problems. E J Oper Res 148 (2003), 1-13.
6. N. Garg, G. Konjevod, and R. Ravi, A polylogarithmic algorithm for the group Steiner tree problem, J Algorithms 37 (2000), 66-84.
7. M.X. Goemans and D.J. Bertsimans, Survivable networks, linear programming relaxation and the parsimonious property, Math Program 60 (1993), 145-166.
8. M.X. Goemans, A.V. Goldberg, S. Plotkin, D.B. Shmoys, E. Tardos, and D.P. Williamson, Improved approximation algorithms for network design problems. Proc. 5th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 1994, pp. 223-232 (http://www.nada.kth.se/viggo/wwwcompendium/ node275.html).
9. M.X. Goemans and D.P. Williamson, A general approximation techniques for constrained forest problems, SIAM J Comput 24 (1995), 296-317.
10. B. Golden, S. Raghavan, and D. Stanojevic Heuristic search for the Generalized Minimum Spanning Tree Problem, IN-FORMS J Comput 17 (2005), 290-304.
11. M. Grötschel, L. Lovász, and A. Schrijver, Geometric algorithms and combinatorial optimization, Springer-Verlag, Berlin, 1988.
12. M. Grötschel, C.L. Monma, and M. Stoer, "Design of survivable networks," Handbook in operations research and management science, M.O. Ball, T.L. Magnanti, C.L. Monma, and G.L. Nemhauser (Editors), Vol. 7, Elsevier, Amsterdam, The Netherlands, 1995.
13. A. Gupta and A. Srinivasan, On the covering Steiner problem, FSTTCS, 2003, 244-251.
14. E. Halperin, G. Kotsarz, R. Krauthgamer, A. Srinivasand, and N. Wang, Integrality ratio for group Steiner trees and directed Steiner trees, ACM-SIAM Sympo Discrete Algorithms, 2003.
15. E. Halperin and R. Krauthgamer, Polylogarithmic inapproximability, STOC, 2003, 585-594.
16. C.S. Helving, G. Robins, and A. Zelikovsky, "Improved approximation bounds for the group Steiner problem," Conf on Design Automation and Test in Europe (DATE'98), 1998.
17. K. Jain, A factor 2 approximation algorithm for the generalized Steiner network problem, Combinatorica 1 (2001), 39-60.
18. G. Konjevod, R. Ravi, and A. Srinivasan, Approximation algorithms for the covering Steiner problem, Probab Methods Comb Optimizat 20 (2002), 465-482.
19. C.L. Monma and C.W. Ko, Methods for designing survivable communication networks, NATO Adv Res Workshop, 1989.
20. C.L. Monma and D.F. Shallcross, Methods for designing communication networks withcertain two-connected survivability constraints. Oper Res 37 (1989), 531-541.
21. Y.-S. Myulg, C.-H. Lee, and D.-W. Tcha, On the generalized minimum spanning tree problem, Networks 26 (1995), 231-241.
22. P.C. Pop, The generalized minimum spanning tree problem, Ph.D. thesis, Department of Operations Research and Mathematical Programming, University of Twente, Enschede, The Netherlands, 2002.
23. P.C. Pop, W. Kern, and G.J. Still, An approximation algorithm for the generalized minimum spanning tree problem with bounded cluster size, Working paper, Department of Operations Research and Mathematical Programming, University of Twente, 2001 (http://www.math.utwente.nl/dos/ ormp/preprints.htm).
24. G. Reich and P. Widmayer, Beyond Steiner's problem: A VLSI oriented generalization, Lecture Notes Comput Sci 411 (1989), 196-211.
25. S. Rozenfeld, An approximation algorithm for the group Steiner network problem. M.Sc. Thesis, Faculty of Industrial Engineering and Management, Technion, Haifa, Israel, 2003 (in Hebrew).