Survivable network design with degree or order constraints

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2007, Pages 651-660

  Lau, Lap Chi ^a   Naor, Joseph ^b   Salavatipour, Mohammad R ^c   Singh, Mohit ^d  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b MICROSOFT RESEARCH   (United States)

^c UNIVERSITY OF ALBERTA   (Canada)

^d CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Approximation algorithms; Bounded degree; Iterative rounding; Network design; NP hard problems

Indexed keywords

BOUNDED DEGREE; ITERATIVE ROUNDING; NETWORK DESIGN;

APPROXIMATION ALGORITHMS; COMPUTATIONAL COMPLEXITY; ITERATIVE METHODS;

TREES (MATHEMATICS);

EID: 35449002005     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1250790.1250886     Document Type: Conference Paper

References (34)

1. B. Awerbuch, Y. Azar, A. Blum and S. Vempala, New approximation guarantees for minimum-weight k-trees and prize-collecting salesmen, SIAM J. Computing 28(1):254-262, 1999.
2. A. Blum, R. Ravi, and S. Vempala, A constant-factor approximation algorithm for the k-MST problem, J. Comput. Syst. Sci. 58(1): 101-108, 1999.
3. K. Chaudhuri, S. Rao, S. Riesenfeld, and K. Talwar, What would Edmonds do? Augmenting paths and witnesses for degree-bounded MSTs, In Proc. of APPROX 2005, pp. 26-39.
4. K. Chaudhuri, S. Rao, S. Riesenfeld, and K. Talwar. Push relabel and an improved approximation algorithm for the bounded-degree mst problem, In Proc. of ICALP 2006.
5. J.Cheriyan, Santosh Vempala and Adrian Vetta, Network design via iterative rounding of setpair relaxations, Combinatorica 26(3):255-275, (2006).
6. T. Feder, R. Motwani, and A. Zhu, k-Connected spanning subgraphs of low degree, ECCC report 41, 2006.
7. L. Fleischer, K. Jain and D.P. Williamson, Iterative rounding 2-approximation algorithms for minimum-cost vertex connectivity problems., J. Comput. Syst. Sci. 72(5):838-867, 2006.
8. M. Fürer and B. Raghavachari, An NC approximation algorithm for the minimum degree spanning tree problem, In Proc. of the 28th Annual Allerton Conf. on Commun., Control and Computing, pages 274-281, 1990.
9. M. Fürer and B. Raghavachari, Approximating the minimum-degree Steiner tree to within one of optimal, J. of Algorithms 17(3):409-423, 1994.
10. U. Feige, G. Kortsarz and D. Peleg, The Dense k-subgraph problem, Algorithmica, 29(3): 410-421, 2001. Preliminary version in the Proc. 34-th IEEE FOCS pp 692-701, 1993.
11. A. Frank, Kernel Systems of Directed Graphs, Acta Sci. Math (Szeged) 41:63-76, 1979.
12. N. Garg, A 3-Approximation for the minim tree spanning k vertices, In Proc. of the 37th IEEE FOCS, 302-309, 1996.
13. N. Garg, Saving an epsilon: a 2-approximation for the k-MSTproblem in graphs, In Proc. of the 37th STOC, 396-402, 2005.
14. M.X. Goemans, Minimum Bounded-Degree Spanning Trees, Proc. of the 47th Annual IEEE Symposium on Foundations of Computer Science, 2006, pp. 273-282.
15. M. Goemans and D. Williamson, A general Approximation Technique for Constrained Forest Problems, SIAM J. on Computing, 24:296-317, 1995.
16. M.Grötschel, L.Lovász and A.Schrijver, Geometric Algorithms and Combinatorial Optimization, Springer-Verlag, New York, 1988.
17. M. Hajiaghayi, G. Kortsarz and M. Salavatipour, Approximating Buy-at-Bulk and Shallow-light k-Steiner trees, In proceedings of APPROX 2006.
18. K.Jain, A factor 2 approximation algorithm for the generalized Steiner network problem, Combinatorica, 21:39-60, 2001.
19. P. Klein, R. Krishan, B. Raghavachari, and R. Ravi, Approximation algorithms for finding low-degree subgraphs, Networks, 44(3): 203-215, (2004).
20. J. Könemann and R. Ravi, Quasi-polynomial time approximation algorithm for low-degree minimum-cost steiner trees. In Proc. of the 23rd Conference on Foundations of Software Technology and Theoretical Computer Science, 2003.
21. J. Könemann and R. Ravi, A matter of degree: Improved approximation algorithms for degree bounded minimum spanning trees, SIAM J. on Computing, 31:1783-1793, 2002.
22. J. Könemann and R. Ravi, Primal-Dual meets local searchapproximating MSTs with nonuniform degree bounds, SIAM J. on Computing, 34(3):763-773, 2005.
23. G. Kortsarz, R. Krauthgamer, and J. Lee, Hardness of approximation for vertex-connectivity network design problems, SIAMJ. on Computing 33(3):704-720, 2003.
24. G. Kortsarz and Z. Nutov, Approximating min-cost connectivity problems, Survey Chapter in Approximation Algorithms and Metaheuristics, Editor T.F. Gonzalez, 2006.
25. N. Megiddo, Combinatorial Optimization with Rational Objective Functions, Mathematics of Operation Research, 4(4):414-424, 1979.
26. V. Melkonian and E. Tardos, Algorithms for a Network Design Problem with Crossing Supermodular Demands, Networks, 43(4):256-265, 2004.
27. R. Ravi, M.V. Marathe, S.S. Ravi, D.J. Rosenkrants, and H.B. Hunt, Many birds with one stone: Multi-objective approximation algorithms, in Proc. of the 25th STOC, pp 438-447, 1993.
28. R. Ravi, R. Sundaram, M.V. Marathe, D.J. Rosenkrants, and S.S. Ravi, Spanning trees short or small, SIAM Journal on Discrete Mathematics, 9(2): 178-200, 1996.
29. R. Ravi, M.V. Marathe, S.S. Ravi, D.J. Rosenkrants, and H.B. Hunt, Approximation Algorithms for degree-constrained minimum-cost network-design problems, Algorithmica 31:58-78, 2001.
30. R. Ravi, B. Raghavachari, and P. Klein, Approximation through local optimality: designing networks with small degree, In Proc. of the 12 Conference on Foundations of Sofware Tech. and Theoret. Comput. Sci., LNCS 652, pp 279-290, 1992.
31. R. Ravi and M. Singh, Delegate and conquer: An LP-based approximation algorithm for minimum degree MSTs. In Proc. of ICALP 2006.
32. A. Schrijver, Combinatorial Optimization - Polyhedra and Efficiency, Springer-Verlag, New York, 2005. Approximation
33. M. Singh, L.C. Lau, Approximating Minimum Bounded Degree Spanning Trees to within One of Optimal, In Proc. of the 39th STOC, 2007.
34. V. Vazirani, Approximation Algorithms, Springer, 2001.