LP rounding approximation algorithms for stochastic network design

Mathematics of Operations Research

Volumn 32, Issue 2, 2007, Pages 345-364

  Gupta, Anupam ^a   Ravi, R ^b   Sinha, Amitabh ^c  

^a Carnegie Mellon University   (United States)

^b CARNEGIE MELLON UNIVERSITY   (United States)

^c UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Approximation algorithm; LP rounding; Network design; Primal dual method; Steiner tree; Stochastic optimization

Indexed keywords

NETWORK DESIGN; PRIMAL DUAL METHOD; STEINER TREE;

APPROXIMATION ALGORITHMS; OPTIMIZATION; PROBLEM SOLVING; RANDOM PROCESSES; TREES (MATHEMATICS);

LINEAR PROGRAMMING;

EID: 38549176849     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1060.0237     Document Type: Article

References (29)

1. Agrawal, Ajit, Philip Klein, R. Ravi. 1995. When trees collide: An approximation algorithm for the generalized Steiner problem on networks. SIAM J. Comput. 24(3) 440-456. (Preliminary version in 23rd STOC, 1991.)
2. Awerbuch, Baruch, Yossi Azar. 1997. Buy-at-bulk network design. Proc. 38th Annual IEEE Sympos. Foundations Comput. Sci., Miami, FL, IEEE Computer Society, 542-547.
3. Beale, E. M. L. 1955. On minimizing a convex function subject to linear inequalities. J. Roy. Statist. Soc. Ser. B. 17 173-184; discussion, 194-203. (Symposium on linear programming.)
4. Birge, John R., François Louveaux. 1997. Introduction to Stochastic Programming. Springer Series in Operations Research. Springer-Verlag, New York.
5. Dantzig, George B. 1955. Linear programming under uncertainty. Management Sci. 1 197-206.
6. Dye, Shane, Leen Stougie, Asgeir Tomasgard. 2003. The stochastic single resource service-provision problem. Naval Res. Legist. 50(8) 869-887.
7. Garg, Naveen, Rohit Khandekar, Goran Konjevod, R. Ravi, F. Sibel Salman, Amitabh Sinha. 2001. On the integrality gap of a natural formulation of the single-sink buy-at-bulk network design formulation. Proc. 8th Integer Programming Combin. Optim. Conf., Utrecht, The Netherlands, Lecture Notes in Computer Science, Vol. 2081, Springer, 170-184.
8. Goemans, Michel X., David P. Williamson. 1995. A general approximation technique for constrained forest problems. SIAM J. Comput. 24(2) 296-317.
9. Guha, Sudipto, Adam Meyerson, Kamesh Mungala. 2001. A constant factor approximation for the single sink edge installation problems. Proc. 33rd Annual ACM Sympos. Theory Comput. (STOC), Crete, Greece, ACM Press, New York, 383-388.
10. Gupta, Anupam, Amit Kumar, Tim Roughgarden. 2003. Simpler and better approximation algorithms for network design. Proc. 35th Annual ACM Sympos. Theory Comput., San Diego, CA, ACM Press, New York, 365-372.
11. Gupta, Anupam, R. Ravi, Amitabh Sinha. 2004. An edge in time saves nine: LP rounding approximation algorithms for stochastic network design. Proc. 45th Annual IEEE Sympos. Foundations Comput. Sci., Rome, Italy, IEEE Computer Society, 218-227.
12. Gupta, Anupam, Martin Pál, R. Ravi, Amitabh Sinha. 2004. Boosted sampling: Approximation algorithms for stochastic optimization problems. Proc. 36th Annual ACM Sympos. Theory Comput., Chicago, IL, ACM Press, New York, 417-425.
13. Gupta, Anupam, Martin Pál, R. Ravi, Amitabh Sinha. 2005. What about Wednesday? Approximation algorithms for multistage stochastic optimization. Proc. 9th Internat. Workshop Approximation Algorithms Combin. Optim. Problems (APPROX), Berkeley, CA, Springer, 86-98.
14. Gupta, Anupam, Amit Kumar, Jon Kleinberg, Rajeev Rastogi, Bulent Yener. 2001. Provisioning a virtual private network: A network design problem for multicommodity flow. Proc. 33rd Annual ACM Sympos. Theory Comput., Crete, Greece, ACM Press, New York, 389-398.
15. Hassin, Refael, R. Ravi, F. S. Salman. 2000. Approximation algorithms for a capacitated network design problem. Internat. Workshop on Approximation Algorithms for Combin. Optim. Problems (APPROX), Saarbrücken, Germany, Springer, 167-176.
16. Hayrapetyan, Ara, Chaitanya Swamy, Éva Tardos. 2005. Network design for information networks. Proc. 15th Annual ACM-SIAM Sympos. Discrete Algorithms, Vancouver, Canada, SIAM, Philadelphia, PA, 933-942.
17. Immorlica, Nicole, David Karger, Maria Minkoff, Vahab Mirrokni. 2004. On the costs and benefits of procrastination: Approximation algorithms for stochastic combinatorial optimization problems. Proc. 15th Annual ACM-SIAM Sympos. Discrete Algorithms, New Orleans, LA, SIAM, Philadelphia, PA, 684-693.
18. Kall, Peter, Stein W Wallace. 1994. Stochastic Programming. Wiley-Interscience Series in Systems and Optimization. John Wiley & Sons Ltd., Chichester, UK.
19. Khuller, Samir, Balaji Raghavachari, Neal E. Young. 1995. Balancing minimum spanning and shortest path trees. Algorithmica 14(4) 305-322.
20. Klein Haneveld, Willem K., Maarten H. van der Vlerk. 1999. Stochastic integer programming: General models and algorithms. Ann. Oper. Res. 85 39-57.
21. Klein Haneveld, Willem K., Maarten H. van der Vlerk. 2003. Stochastic Programming. Department of Econometrics, University of Groningen, Netherlands.
22. Mansour, Yishay, David Peleg. 2000. An approximation algorithm for minimum-cost network design. Robust Communication Networks: Interconnection and Survivability (New Brunswick, NJ, 1998). DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 53. American Mathematical Society, Providence, RI, 97-106.
23. Ravi, R., F. S. Salman. 1999. Approximation algorithms for the traveling purchaser problem and its variants in network design. Algorithms-ESA '99 (Prague), Lecture Notes in Computer Science, Vol. 1643. Springer, Berlin, Germany, 29-40.
24. Ravi, R., Amitabh Sinha. 2006. Hedging uncertainty: Approximation algorithms for stochastic optimization problems. Math. Programming A 108(1) 97-114.
25. Robins, Gabriel, Alexander Zelikovsky. 2000. Improved Steiner tree approximation in graphs. Proc. 11th Annual ACM-SIAM Sympos. Discrete Algorithms, San Francisco, CA, SIAM, Philadelphia, PA, 770-779.
26. Salman, F. Sibel, Joseph Cheriyan, R. Ravi, Sairam Subramanian. 1997. Buy-at-bulk network design: Approximating the single-sink edge installation problem. Proc. 8th Annual ACM-SIAM Sympos. Discrete Algorithms, New Orleans, LA, SIAM, Philadelphia, PA, 619-628.
27. Shmoys, David, Chaitanya Swamy. 2004. Stochastic optimization is (almost) as easy as deterministic optimization. Proc. 45th Annual IEEE Sympos. Foundations of Comput. Sci., Rome, Italy, IEEE Computer Society, 228-237.
28. Talwar, Kunal. 2002. Single-sink buy-at-bulk LP has constant integrality gap. Proc. 9th Integer Programming Combin. Optim. Conf., Cambridge, MA, Lecture Notes in Computer Science, Vol. 2337, Springer, 475-486.
29. Vazirani, Vijay V. 2001. Approximation Algorithms. Springer-Verlag, Berlin, Germany.