Integer Programming and Combinatorial Optimization
Volume 3509 of the series Lecture Notes in Computer Science pp 321-334
On Two-Stage Stochastic Minimum Spanning Trees
- Kedar DhamdhereAffiliated withDept. of Computer Science, Carnegie Mellon University
- , R. RaviAffiliated withTepper School of Business, Carnegie Mellon University
- , Mohit SinghAffiliated withTepper School of Business, Carnegie Mellon University
Abstract
We consider the undirected minimum spanning tree problem in a stochastic optimization setting. For the two-stage stochastic optimization formulation with finite scenarios, a simple iterative randomized rounding method on a natural LP formulation of the problem yields a nearly best-possible approximation algorithm.
We then consider the Stochastic minimum spanning tree problem in a more general black-box model and show that even under the assumptions of bounded inflation the problem remains log n-hard to approximate unless P = NP; where n is the size of graph. We also give approximation algorithm matching the lower bound up to a constant factor.
Finally, we consider a slightly different cost model where the second stage costs are independent random variables uniformly distributed between [0,1]. We show that a simple thresholding heuristic has cost bounded by the optimal cost plus \(\frac{\zeta(3)}{4}+o(1)\).
- Title
- On Two-Stage Stochastic Minimum Spanning Trees
- Book Title
- Integer Programming and Combinatorial Optimization
- Book Subtitle
- 11th International IPCO Conference, Berlin, Germany, June 8-10, 2005. Proceedings
- Pages
- pp 321-334
- Copyright
- 2005
- DOI
- 10.1007/11496915_24
- Print ISBN
- 978-3-540-26199-5
- Online ISBN
- 978-3-540-32102-6
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- 3509
- Series ISSN
- 0302-9743
- Publisher
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Topics
- Industry Sectors
- eBook Packages
- Editors
-
- Michael Jünger (16)
- Volker Kaibel (17)
- Editor Affiliations
-
- 16. Institut für Informatik, Universität zu Köln
- 17. Fakultät für Mathematik, Otto-von-Guericke Universität Magdeburg
- Authors
-
- Kedar Dhamdhere (18)
- R. Ravi (19)
- Mohit Singh (19)
- Author Affiliations
-
- 18. Dept. of Computer Science, Carnegie Mellon University, Pittsburgh, PA, 15213, USA
- 19. Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, 15213, USA
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