On Two-Stage Stochastic Minimum Spanning Trees

  • Kedar Dhamdhere
  • R. Ravi
  • Mohit Singh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3509)

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 \(\frac{\zeta(3)}{4}+o(1)\).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Kedar Dhamdhere
    • 1
  • R. Ravi
    • 2
  • Mohit Singh
    • 2
  1. 1.Dept. of Computer ScienceCarnegie Mellon UniversityPittsburghUSA
  2. 2.Tepper School of BusinessCarnegie Mellon UniversityPittsburghUSA

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