On two-stage stochastic minimum spanning trees

  • Authors:

  • Kedar Dhamdhere;R. Ravi;Mohit Singh

  • Affiliations:

  • Dept. of Computer Science, Carnegie Mellon University, Pittsburgh, PA;Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA;Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA

  • Venue:
  • IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
  • Year:
  • 2005

Quantified Score

Hi-index 0.01

Visualization

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