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 \(\frac{\zeta(3)}{4}+o(1)\).
Supported in part by NSF grant CCR-0105548 and ITR grant CCR-0122581 (The ALADDIN project).
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Dhamdhere, K., Ravi, R., Singh, M. (2005). On Two-Stage Stochastic Minimum Spanning Trees. In: Jünger, M., Kaibel, V. (eds) Integer Programming and Combinatorial Optimization. IPCO 2005. Lecture Notes in Computer Science, vol 3509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496915_24
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DOI: https://doi.org/10.1007/11496915_24
Publisher Name: Springer, Berlin, Heidelberg
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