Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, February 22, 2005, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Abraham Flaxman (Carnegie Mellon Univ.)

Two stage stochastic programming on average: Minimum Spanning Trees

In real-life optimization, the costs and constraints are sometimes not known exactly. Stochastic programming is one approach used in these situations.

Designing minimum spanning trees is a classical problem in combinatorial optimization. A remarkable fact about average case minimum spanning trees is that when the cost of the edges between n nodes are selected independently and uniformly from [0,1], the cost of the MST converges to a constant, and the constant is ζ(3) = 1/1³ + 1/2³ + 1/3³ + ....

In the two-stage stochastic programming version of this problem, known are the costs of each edge on Monday and the distribution of the costs of each edge on Tuesday. The goal is to select a set of edges to buy on Monday so that when the tree is completed on Tuesday, the expected total cost is minimized.

This talk will focus on the two-stage version where the Monday and Tuesday costs are all selected independently and uniformly from [0,1]. In this case, a simple threshold heuristic produces a solution with expected cost ζ(3) - 1/2. This is not the optimal two-stage solution, however.

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