Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**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.)

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) = 1/1 ^{3}
+ 1/2^{3} + 1/3^{3} + ....*

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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