We give an overview of new and existing cut- and flow-based ILP formulations for the two-stage stochastic Steiner tree problem and compare the strength of the LP relaxations.
This issue’s column is written by guest columnists, David Shmoys and Chaitanya Swamy. Iam delighted that they agreed to write this timely column on the topic related to stochasticoptimization that has received much attention recently. Their column introduces the readerto several recent results and provides references for further readings.Samir Khuller We study two-stage, finite-scenario stochastic versions of several combinatorial optimization problems, and provide nearly tight approximation algorithms for them. Our problems range from the graph-theoretic (shortest path, vertex cover, facility location) to set-theoretic (set cover, bin packing), and contain representatives with different approximation ratios.The approximation ratio of the stochastic variant of a typical problem is found to be of the same order of magnitude as its deterministic counterpart. Furthermore, we show that common techniques for designing approximation algorithms such as LP rounding, the primal-dual method, and the greedy algorithm, can be adapted to obtain these results.