Hedging Uncertainty: Approximation Algorithms for Stochastic Optimization Problems

We initiate the design of approximation algorithms for stochastic combinatorial optimization problems; we formulate the problems in the framework of two-stage stochastic optimization, and provide nearly tight approximation algorithms. Our problems range from the simple (shortest path, vertex cover, bin packing) to complex (facility location, set cover), and contain representatives with different approximation ratios. The approximation ratio of the stochastic variant of a typical problem is of the same order of magnitude as its deterministic counterpart. Furthermore, common techniques for designing approximation algorithms such as LP rounding, the primal-dual method, and the greedy algorithm, can be carefully adapted to obtain these results.