Robust Combinatorial Optimization with Exponential Scenarios

Following the well-studied two-stage optimization framework for stochastic optimization [15, 18], we study approximation algorithms for robust two-stage optimization problems with an exponential number of scenarios. Prior to this work, Dhamdhere et al. [8] introduced approximation algorithms for two-stage robust optimization problems with explicitly given scenarios. In this paper, we assume the set of possible scenarios is given implicitly, for example by an upper bound on the number of active clients. In two-stage robust optimization, we need to pre-purchase some resources in the first stage before the adversary’s action. In the second stage, after the adversary chooses the clients that need to be covered, we need to complement our solution by purchasing additional resources at an inflated price. The goal is to minimize the cost in the worst-case scenario. We give a general approach for solving such problems using LP rounding. Our approach uncovers an interesting connection betwee...

• Type: Conference
• Year: 2007
• Where: IPCO
• Authors: Uriel Feige, Kamal Jain, Mohammad Mahdian, Vahab S. Mirrokni
• Keywords: Approximation Algorithms, IPCO 2007, Optimization, Two-stage Robust Optimization, first Stage