General Framework of Stochastic Combinatorial Optimization Problems with Queries

Abstract

Many combinatorial problems that arises from real-world applications contain uncertainty in its parameters. The framework called the optimization with queries handles the uncertainty by modeling the parameters drawn from stochastic distributions, and conducting queries to reveal these realized values. The objective of this framework is to obtain high-quality solutions by conducting a small number of queries. In this paper, we introduce a general framework to derive efficient query strategies for packing-type combinatorial optimization problems. The main technique used in our framework is called the witness cover, that is a combination of linear programming duality and counting argument.