Bounding the Inefficiency via the Primal-Dual Method

The main tool used to show all the results in this book is the primal-dual method. Introduced by Bil`o [22], this framework is based on the construction and analysis of a primal-dual pair of linear programs, where the dual is used to provide tight (or almost tight) upper bounds on the performance guarantee of a certain efficiency metric, and the primal is used to construct tight (or almost tight) lower bounds.