Sub-optimality approximations

Abstract

The sub-optimality approximation problem considers an optimization problem script O sign, its optimal solution σ*, and a variable x with domain {d1, . . . , dm} and returns approximations to script O sign[x ← d1], . . . , script O sign[x ← dm], where script O sign[x ← d1] denotes the problem script O sign with x assigned to di. The sub-optimality approximation problem is at the core of online stochastic optimization algorithms and it can also be used for solution repair and approximate filtering of optimization constraints. This paper formalizes the problem and presents sub-optimality approximation algorithms for metric TSPs, packet scheduling, and metric k-medians that run faster than the optimal or approximation algorithms. It also presents results on the hardness/easiness of sub-optimality approximations. © Springer-Verlag Berlin Heidelberg 2005.