Online Primal-Dual Algorithms for Covering and Packing Problems

We study a wide range of online covering and packing optimization problems. In an online covering problem a linear cost function is known in advance, but the linear constraints that define the feasible solution space are given one by one in an online fashion. In an online packing problem the profit function as well as the exact packing constraints are not fully known in advance. In each round additional information about the profit function and the constraints is revealed. We provide general deterministic primal-dual schemes for online fractional covering and packing problems. We also provide deterministic algorithms for several integral online covering and packing problems. Our scheme is designed via a novel primal-dual technique that extends the scheme used for many offline optimization problems. Recently, it was shown that this general primal-dual framework is useful for capturing many more online problems. We list several of the later results that follow from this approach.