Primal beats dual on online packing LPs in the random-order model

Abstract

We study packing LPs in an online model where the columns are presented to the algorithm in random order. This natural problem was investigated in various recent studies motivated, e.g., by online ad allocations and yield management where rows correspond to resources and columns to requests specifying demands for resources. Our main contribution is a 1 -- O(√(log d/B))-competitive online algorithm. Here d denotes the column sparsity, i.e., the maximum number of resources that occur in a single column, and B denotes the capacity ratio B, i.e., the ratio between the capacity of a resource and the maximum demand for this resource. In other words, we achieve a (1--ε)-approximation if the capacity ratio satisfies B=Ω(logd/ε2), which is known to be best-possible for any (randomized) online algorithms.