Date of Original Version

7-22-2014

Type

Conference Proceeding

Rights Management

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-662-44777-2_43

Abstract or Description

We consider the problem of solving packing/covering LPs online, when the columns of the constraint matrix are presented in random order. This problem has received much attention: the main open question is to figure out how large the right-hand sides of the LPs have to be (compared to the entries on the left-hand side of the constraint) to get (1 + ε)-approximations online? It is known that the RHS has to be Ω(ε − 2 logm) times the left-hand sides, where m is the number of constraints.

In this paper we show how to achieve this bound for all packing LPs, and also for a wide class of mixed packing/covering LPs. Our algorithms construct dual solutions using a regret-minimizing online learning algorithm in a black-box fashion, and use them to construct primal solutions. The adversarial guarantee that holds for the constructed duals help us to take care of most of the correlations that arise in the algorithm; the remaining correlations are handled via martingale concentration and maximal inequalities. These ideas lead to conceptually simple and modular algorithms, which we hope will be useful in other contexts.

DOI

10.1007/978-3-662-44777-2_43

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Published In

Lecture Notes in Computer Science, 8737, 517-529.