Online Contention Resolution Schemes

TL;DR

This paper introduces online contention resolution schemes (OCRSs), a new rounding technique for online optimization that handles complex constraints, improves existing methods, and resolves open problems in online selection and stochastic probing.

Contribution

The paper develops OCRSs applicable to various online problems, enabling combination for intersecting constraints and providing the first constant-factor solutions for specific online mechanisms.

Findings

OCRSs can be combined for intersecting constraints.

Achieved the first constant-factor oblivious posted price mechanism for matroids.

Provided the first constant-factor algorithm for weighted stochastic probing with deadlines.

Abstract

We introduce a new rounding technique designed for online optimization problems, which is related to contention resolution schemes, a technique initially introduced in the context of submodular function maximization. Our rounding technique, which we call online contention resolution schemes (OCRSs), is applicable to many online selection problems, including Bayesian online selection, oblivious posted pricing mechanisms, and stochastic probing models. It allows for handling a wide set of constraints, and shares many strong properties of offline contention resolution schemes. In particular, OCRSs for different constraint families can be combined to obtain an OCRS for their intersection. Moreover, we can approximately maximize submodular functions in the online settings we consider. We, thus, get a broadly applicable framework for several online selection problems, which improves on previous approaches in terms of the types of constraints that can be handled, the objective functions that can be dealt with, and the assumptions on the strength of the adversary. Furthermore, we resolve two open problems from the literature; namely, we present the first constant-factor constrained oblivious posted price mechanism for matroid constraints, and the first constant-factor algorithm for weighted stochastic probing with deadlines.