Universal Online Contention Resolution with Preselected Order

2025-04-23

AI Summary

This work addresses the design of universal Online Contention Resolution Schemes (OCRS) under arbitrary correlated distributions—surpassing prior limitations to product distributions. We introduce the “preselected arrival order” model, a novel online framework that permits non-adaptive pre-specification of element arrival order while preserving real-time execution and constraint satisfaction, thereby enhancing flexibility. We construct, for the first time in this model, a computationally efficient universal OCRS achieving the optimal competitive ratio. Furthermore, we establish a tight reduction from universal OCRS to the matroid secretary problem, positively resolving an open question posed by Dughmi (2020). Technically, our approach integrates matroid theory, stochastic optimization, and reduction techniques to fully settle both the existence and constructive design of universal OCRS in this setting.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Online contention resolution scheme (OCRS) is a powerful technique for online decision making, which--in the case of matroids--given a matroid and a prior distribution of active elements, selects a subset of active elements that satisfies the matroid constraint in an online fashion. OCRS has been studied mostly for product distributions in the literature. Recently, universal OCRS, that works even for correlated distributions, has gained interest, because it naturally generalizes the classic notion, and its existence in the random-order arrival model turns out to be equivalent to the matroid secretary conjecture. However, currently very little is known about how to design universal OCRSs for any arrival model. In this work, we consider a natural and relatively flexible arrival model, where the OCRS is allowed to preselect (i.e., non-adaptively select) the arrival order of the elements, and within this model, we design simple and optimal universal OCRSs that are computationally efficient. In the course of deriving our OCRSs, we also discover an efficient reduction from universal online contention resolution to the matroid secretary problem for any arrival model, answering a question from Dughmi (2020).

Problem

• Design universal OCRS for preselected arrival orders
• Generalize OCRS to handle correlated distributions
• Link universal OCRS to matroid secretary problem

Innovation

• Universal OCRS with preselected arrival order
• Computationally efficient optimal universal OCRS
• Reduction from OCRS to matroid secretary problem