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arXiv · 2403.05378

Online Contention Resolution Schemes for Network Revenue Management and Combinatorial Auctions

Will Ma·Calum MacRury·Jingwei Zhang
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Abstract

We study the Network Revenue Management (NRM) and Online Combinatorial Auctions (OCA) problems, in which products composed of up to L resources are allocated in an online fashion. We take a randomized rounding approach to these problems, employing the modern tool of Online Contention Resolution Schemes (OCRS) and their random-order analogues (RCRS). However in NRM and OCA, there can be negative correlation in different products being demanded, making the standard definitions of OCRS/RCRS inapplicable. This motivates a new definition of random-element OCRS/RCRS, in which batches of elements arrive, and at most one element in each batch is demanded. We first establish a simple random-element OCRS for achieving the well-known guarantee of 1/(1+L). We then prove that this guarantee is a fundamental barrier---it is tight for all prime-power values of L, using a construction based on finite affine planes. Next, we break this barrier in several settings: the standard OCRS setting, on L-partite hypergraphs, and in the RCRS setting. The first setting importantly establishes a separation between standard and random-element OCRS, showing that the negative correlation between elements being demanded in random-element OCRS can actually worsen guarantees. We also establish a separation between standard and random-element RCRS. Although the general formulations of NRM and OCA require random-element OCRS, we also identify special cases in which standard OCRS or RCRS suffice. This includes establishing new reductions from NRM with Poisson arrivals to standard OCRS, and NRM with time-homogeneous Poisson arrivals to standard RCRS.

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Will Ma, Calum MacRury, Jingwei Zhang. 2024-03-08. Online Contention Resolution Schemes for Network Revenue Management and Combinatorial Auctions. https://arxiv.org/abs/2403.05378

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