Online Advertising with Spatial Interactions
Gagan Aggarwal, Yifan Wang, Mingfei Zhao
TL;DR
The paper develops a principled framework for online ad allocation that accounts for spatial externalities by modeling ad slots as points in a metric space and introducing two canonical discount rules, δ_{ ext{min}} and δ_{ ext{mul}}. It provides algorithmic and mechanism-design guarantees under the two models: a constant-factor, monotone allocation for the Nearest-Neighbor model, with LP-rounding and Myerson-style truthfulness; plus a PTAS for 2D Euclidean space in the unweighted case, and scalable simple auctions for factorized or stochastic valuations. In contrast, the Product-Distance model is shown to be intractable to approximate within any polynomial factor (unless P=NP) via a reduction from Max-Independent-Set, highlighting a fundamental hardness gap between local and global spatial interference. Overall, the work lays a foundation for designing efficient, truthful ad-allocation mechanisms that explicitly incorporate spatial crowding effects, bridging combinatorial optimization, geometry, and mechanism design.
Abstract
Online advertising platforms must decide how to allocate multiple ads across limited screen real estate, where each ad's effectiveness depends not only on its own placement but also on nearby ads competing for user attention. Such spatial externalities - arising from proximity, clutter, or crowding - can significantly alter welfare and revenue outcomes, yet existing auction and allocation models typically treat ad slots as independent or ordered along a single dimension. We introduce a new framework for spatial externalities in online advertising, in which the value of an ad depends on both its slot and the configuration of surrounding ads. We model ad slots as points in a metric space, and model an advertiser's value as a function of both their bid and a discount factor determined by the configuration of other displayed ads. Within this framework, we analyze two natural models. For the Nearest-Neighbor model, where the value suppression depends only on the closest neighboring ad, we present a polynomial-time algorithm that achieves a constant approximation for the general case. We show that the allocation rule is monotone and can be implemented as a truthful mechanism. For a structured setting of 2D Euclidean space, we provide a PTAS. In contrast, for the Product-Distance model, where interference is aggregated multiplicatively across all neighbors, we establish a strong (and nearly-tight) hardness of approximation - no polynomial-time algorithm can achieve any polynomial-factor approximation unless P=NP, via a reduction from Max-Independent-Set. Our results provide a foundation for reasoning about spatial externalities in ad allocation and for designing efficient, truthful mechanisms under such interactions.