Online Matching: A Brief Survey
Zhiyi Huang, Zhihao Gavin Tang, David Wajc
TL;DR
Online Matching: A Brief Survey surveys the landscape of online matching and ad allocation from adversarial and stochastic viewpoints, covering bipartite and generalized models, including fully online and reusable resources. It highlights core algorithms such as Ranking and Balance, and framework-driven approaches like Primal-Dual, Randomized Rounding, OCRS, and OCS, detailing proven ratios such as $1-1/e$ in classic settings and breakthroughs beyond $1/2$ via OCS. The survey also connects online matching to mechanism design through prophet and philosopher inequalities, and reports state-of-the-art results and open gaps (e.g., achieving $1-1/e$ for display ads/AdWords, heterogeneous durations in reusable resources). It emphasizes practical relevance to online markets (ads, rides, crowdsourcing) and outlines a suite of techniques that unify theory across adversarial and stochastic regimes. Overall, the work maps a rich toolkit for designing and analyzing online allocation mechanisms with broad applicability and several key unresolved questions.
Abstract
Matching, capturing allocation of items to unit-demand buyers, or tasks to workers, or pairs of collaborators, is a central problem in economics. Indeed, the growing prevalence of matching-based markets, many of which online in nature, has motivated much research in economics, operations research, computer science, and their intersection. This brief survey is meant as an introduction to the area of online matching, with an emphasis on recent trends, both technical and conceptual.