Edge-weighted Matching in the Dark
Abstract
We present a -competitive Quadratic Ranking algorithm for the Oblivious Bipartite Matching problem, a distribution-free version of Query-Commit Matching. This result breaks the barrier, addressing an open question raised by Tang, Wu, and Zhang (JACM 2023). Moreover, the competitive ratio of this distribution-free algorithm improves the best existing ratio for Query-Commit Matching achieved by the distribution-dependent algorithm of Chen, Huang, Li, and Tang (SODA 2025). Quadratic Ranking is a novel variant of the classic Ranking algorithm. We parameterize the algorithm with two functions, and let two key expressions in the definition and analysis of the algorithm be quadratic forms of the two functions. We show that the quadratic forms are the unique choices that satisfy a set of natural properties. Further, they allow us to optimize the choice of the two functions using powerful quadratic programming solvers.
Cite
@article{arxiv.2507.19366,
title = {Edge-weighted Matching in the Dark},
author = {Zhiyi Huang and Enze Sun and Xiaowei Wu and Jiahao Zhao},
journal= {arXiv preprint arXiv:2507.19366},
year = {2025}
}