Year: 2026
Type: preprint
Abstract: We study edge-weighted online bipartite matching under random arrival order, parameterized by the maximum offline degree $d$ and sampling fraction $θ$. We analyze two sampling-based frameworks. For \emph{Deterministic Greedy Sampling}, which computes prices from a fixed-size initial sample and then applies a local threshold rule, we derive an explicit worst-case competitive ratio and prove it tight within this policy family for every fixed $d\ge2$ and $θ\in[0,1]$. The optimal sampling choice interpolates between no sampling for $d=1,2$ and a dense-limit guarantee of approximately $0.2562$, improving on the classical $1/8$ analysis while retaining linear per-arrival time. We also derive worst-case bounds on the variance of the number of matched offline agents, including order-tight behavior as $θ\to1_-$ and an $O(θ)$ bound as $θ\to0_+$ for fixed $m,d$. For \emph{Black-Box Sampling--Matching}, we introduce prefix-dependent reweighting followed by an arbitrary approximate offline matching solver and prove a transfer theorem whose guarantee is the offline approximation ratio times an explicit function of $d$ and $θ$. With exact matching, the framework recovers the classical $1/e$ guarantee in the unbounded-degree limit.
Source: arXiv (Cornell University)
Author: Xu, Pan
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Award: G6671297155
OpenAlex ID: W7213364508
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