随机顺序在线二分匹配中的到达时间激励相容性

中文摘要 AI 辅助

在这项工作中，我们开创了对具有到达时间激励相容性的随机顺序在线二分匹配竞争算法的研究，其背景是用户只关心是否获得服务（匹配成功或未匹配），而不关心哪个离线资源为其服务，而平台的目标是最大化总匹配收益。这涵盖了诸如拼车之类的应用，其中用户主要关心是否匹配到行程，而平台内部化派遣远处司机的成本；将同质服务请求分派给异构服务器（云/边缘路由）；以及将客户请求分配给具有不同灵活性的服务提供商池（例如，仅英语与双语代理）。我们的主要问题是：\textit{在完全二分图上，对于激励相容的随机顺序边加权匹配，是否存在常数竞争比的匹配算法？}受Buchbinder等人对经典秘书问题中激励相容性的基于LP的处理方法的启发，我们施加了一个约束，即选择的事前概率在所有到达位置上均等。我们对我们的主要问题给出了肯定回答，并提出了第一个针对完全二分图上激励相容的边加权随机顺序在线匹配的常数竞争比算法。我们算法的竞争比由不平衡因子$k:= n/m$参数化——其中$n$和$m$分别是在线和离线节点的数量，且$k$为正整数。特别地，我们获得了形如$c_k - O(1/\sqrt{m})$的竞争保证，其中$c_1 \approx 0.162$，且当$k \to \infty$时$c_k \to 0.02308\ldots$。我们还针对二元加权情况（$0$-$1$奖励）提出了竞争比严格改进为$\approx 0.07 + O(1/m)$的算法。

英文摘要

In this work we initiate the study of competitive algorithms with arrival-time incentive compatibility for random-order online bipartite matching in settings where the users care only about receiving service (matched vs. unmatched) and not which offline resource serves them, while the platform's objective is to maximize total matching reward. This captures applications such as ride-sharing where the users primarily care about being matched to a ride while the platform internalizes the cost of dispatching a distant driver; dispatching homogeneous service requests to heterogeneous servers (cloud/edge routing); and assigning customer requests to a pool of providers with different flexibility (e.g., English-only vs. bilingual agents). Our main question is: \textit{Is constant-competitive matching possible for incentive-compatible, random-order edge-weighted matching on complete bipartite graphs?} Motivated by the LP-based treatment of incentive compatibility in the classical secretary problem by Buchbinder et al., we impose a constraint that the ex ante probability of selection is equalized across all arrival positions. We answer our main question in the affirmative and propose the first constant-competitive algorithm for incentive compatible edge-weighted random-order online matching on complete bipartite graphs. The competitive ratio of our algorithm is parameterized by the imbalance factor $k := n/m$ -- where $n$ and $m$ are the numbers of online and offline nodes, respectively, and $k$ is a positive integer. In particular, we obtain a competitive guarantee of the form $c_k - O(1/\sqrt{m})$ where $c_1 \approx 0.162$ and $c_k \to 0.02308\ldots$ as $k \to \infty$. We also present algorithms with strictly improved competitive ratio of $\approx 0.07 + O(1/m)$ for the binary-weighted case ($0$-$1$ rewards).

发表机构

• Tata Institute of Fundamental Research（塔塔基础研究所）
• University of Utah（犹他大学）

机构由 AI 辅助整理，请以论文原文为准。

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Appearing in WINE 2026