Problem
Research questions and friction points this paper is trying to address.
Online Bipartite Matching
Incentive Compatibility
Random Order
Competitive Ratio
Edge-Weighted Matching
Arrival-Time Incentive Compatibility in Random Order Online Bipartite Matching
🤖 AI Summary
This study addresses the joint optimization of arrival-time incentive compatibility and competitive ratio in online bipartite matching under the random order model. Motivated by scenarios where users solely seek service while the platform aims to maximize revenue, this work introduces prior probability equilibrium constraints and integrates linear programming-based secretary problem techniques with random-order online matching theory to effectively resolve the incentive compatibility challenge for edge-weighted matching in complete bipartite graphs. The primary contribution is the design of the first incentive-compatible algorithm achieving a constant competitive ratio, which provides rigorous competitive guarantees contingent upon an imbalance factor. Specifically, the proposed algorithm attains a competitive ratio of approximately 0.07 in binary-weight settings, establishing a foundational framework for jointly optimizing strategic behavior and algorithmic performance in online matching environments.
📝 Abstract
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).
Innovation
Methods, ideas, or system contributions that make the work stand out.
Incentive Compatibility
Online Bipartite Matching
Random Order
Competitive Algorithm
Secretary Problem
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