Efficient Interview Scheduling for Stable Matching

2026-02-23

AI Summary

This study addresses the challenge of efficiently achieving provisionally stable matchings in settings where agents’ preferences are initially unknown and must be revealed through costly interviews. The authors propose two adaptive interview scheduling algorithms: one purely sequential and another hybrid that integrates parallel and sequential strategies, both leveraging expected utility modeling within a deferred acceptance framework. Theoretical analysis establishes that, on average, each agent must participate in at least two interviews; the proposed sequential algorithm meets this lower bound exactly. Meanwhile, the hybrid algorithm achieves a comparable total number of interviews while reducing the expected number of rounds to polylogarithmic complexity, and guarantees that the resulting matching satisfies provisional stability.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The study of stable matchings usually relies on the assumption that agents'preferences over the opposite side are complete and known. In many real markets, however, preferences might be uncertain and revealed only through costly interactions such as interviews. We show how to reach interim-stable matchings, under which all matched pairs must have interviewed and agents use expected utilities whenever true values remain unknown, while minimizing both the expected number of interviews and the expected number of interview rounds. We introduce two adaptive algorithms that produce interim-stable matchings: one operates sequentially, and another is a hybrid algorithm that begins by scheduling some interviews in parallel and continues sequentially. Focusing on cases where agents are ex-ante indifferent between agents on the other side, we show that the sequential algorithm performs 2 interviews per agent in expectation. We complement this by showing that any algorithm that performs less than 2 interviews per agent, does not always guarantee interim-stability. We also demonstrate that the hybrid algorithm requires only polylogarithmic expected number of rounds, while still performing only about 2 interviews per agent in expectation. Additionally, the interviews scheduled by our algorithms guarantee an interim-stable matching when Deferred-Acceptance is run after all interviews are completed.

Problem

• stable matching
• interview scheduling
• preference uncertainty
• interim stability
• expected utility

Innovation

• interim-stable matching
• adaptive interview scheduling
• stable matching with incomplete preferences
• hybrid algorithm
• expected utility under uncertainty