Competitive Query Minimization for Stable Matching with One-Sided Uncertainty

TL;DR

This paper investigates efficient algorithms for stable matching under one-sided uncertainty, focusing on minimizing queries needed to find or verify stable matchings across different query models.

Contribution

It introduces competitive algorithms and bounds for query minimization in stable matching with one-sided preference uncertainty.

Findings

Established upper and lower bounds on the competitive ratio.

Analyzed the complexity of the offline optimal query set.

Compared different query models for efficiency.

Abstract

We study the two-sided stable matching problem with one-sided uncertainty for two sets of agents A and B, with equal cardinality. Initially, the preference lists of the agents in A are given but the preferences of the agents in B are unknown. An algorithm can make queries to reveal information about the preferences of the agents in B. We examine three query models: comparison queries, interviews, and set queries. Using competitive analysis, our aim is to design algorithms that minimize the number of queries required to solve the problem of finding a stable matching or verifying that a given matching is stable (or stable and optimal for the agents of one side). We present various upper and lower bounds on the best possible competitive ratio as well as results regarding the complexity of the offline problem of determining the optimal query set given full information.