Competitive Query Minimization for Stable Matching with One-Sided Uncertainty
Evripidis Bampis, Konstantinos Dogeas, Thomas Erlebach, Nicole Megow, Jens Schlöter, Amitabh Trehan
TL;DR
The paper tackles stable matching under one-sided uncertainty, where $|A|=|B|=n$ and only $A$-side preferences are known initially. It introduces three query models and applies competitive analysis to minimize queries needed to find or verify stable and optimal matchings, yielding tight bounds and hardness results. Key contributions include 1-competitive algorithms for both stability verification and $A$-optimal stability in the comparison model, an $ ext{O}(n)$-competitive algorithm for a $B$-optimal stable matching with matching lower bounds, and NP-hardness results for offline query-set optimization with an $ ext{O}( ext{log}n ext{ log log }n)$-approximation. The results demonstrate that worst-case query counts differ meaningfully from competitive benchmarks and provide efficient strategies for query-efficient stabilization in one-sided uncertain markets.
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.