TL;DR
This paper develops online algorithms for eliciting necessarily optimal matchings in house allocation, including a 3/2-competitive algorithm for rank-maximal matchings, and explores new models and their complexities.
Contribution
It provides the first online algorithm for eliciting necessarily rank-maximal matchings with a 3/2-competitive ratio and introduces new elicitation models with complexity analysis.
Findings
The online algorithm for NRM matching is 3/2-competitive.
New elicitation models are introduced and their complexities analyzed.
Extensions to the elicitation of necessarily Pareto optimal matchings are provided.
Abstract
In this paper, we study the problem of eliciting preferences of agents in the house allocation model. For this we build on a recent model of Hosseini et al.[AAAI'21] and focus on the task of eliciting preferences to find matchings which are necessarily optimal, i.e., optimal under all possible completions of the elicited preferences. In particular, we follow the approach of Hosseini et al. and investigate the elicitation of necessarily Pareto optimal (NPO) and necessarily rank-maximal (NRM) matchings. Most importantly, we answer their open question and give an online algorithm for eliciting an NRM matching in the next-best query model which is 3/2-competitive, i.e., it takes at most 3/2 as many queries as an optimal algorithm. Besides this, we extend this field of research by introducing two new natural models of elicitation and by studying both the complexity of determining whether a…
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