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Stable Matching with Uncertain Linear Preferences.

Haris Aziz1,2, Péter Biró3,4, Serge Gaspers1

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Summary
This summary is machine-generated.

This study explores stable matching with uncertain preferences using three models: lottery, compact indifference, and joint probability. The complexity of finding stable matchings varies significantly based on the uncertainty model used.

Keywords:
NP-hard problemsPolynomial-time algorithmsStable marriage problemStable matchingsUncertain preferences

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Area of Science:

  • Computer Science
  • Algorithmic Game Theory
  • Computational Social Choice

Background:

  • Stable matching problems are fundamental in resource allocation.
  • Uncertainty in agent preferences complicates traditional stable matching algorithms.
  • Real-world scenarios often involve incomplete or probabilistic preference information.

Purpose of the Study:

  • To analyze the computational complexity of stable matching under various uncertainty models.
  • To investigate methods for computing the stability probability of a given matching.
  • To develop algorithms for finding matchings with the highest probability of being stable.

Main Methods:

  • Considered three distinct models of preference uncertainty: lottery, compact indifference, and joint probability.
  • Analyzed the computational complexity of determining matching stability probabilities.
  • Examined the problem of finding a maximum stability probability matching.
  • Investigated restricted problems, such as the existence of a certainly stable matching.

Main Results:

  • Demonstrated that the computational complexity of stable matching problems differs across the three uncertainty models.
  • Identified a 'rich complexity landscape,' highlighting the impact of uncertainty form.
  • Established varying computational difficulties for computing stability probabilities and finding optimal matchings.

Conclusions:

  • The specific model of uncertainty significantly influences the complexity of stable matching problems.
  • Algorithmic approaches must account for the nature of preference uncertainty.
  • Further research is needed to develop efficient algorithms for stable matching in uncertain environments.