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Matching-Updating Mechanism: A Solution for the Stable Marriage Problem with Dynamic Preferences
Akhmad Alimudin1,2, Yoshiteru Ishida1
1Department of Computer Science and Engineering, Toyohashi University of Technology, Toyohashi 441-8580, Japan.
Entropy (Basel, Switzerland)
|February 25, 2022
Summary
This study addresses the stable marriage problem with dynamic preferences, introducing an update mechanism to efficiently revise existing matches instead of restarting. The novel approach avoids cyclic processes, ensuring stable matching is achieved with minimal cost.
Area of Science:
- Algorithmic Game Theory
- Discrete Mathematics
- Computer Science Theory
Background:
- The stable marriage problem (SMP) traditionally assumes static preferences.
- Dynamic preferences introduce complexity, potentially destabilizing existing matches.
- Revising matches from scratch is computationally intensive.
Purpose of the Study:
- To develop an efficient update mechanism for stable matching with dynamic preferences.
- To minimize revision costs when preferences change.
- To avoid cyclic processes that prevent stable matching.
Main Methods:
- Introduced a novel update mechanism for SMP instances with dynamic preferences.
- Analyzed the conditions under which preference changes occur.
- Designed the mechanism to detect and prevent cyclic processes during updates.
Main Results:
- The proposed mechanism successfully updates existing matches under dynamic preferences.
- It effectively avoids cyclic processes, guaranteeing stable matching.
- The update approach minimizes the cost of rematching compared to restarting.
Conclusions:
- An efficient method for updating stable matches in dynamic preference scenarios has been developed.
- This approach offers a practical solution for real-world applications where preferences evolve.
- The mechanism ensures stability and reduces computational overhead.
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