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Summary
This summary is machine-generated.

This study introduces relaxation methods for the three-dimensional stable matching problem with cyclic preferences (3dsm-cyc). These methods efficiently find the minimal changes needed to satisfy previously impossible instances.

Keywords:
3dsm-cycAlmost stable matchingConstraint ProgrammingRelaxationThree-dimensional stable matching with cyclic preferences

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Area of Science:

  • Constraint Programming
  • Combinatorial Optimization
  • Stable Matching Problems

Background:

  • Constraint programming effectively solves the three-dimensional stable matching problem with cyclic preferences (3dsm-cyc).
  • Current methods only declare unsatisfiable instances as impossible, lacking information on how to resolve them.

Purpose of the Study:

  • To adapt existing 3dsm-cyc constraint models for maximum relaxation.
  • To compute the smallest modification needed for satisfiability in 3dsm-cyc instances.
  • To incorporate costs and find minimum-cost relaxations.

Main Methods:

  • Developing four distinct relaxation strategies for 3dsm-cyc constraint models.
  • Extending models to handle element costs and identify lowest-cost relaxations.
  • Empirical evaluation of the efficiency and overhead of the proposed relaxation models.

Main Results:

  • Successfully adapted constraint models for the maximum relaxation of 3dsm-cyc instances.
  • Implemented cost-aware relaxation, enabling the selection of minimum-cost solutions.
  • Demonstrated that relaxation models exhibit minimal overhead compared to satisfaction-only models.

Conclusions:

  • The proposed relaxation models provide valuable insights into unsatisfiable 3dsm-cyc instances.
  • These methods efficiently compute minimal modifications and lowest-cost relaxations.
  • The approach offers a practical extension to existing constraint programming techniques for stable matching problems.