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Advanced Specialized Constraints for Stable Matching Problems in Marriage and Residency

This paper explores specialized constraint approaches for solving stable matching problems, including the Stable Marriage and Hospital/Residents problems. It highlights an optimal algorithm known as EGS which operates in O(n²) time and discusses optimal constraint encodings. The contribution includes the development of fast specialized constraints and extensive empirical testing across large datasets to demonstrate their versatility. The study also examines eight variants of stable matching problems, optimization challenges, and future directions, including heuristics and adaptations of existing constraint models.

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Advanced Specialized Constraints for Stable Matching Problems in Marriage and Residency

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  1. Chris Unsworth A Specialised Constraint approach for Stable Matching problems

  2. The Stable marriage problem • There exists an optimal algorithm • EGS runs in O(n2) time • There are optimal constraint encodings • Boolean encoding proposed CP’01 • Limitations • EGS is highly specialised • CP encodings are slow • Require large supporting data structures • My contribution • Fast specialised constraints for SM • SM2, SMN, BSMN, CSMN • Theoretically and empirically tested • Proven to be sound and complete • Demonstrated their versatility

  3. The Hospital/Residents problem • Two linear time algorithms exist • The Resident-oriented and Hospital-oriented algorithms • Constraint models have been proposed • Constraint based encoding proposed at CPAIOR’07 • My contribution • Fast specialised constraint for HR • HRN • Theoretically and empirically tested • Demonstrated its versatility

  4. Large scale empirical study • Compared all stable marriage constraint models • Over 20,000 randomly generated instances • Demonstrated Versatility • Eight variants of stable matching problems taken from the literature • Optimisation problems • Sex-equal, balanced, egalitarian • Specialisations • Man-exchange, forced pairs, couples

  5. Future directions • Optimisation problems • Variable and value ordering heuristics • Different search strategies • Ties and incomplete preference lists • How current constraint models can be adapted • How the problem can be reformulated • Higher levels of consistency • Enforcing GAC over SMN • Emulating stable pairs algorithm

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