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Chris Unsworth. A Specialised Constraint approach for Stable Matching problems. The Stable marriage problem. There exists an optimal algorithm EGS runs in O(n 2 ) time There are optimal constraint encodings Boolean encoding proposed CP’01 Limitations EGS is highly specialised
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Chris Unsworth A Specialised Constraint approach for Stable Matching problems
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
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
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
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