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Enhancing Stable Matching Problem Solutions through Advanced Constraints and Empirical Studies

This work details the advancements made in the field of stable matching problems, focusing on a new description for SMN to align it more intuitively with an AC5-style algorithm. It includes a comprehensive empirical study of various constraint solutions, such as Boolean and N-Valued encodings, and establishes a new complexity argument related to stable matchings. The research compares the efficiency of SMN with the EGS algorithm, revealing conditions under which SMN can outperform traditional solutions. A provisional thesis statement posits that specialized constraint solutions can achieve comparable performance to algorithmic approaches while offering greater versatility.

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Enhancing Stable Matching Problem Solutions through Advanced Constraints and Empirical Studies

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  1. Second Year Viva Chris Unsworth

  2. What I have done • A new description for SMN. • Why? • To fit more intuitive into an AC5 style arc-consistency algorithm. • As a blueprint for future constraint discriptions. • A new complexity argument to fit the new description. • Proofs • soundness and completeness • Equivalence to the EGS algorithm • Failure free enumeration of all stable matchings

  3. What I have done • Empirical study of constraint solutions to the stable marriage problem. • Solutions included: • Conflict matrix encoding • Boolean encoding • N-Valued encoding • 4-Valued encoding • SM2 constraint • SMN constraint • EGS algorithm • Instance sizes and sample sizes • 10 – 100 sample size 1000 • 100 – 1000 sample size 1000 • 1000 – 8000 sample size 20 • SMN is comparable to EGS • when n >= 1000, EGS at most 4 times faster than EGS

  4. What I have done • Comparing the average number of solutions lead the conjecture that: “after arc-consistency has been enforced over a constraint model which uses the SMN constraint, the first stable matching can be found in n time and each subsequent solution can also be found in n time”

  5. What I am doing • Starting 17th October 2005 • Check implementation of all CP SM models, including: • FT, Bool, DG1, DG2, SM2 and SMN • Get a reasonable implementation of the EGS algorithm in Java • Design, run and tabulate an empirical study of the above models • Starting November 2005 • Check implementation of SMTI2 • Implement SMTIN • Recreate ECAI 02 experiments and include the new models • Increase the instance sizes to explore the limits of the new solutions • Write up the work with a view to submitting to ECAI 06 (deadline for summaries 8th February 2006)

  6. What I am going to do • Provisional thesis statement • “A Specialised constraint solution for a stable matching problem can solve the problem in comparable time to an algorithmic solution, and it can significantly outperform a more traditional toolbox constraint solution whilst maintaining its versatility ”

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