Modeling Stable Matching Problems with Answer Set Programming

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Modeling Stable Matching Problems with Answer Set Programming

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Jul 13, 2013 ... sex-equalness,. ✤ minimal or maximal cardinality. Proposition. 14. For every answer set of the ASP program induced by an. SMP instance with ...

Modeling Stable Matching Problems with Answer Set Programming Sofie De Clercqa Steven Schockaertb, Martine De Cocka, Ann Nowéc a Dept.

of Applied. Mathematics, Computer Science and Statistics, Ghent University, Belgium b School of Computer Science and Informatics, Cardiff University, UK c Computational Modeling Lab, Vrije Universiteit Brussel, Belgium

RuleML 2013, Seattle, Saturday, July 13th, 2013

The Stable Marriage Problem (SMP) I prefer Batgirl to Supergirl

Kirk

I prefer Batgirl to Supergirl

Spock

I prefer Spock to Kirk

I prefer Kirk and find Spock unacceptable

Batgirl

Supergirl 2

Stability {(Spock, Supergirl), (Kirk, Batgirl)}

I found Spock unacceptable but got paired to him after all!

Supergirl blocks this set of marriages 3

Stability {(Spock, Supergirl), (Kirk, Batgirl)}

I strictly prefer Batgirl to this woman

I strictly prefer Spock to this guy

Batgirl and Spock block the set of marriages 4

Stable set of marriages ✤ no blocking individuals ✤ no blocking pairs But... the notion of stability is too weak to distinguish good sets of marriages from great sets of marriages

5

Optimality I prefer Spock to Kirk

Batgirl

I am indifferent between Spock and Kirk

Supergirl

I prefer Batgirl to Supergirl

I prefer Supergirl to Batgirl

Kirk

Spock

6

Optimality 2+1+2+1=6 She is my He is my She is my He is my first first second second choice. choice! choice. choice!

She is my first choice!

He is my first choice!

She is my first choice!

He is my second choice.

1+1+1+2=5 5