SLIDE 2 1/12/18 2
Propose-And-Reject Algorithm
Jan 12, 2018 Sprenkle - CSCI211 3
Initialize each person to be free Initialize each person to be free while while (some man is free and hasn't proposed to every woman) (some man is free and hasn't proposed to every woman) Choose such a man Choose such a man m w = 1 = 1st
st woman on m's list to whom
woman on m's list to whom m has not yet proposed has not yet proposed if if w is free w is free assign assign m and and w to be engaged to be engaged else else if if w prefers m to her fiancé m' w prefers m to her fiancé m' assign assign m and and w to be engaged and to be engaged and m' to be free ' to be free else else w rejects rejects m
[Gale-Shapley 1962]
Review: Observa&ons about the Algorithm
- What can we say about any woman’s partner
during the execu&on of the algorithm?
Ø Observa&on 1. He gets “beTer” à she prefers him
- ver her last partner
- How does a woman’s state change over the
execu&on of the algorithm?
Ø Observa&on 2. Once a woman is matched, she never becomes unmatched; she only "trades up”
- What can we say about a man’s partner?
Ø Observa&on 3. She gets “worse”
Jan 12, 2018 Sprenkle - CSCI211 4
