lecture 6 cse 331 sep 14. a run of the gs algorithm mal wash simon inara zoe kaylee
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![Page 1: Lecture 6 CSE 331 Sep 14. A run of the GS algorithm Mal Wash Simon Inara Zoe Kaylee](https://reader038.vdocuments.site/reader038/viewer/2022103022/56649d415503460f94a1c506/html5/thumbnails/1.jpg)
Lecture 6
CSE 331Sep 14
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A run of the GS algorithm
Mal
Wash
Simon
Inara
Zoe
Kaylee
![Page 3: Lecture 6 CSE 331 Sep 14. A run of the GS algorithm Mal Wash Simon Inara Zoe Kaylee](https://reader038.vdocuments.site/reader038/viewer/2022103022/56649d415503460f94a1c506/html5/thumbnails/3.jpg)
The Preferences
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Gale-Shapley AlgorithmIntially all men and women are free
While there exists a free woman who can propose
Let w be such a woman and m be the best man she has not proposed to
w proposes to m
If m is free
(m,w) get engaged
Else (m,w’) are engaged
If m prefers w’ to w
w remains freeElse
(m,w) get engaged and w’ is free
Output the engaged pairs as the final output
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GS algorithm: Firefly Edition
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Last LectureIntially all men and women are free
While there exists a free woman who can propose
Let w be such a woman and m be the best man she has not proposed to
w proposes to m
If m is free
(m,w) get engaged
Else (m,w’) are engaged
If m prefers w’ to w
w remains freeElse
(m,w) get engaged and w’ is free
Output the engaged pairs as the final output
At most n2 iterationsAt most n2 iterations
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Two Observations
Every man is free until he gets engaged
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After that he gets engaged to better women
No monotone property for a woman
Her engagements get worse and worse