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Gale-Shapley: Prove or dissprove the following theorem In every execution of the hospitals-propose Stable Matching algorithm, there...

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Basic Math

Gale-Shapley: Prove or dissprove the following theorem

In every execution of the hospitals-propose Stable Matchingalgorithm, there is at most one hospital that makes offers to everydoctor.

If anyone can help me with a long-form proof or an example thatdissproves this claim!

Answer & Explanation Solved by verified expert
4.5 Ratings (833 Votes)
Let the hospitals do the selecting let H represent the hospitals and S represent the students each h in H need to fill slots the number of slots can vary but the total combined number of slots includes every hospital is less than the total number of students each student s is free until he or she has accepted at least temporarily an offer from a hospital then    See Answer
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