Let m, m be two of the men and w, w be two of the women...
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Let m₁, m₂ be two of the men and w₁, wê be two of the women in an instance of the Stable Matching Problem with n men and n women. Assume m₁, M₂, W₁, W2's preference lists are: m₁'s preference: W₁ > W₂>….. m₂'s preference: W2₂ > W₁ >... w₁'s preference: m₂ > m₁ > w₂'s preference: m₁ > m₂ >... So, we only know the favorite and the second favorite of each of these four persons. (a) (10 pt) Show that if we run Gale-Shapley algorithm with men proposing, then m₁ is matched to w₁ and m₂ is matched to w₂. (b) (10 pt) Show that in every stable matching, m₁, m² are matched to w₁, W2, i.e., (m₁, W₁), (m₂, W₂) or (m₁, W2), (m2, W₁) must be part of any stable matching. Let m₁, m₂ be two of the men and w₁, wê be two of the women in an instance of the Stable Matching Problem with n men and n women. Assume m₁, M₂, W₁, W2's preference lists are: m₁'s preference: W₁ > W₂>….. m₂'s preference: W2₂ > W₁ >... w₁'s preference: m₂ > m₁ > w₂'s preference: m₁ > m₂ >... So, we only know the favorite and the second favorite of each of these four persons. (a) (10 pt) Show that if we run Gale-Shapley algorithm with men proposing, then m₁ is matched to w₁ and m₂ is matched to w₂. (b) (10 pt) Show that in every stable matching, m₁, m² are matched to w₁, W2, i.e., (m₁, W₁), (m₂, W₂) or (m₁, W2), (m2, W₁) must be part of any stable matching.
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Building Java Programs A Back To Basics Approach
ISBN: 9780135471944
5th Edition
Authors: Stuart Reges, Marty Stepp
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