The U.S. Supreme Court is being asked to determine, in part,…
The U.S. Supreme Court is being asked to determine, in part, the constitutionality of certain aspects of the ability of a bankruptcy court to provide releases of liability for third parties in the Purdue bankruptcy case. The power of the Supreme Court to make this determination is the power of
Read DetailsFor any natural number n, it is possible to construct a stab…
For any natural number n, it is possible to construct a stable matching problem input instance with n hospitals and n students, such that there is a feasible solution assigning all hospitals and all students to their last choices.
Read DetailsConsider an instance of the Stable Matching Problem in which…
Consider an instance of the Stable Matching Problem in which there exists a hospital h and a medical student s such that h and s are ranked last on each other’s preference list. Then, no stable matching of this instance can include the pair (h,s).
Read DetailsFor any natural number n, it is possible to construct a stab…
For any natural number n, it is possible to construct a stable matching problem input instance with n hospitals and n students, such that there is a feasible solution assigning all hospitals and all students to their first choices.
Read DetailsConsider an instance of the Stable Matching Problem in which…
Consider an instance of the Stable Matching Problem in which there exist n hospitals to be matched with n medical students. Gale-Shapley algorithm guarantees that fewer students than hospitals are matched to their first choices.
Read DetailsConsider the following preference tables for three universit…
Consider the following preference tables for three university hospitals and three medical students. 1st 2nd 3rd DUKE Cam Ada Bea NYU Ada Cam Bea UIUC Cam Bea Ada 1st 2nd 3rd Ada DUKE UIUC NYU Bea UIUC DUKE NYU Cam UIUC NYU DUKE (i) Which of the following is the output of the Gale-Shapley algorithm? [GaleShapley] (ii) Which of the following is a stable matching that assigns each student to their best valid partner?[StudentBestMatching] (iii) Which of the following is an unstable pair with respect to the matching (DUKE-Ada, NYU-Cam, UIUC-Bea)?[UnstablePair] (iv) Which student (if any) can improve his/her/their match in the Gale-Shapley output by lying? [TrickingTheAlgorithm]
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