PPT-Stable Matching and Orderly Markets

Medical Residents Law Clerks and College Admissions 1 Todays Class Last time introduced the basic model of twosided matching and idea of stable matching Today discuss organization of matching markets in practice using examples. Week . 10: Stable Matching and Secretary Problem. CSC3160: Design and Analysis of Algorithms. 1. Bipartite graph. (Undirected) . Bipartite. graph: . for which . can be partitioned into two parts . Algorithms. and Networks 2014/2015. Hans L. . Bodlaender. Johan M. M. van Rooij. A Prize Winning Algorithm. Lloyd Shapley, Nobel Prize Winner 2012 in economics.. Obtained the prize for a number of contributions, one being the Gale-Shapley algorithm, discussed today.. History. Internship introduced around the turn of the 20. th. century. A concentrated exposure to clinical medicine to students. Cheap labor for hospitals. The number of positions offered greater than the number of graduating medical students. Lecture 19: Nov 23. This Lecture. Graph matching is an important problem in graph theory.. It has many applications and is the basis of more advanced problems.. In this lecture we will cover two versions of graph matching problems.. Dr. Briggs (1. st. five weeks). Dr. . Meehean. (2. nd. five weeks). Dr. Ribler (3. rd. five weeks). 3. rd. Five Weeks. Great Ideas in Computer Science. How do Computer Scientists Think?. What do Computer Scientists Do?. Statement of the problem. Two sides of the market to be . matched.. Participants . on . both sides care about to whom they are matched.. M. oney can’t . be used to . determine . the assignment. .. Examples . (A Case Study). Based on joint works with: . Rachel Cummings, Justin Hsu, . Zhiyi. Huang, . Sampath. Kannan, Michael Kearns, . Mallesh. . Pai. , Jamie Morgenstern, Ryan Rogers, Tim . Roughgarden. Jon Ullman, and Steven Wu. Matching and Market Design Algorithmic Economics Summer School, CMU Itai Ashlagi Topics Stable matching and the National Residency Matching Program (NRMP) Kidney Exchange 2 The US Medical Resident Market Algorithms. and Networks 2017/2018. Johan M. M. van Rooij. Hans L. . Bodlaender. A prize winning algorithm. Lloyd Shapley, Nobel Prize Winner 2012 in economics.. Obtained the prize for a number of contributions, one being the Gale-Shapley algorithm, discussed today.. Propose-and-reject algorithm. . [Gale-Shapley 1962]. . Intuitive method . that’s guaranteed . to find a stable matching.. 2. Stable Matching Problem. Perfect matching: . everyone is matched monogamously. . Reminders. HW1 is out on ELMS + . Gradescope. Check that you can upload. No class Monday (Labor Day). No in-person lecture on Wednesday. Lecture will . be pre-recorded; available . on ELMS. Stable matching. [webster.com]. A procedure for solving a mathematical problem (as of finding the greatest common divisor) in a finite number of steps that frequently involves repetition of an operation.. [Knuth, TAOCP]. . each agent ranks . every. agent in the other set.. Goal: Match each agent to . exactly one. agent in the other set, respecting their preferences.. How do we “respect preferences”?. Avoid . blocking pairs. Gale-Shapley Algorithm. Christian Reyes. Enrique Treviño. Think About…. Imagine…. Finally…. Outline. Stable Matching and the Stable Marriage Problem. Richter Matching. What Next?. Stable Matching.