lec2 - n CS 323/700 Lecture 2 o Design and Analysis of...

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Unformatted text preview: n CS 323/700 Lecture 2 o Design and Analysis of Algorithms Hoeteck Wee · hoeteck@cs.qc.cuny.edu http://algorithms.qwriting.org/ College admissions QUESTION. Can we design a college admissions process or a job recruitment process that finds a self-enforcing assignment? I each college admits many students I each student is assigned to one college I each college ranks the students I each student ranks the colleges I not self-enforcing: some (college, applicant) pair wants to “switch” Hoeteck Wee CS 323 Feb 3, 2010 2 / 17 College admissions QUESTION. Can we design a college admissions process or a job recruitment process that finds a self-enforcing assignment? UNSTABLE PAIR. college C and applicant A are unstable if I A prefers C to its assigned college. I C prefers A to one of its admitted students. STABLE ASSIGNMENT. assignment with no unstable pairs. I natural and desirable condition. I no incentive for any college/applicant pair to make a deal. SPECIAL CASE. # colleges = # students, each college admits 1 student. I mathematical formulation I design an algorithm I analyze the algorithm – running time and correctness I discuss implementation Hoeteck Wee CS 323 Feb 3, 2010 3 / 17 Stable matching problem INPUT. given n men and n women, I each man ranks the women from best to worst. I each woman ranks the men from best to worst. GOAL. find a stable matching (i.e. no unstable pairs). I everyone is matched monogamously & no extramarital affairs. I an unmatched pair ( m , w ) is unstable if man m and women w prefer each other to current partners....
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lec2 - n CS 323/700 Lecture 2 o Design and Analysis of...

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