Suppose that preferences in a stable matching instance are universal: all n jobs share the prefer- ences C₁ C₂ > ... > C₂ and all candidates share the preferences J₁ > J₂ > · · · > Jn. (a) What pairing do we get from running the algorithm with jobs proposing? Can you prove this happens for all n? (b) What pairing do we get from running the algorithm with candidates proposing? (c) What does this tell us about the number of stable pairings?

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Question
Please step by step Use induction
Suppose that preferences in a stable matching instance are universal: all n jobs share the prefer-
ences C₁ C₂ > ... > Cn and all candidates share the preferences J₁ > J₂ > ··· > Jn.
(a) What pairing do we get from running the algorithm with jobs proposing? Can you prove this
happens for all n?
(b) What pairing do we get from running the algorithm with candidates proposing?
(c) What does this tell us about the number of stable pairings?
Transcribed Image Text:Suppose that preferences in a stable matching instance are universal: all n jobs share the prefer- ences C₁ C₂ > ... > Cn and all candidates share the preferences J₁ > J₂ > ··· > Jn. (a) What pairing do we get from running the algorithm with jobs proposing? Can you prove this happens for all n? (b) What pairing do we get from running the algorithm with candidates proposing? (c) What does this tell us about the number of stable pairings?
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