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?

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

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