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(a) In the notes, we show that the stable matching algorithm terminates in at most n² days. Prove the following stronger result: the stable matching algorithm will always terminate in at most (n − 1)² + 1 = n² −2n+2 days. (b) Provide a set of preference lists for 4 jobs and 4 candidates that will result in the upper bound from part (a) when running the Propose-and-Reject algorithm. Verify this by running the Propose-and-Reject algorithm on your preference lists.

(a) In the notes, we show that the stable matching algorithm terminates in at most n² days. Prove the following stronger result: the stable matching algorithm will always terminate in at most (n − 1)² + 1 = n² −2n+2 days. (b) Provide a set of preference lists for 4 jobs and 4 candidates that will result in the upper bound from part (a) when running the Propose-and-Reject algorithm. Verify this by running the Propose-and-Reject algorithm on your preference lists.

Database System Concepts
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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(a) In the notes, we show that the stable matching algorithm terminates in at most n² days. Prove the following stronger result: the stable matching algorithm will always terminate in at most (n-1)²+1=n²-2n+2 days. (b) Provide a set of preference lists for 4 jobs and 4 candidates that will result in the upper bound from part (a) when running the Propose-and-Reject algorithm. Verify this by running the Propose-and-Reject algorithm on your preference lists.
Transcribed Image Text:(a) In the notes, we show that the stable matching algorithm terminates in at most n² days. Prove the following stronger result: the stable matching algorithm will always terminate in at most (n-1)²+1=n²-2n+2 days. (b) Provide a set of preference lists for 4 jobs and 4 candidates that will result in the upper bound from part (a) when running the Propose-and-Reject algorithm. Verify this by running the Propose-and-Reject algorithm on your preference lists.
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