Part A step by step (a) In the notes, we show that the stable matching algorithm terminates in at most n² days. Provethe 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 boundfrom part (a) when running the Propose-and-Reiect algorithm Verify this by running the

(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.

(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.

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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Concept of Randomized Approximation Algorithms

Randomized algorithms are algorithms that use random numbers to determine what to do next at any point in their logic. This means that it uses randomization for operation in the logic. Due to this randomness, the time and space complexity of the standard algorithm is reduced.

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Part A step by step

(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-Reiect algorithm Verify this by running the

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