3.- Prove that the bound 2/2ª in Lemma 4.1 is the best possible bound by showing that, if x = 2-d-1 and y = 3x, then Pr[hash(x) = hash(y)] = 2/2². (Hint look at the binary representations of zx and 23x and use the fact that z3x = zx + 2zx.) Lemma 4.1. Let x and y be any two values in {0,..., 2 − 1} with x ±y. Then Pr{hash(x) = hash(y)} ≤ 2/2ª.
3.- Prove that the bound 2/2ª in Lemma 4.1 is the best possible bound by showing that, if x = 2-d-1 and y = 3x, then Pr[hash(x) = hash(y)] = 2/2². (Hint look at the binary representations of zx and 23x and use the fact that z3x = zx + 2zx.) Lemma 4.1. Let x and y be any two values in {0,..., 2 − 1} with x ±y. Then Pr{hash(x) = hash(y)} ≤ 2/2ª.
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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Hello. Please answer the attached Data Structures question correctly and follow all directions. Create a proof for this problem.
*If you answer correctly, I will provide a thumbs up. Thank you.
![3.- Prove that the bound 2/2d in Lemma 4.1 is the best possible bound by showing that, if x = 2w-d-1 and y = 3x, then
Pr[hash(x) = hash(y)] = 2/2². (Hint look at the binary representations of zx and z3x and use the fact that z3x = zx + 2zx.)
Lemma 4.1. Let x and y be any two values in {0,..., 2w - 1} with x = y. Then
Pr{hash(x) = hash(y)} ≤ 2/2ª.
With Lemma 4.1, the performance of remove(x), and find(x) are easy
to analyze:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1223c4c6-4ebb-4911-bc0d-edb37c26385f%2F32d3eb23-9644-4e8a-a4f4-6f6fa6fac62b%2Flmcm6sk_processed.png&w=3840&q=75)
Transcribed Image Text:3.- Prove that the bound 2/2d in Lemma 4.1 is the best possible bound by showing that, if x = 2w-d-1 and y = 3x, then
Pr[hash(x) = hash(y)] = 2/2². (Hint look at the binary representations of zx and z3x and use the fact that z3x = zx + 2zx.)
Lemma 4.1. Let x and y be any two values in {0,..., 2w - 1} with x = y. Then
Pr{hash(x) = hash(y)} ≤ 2/2ª.
With Lemma 4.1, the performance of remove(x), and find(x) are easy
to analyze:
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