We have n elements {x1,... , xn} we want to hash into a table T of size s = Let us consider the following method of hashing these n elements into T: 2п. For each i = 1, . п, do the following: 1. Pick a permutation of [1, ... , s] uniformly at random. Call this permutation T; : [s] → [s], which maps each index to the element which ends up in that index. 2. Set j = 1. 3. While T[T;(j)] has an element in it, increment j. 4. Place x; in T[T;(j)]. 1.1 Show that while inserting any xi, the probability that there are at least t iterations of the while loop in Step 3 is at most 2–t.

We have n elements {x1,... , xn} we want to hash into a table T of size s = Let us consider the following method of hashing these n elements into T: 2п. For each i = 1, . п, do the following: 1. Pick a permutation of [1, ... , s] uniformly at random. Call this permutation T; : [s] → [s], which maps each index to the element which ends up in that index. 2. Set j = 1. 3. While T[T;(j)] has an element in it, increment j. 4. Place x; in T[T;(j)]. 1.1 Show that while inserting any xi, the probability that there are at least t iterations of the while loop in Step 3 is at most 2–t.

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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