Given a stream of updates about items drawn from a universe {1,...,n}, the stream's fre-quency vector f e R" is the vector whose i'th component fi equals the frequency of item iin the stream. For example, for the stream ((add, 5), (add, 7), (add, 5), (add, 7), (delete, 7))with universe {1,...,7}, its frequency vector is (0,0,0,0, 2, 0, 1).A streaming algorithm is said to maintain a linear sketch of size k if it stores in memory' Aƒfor a matrix A e R**n that is fixed at the initialization.(a) Show that the algorithm discussed in class for frequency estimation is a linear sketch.What is the matrix A in this case?(b) Suppose a streaming algorithm is a linear sketch. Assume the matrix A mentionedabove is explicitly known to the algorithm. Explain how the algorithm should updateits storage each time a stream update comes of the form (add, i) or (delete, i).

Answered: Given a stream of updates about items…

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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