Give the asymptotic complexity of each of the following functions in simplest terms andthen order the functions by asymptotic dominance. That is, produce a permutation, f₁(n),f₂(n), such that fi(n) = O(fi+1(n)). Note if any two functions are asymptotically equivalent,i.e., if fi (n) = O(fi+1(n)). Note: 'Ig x' is a simpler notation for 'log₂ x'.fe(n)= 4 lg (n²+ 2n) + 6nº.7f(n) = n5 + 10¹0 lg (n+100)fe(n)= 3n lg (n² + 2) + n²

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Give the asymptotic complexity of each of the following functions in simplest terms and then order the functions by asymptotic dominance. That is, produce a permutation, f₁(n), 2(n), ..., such that fi(n) = O(f₁+1(n)). Note if any two functions are asymptotically equivalent, .e., if f¡ (n) = O(fi+1(n)). Note: 'Ig x' is a simpler notation for 'log₂ x'. fe(n) = 4 lg (n² + 2n) + 6n0.7 f(n) = n5 + 10¹⁰ lg (n+100) fe(n) = 3n lg (n²+ 2) + n² . ● .

Give the asymptotic complexity of each of the following functions in simplest terms and then order the functions by asymptotic dominance. That is, produce a permutation, f₁(n), 2(n), ..., such that fi(n) = O(f₁+1(n)). Note if any two functions are asymptotically equivalent, .e., if f¡ (n) = O(fi+1(n)). Note: 'Ig x' is a simpler notation for 'log₂ x'. fe(n) = 4 lg (n² + 2n) + 6n0.7 f(n) = n5 + 10¹⁰ lg (n+100) fe(n) = 3n lg (n²+ 2) + n² . ● .

Database System Concepts

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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 explainers

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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Give the asymptotic complexity of each of the following functions in simplest terms and
then order the functions by asymptotic dominance. That is, produce a permutation, f₁(n),
f₂(n), such that fi(n) = O(fi+1(n)). Note if any two functions are asymptotically equivalent,
i.e., if fi (n) = O(fi+1(n)). Note: 'Ig x' is a simpler notation for 'log₂ x'.
fe(n)= 4 lg (n²+ 2n) + 6nº.7
f(n) = n5 + 10¹0 lg (n+100)
fe(n)= 3n lg (n² + 2) + n²

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