4. Suppose that you have constructed a parallel algorithm to solve a problem A in O(n³) time with n³ number of processors and the optimal sequential algorithm solves A in O(n5 loa(n)). Is the parallel solution cost-optimal?

4. Suppose that you have constructed a parallel algorithm to solve a problem A in O(n³) time with n³ number of processors and the optimal sequential algorithm solves A in O(n5 loa(n)). Is the parallel solution cost-optimal?

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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Given an array of intervals I[1, . . . , n] where I[i] = [si, fi], find the minimumnumber of intervals you need to remove to make the rest of the intervals non-overlapping. Precisely define the subproblem.Provide the recurrence equation.Describe the algorithm in pseudocode to compute the optimal value.Describe the algorithm in pseudocode to print out an optimal solution.
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1. If I prove that an algorithm takes Θ(k^2) worst-case time, can it take o(k^2) on some inputs? 2. If I prove that an algorithm takes Θ(k^2) worst-case time, can it take o(k^2) on all inputs?
No plagarism please! Correct and detailed answer will be Upvoted else downvoted. Thank you!
Consider the following functions as time complexities of some algorithms. (a) First write the worst-case runtime of each algorithm in Big-O notation. (b) Then arrange functions from low to high (Consider their Big-O notations as you arrange them; as n grows, the function that grows slower should come sooner than the one that grows faster). (c) Arbitrary, select TWO of arrangements in part (b) and for each one of them justify why you have chosen such an ordering for the corresponding function. Provide formal proof. For example if fl<=f2<= f3<= f4<=f5 you may choose to formally justify why (1) fl<=f2 and why (2) f4<=f5 . fI(n)=n², f2(n)=210 nlogn, f3(n)=3", f4(n)=n, f5(n)=1, f6(n)=5*logn, f7(n)= n", f8(n)=4 n*n, f9(n)=2log(n³)
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