Answered: 1. Big-O Notation Let f and g be…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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1. Big-O Notation Let f and g be functions from the set of integers or the set of real numbers to the set of real numbers. We say that f ( x ) is O ( g ( x ) ), read as "f ( x ) is big-oh of g ( x )", if there are constants C and k such that | f ( x ) | ≤ C | g ( x ) | whenever x > k. (a) Show that f(x) = x2 + 2x + 1 is O(x2) Solution: When x>1; ? 2 (1 + 2 ? + 1 ? 2 ) < ? 2 (1 + 2 1 + 1 1 2 ) = 4? 2 So, ??? ? > 1, ? 2 + 2? + 1 < 4? 2 From the definition 0 ≤ f(x) ≤ cg(x) for x≥1 Hence, for N0 = 1; c=4; and g(x)=x2 for N0 = 2; c=3; and g(x)=x2 for N0 = 3; c=2; and g(x)=x2 … Therefore, ? ? + ?? + ? = ?(? ? ) O(g(x)) = {f(x)|there exist positive constant c and N0 such that 0 ≤ f(x) ≤ cg(x) for all x≥N0} 2. Show that 7x2 is O(x3). 3. Suppose there are x number of boxes to be delivered to x number of household that is 2km apart, what is the distance travelled by the transport delivery service? 4. In number 3, suppose that each boxes must be coming from the Warehouse and the transport delivery service must need to back-and-port to pick-up each box. What is the distance travelled by the transport delivery service? 5. Evaluate the methods used in number 3 and number 4 method of delivery. If the function x2 is considered as the dominant term for each method used. 6. What will happen to the term 2x + 5 of the original function x2 + 2x + 5 when compared to the dominant term which is x2. Show a simple analysis for this function

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