Question: As it appears above, the Floyd-War shall algorithm requires (n3) space, since we compute for d (k) i, j, k = 1, 2,...,n. Show that

As it appears above, the Floyd-War shall algorithm requires Θ (n3) space, since we compute for d (k) i, j, k = 1, 2,...,n. Show that the following procedure, which simply drops all the superscripts, is correct, and thus only Θ (n2) space is required.

Step by Step Solution

★★★★★

3.39 Rating (177 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

With the superscripts the computation is d min dk dik dk If having dropped ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

C-S-A (138).docx

120 KBs Word File

Students Have Also Explored These Related Algorithms Questions!

Show that Sollin's algorithm requires at most log n iterations to produce a minimum spanning tree from a connected undirected weighted graph with n vertices.

Show that if n is an integer and n3 + 5 is odd, then n is even using a) A proof by contraposition. b) A proof by contradiction.

Show that in R3, (a) i i = j j = k k = 1; (b) i j = i k = j k = 0.

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

HW 12, MAT 312/AMS 351: SPRING 2017 Problem 1. (1) Set H = {4a + 6b | a, b Z} Z. Show that H is a subgroup of Z. (2) Is H cyclic? Problem 2. Write down all the cyclic subgroups of the following...

PowerPoint Assignment for BUS 401: Principles of Finance You have been asked by a manager in your organization to put together a training program explaining Net Present Value (NPV) and Future Value...

2. Consider the following data set consisting of four points: X1 = - [8], --[1].-= []. - [ ] Plot these points. We want to split this set to two classes. (a) Suppose you start the K-means algorithm...

can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...

10 Green's functions for PDEs In this final chapter we will apply the idea of Green's functions to PDEs, enabling us to solve the wave equation, diffusion equation and Laplace equation in unbounded...

1. Calculate the sample size needed given these factors: one-tailed t-test with two independent groups of equal size small effect size (see Piasta, S.B., & Justice, L.M., 2010) alpha =.05 beta = .2...

If you were traveling away from earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on earth using telescope say about...

In many applications it is necessary to expand or to decrease the diameter of a beam of parallel rays of light. This change can be made by using a converging lens and a diverging lens in combination....

12 Estimate the answers by rounding numbers to the nearest 10. a 92-28.5 b -41-18.9 C 83.8-11.6 d -7719

A spring with Mass We usually ignores the kinetic energy of the moving coils of a spring, but lets tries to get a reasonable approximation to this. Consider a spring of mass M, equilibrium length Lo,...

In Figure three thin plastic rods form quarter-circles with a common center of curvature at the origin. The uniform charges on the rods are Q1 = + 30nC, Q2 = + 3.0 Q1 and Q3 = ?? 8.0 Q1 what is the...

Use the results of Exercises 1.28 and 1.29 to create a plot that illustrates the interaction evident from the data. Use the plot in Figure in Example 1.3 as a guide. Could the type of information...

Saturated steam at 110C is condensed in a shell-and-tube heat exchanger (1 shell pass; 2, 4,... tube passes) with a UA value of 2.5 kW/K. Cooling water enters at 40C. (a) Calculate the cooling water...

A uniform chain of length 8.00 m initially lies stretched out on a horizontal table. (a) If the coefficient of static friction between chain and table is 0.600, show that the chain will begin to...

Within 1 or 2 percentage points, what has the U.S. inflation rate been during the last 20 years? Draw a graph to show the data.

Sanders, Incorporated, paid a $4 dividend per share last year and is expected to continue to pay out 60% of its earnings as dividends for the foreseeable future. If the firm is expected to generate a...

Maturity Value after Partial Payments Form Use the formula for all steps: Interest = Principal Rate Time Ordinary Interest = 3 6 0 days On Day 2 0 of the loan a partial payment of $ 4 , 0 0 0 is...

The Dauphin Company was started by a group of investors on January 1, 20X0, when the balance sheet was made up of total assets of $10,000 and total liabilities of $7,000. Partial financial data for...