Question: Why does Johnsons algorithm add vertex s to V in its first step? Why not just use any existing vertex in the input graph? Explain,

Why does Johnson’s algorithm add vertex s to V in its first step? Why not just use any existing vertex in the input graph? Explain, and give an example of a directed graph for which Johnson’s algorithm would not work without adding a vertex s to V in the initial step.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Ans Johnsons algorithm is used for finding the shortest paths between all pairs of vertices in a wei... 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

Students Have Also Explored These Related Algorithms Questions!

KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...

Give an example of a directed graph G = (V, E), a source vertex s V, and a set of tree edges E E such that for each vertex v V, the unique path in the graph (V, E ) from s to v is a shortest path...

a. The incidence matrix for an undirected graph G D (V, E) is a |V| |E| matrix M such that M e = 1 if edge e is incident on vertex , and M e = 0 otherwise. Argue that a set of columns of M is...

(i) Write down the linear program relaxation for the vertex cover problem and solve the linear program. [6 marks] (ii) Based on the solution of the linear program in (b)(i), derive an integer...

A seismic probe bores itself into the seabed, going as deep as it can before running out of fuel. This takes about five minutes. It rotates its spiral drill head at rate R(t) that follows a...

Objective: Implement Johnson's algorithm to solve the all - pairs shortest path problem in a given graph. Use Java programming language. Background: Johnson's algorithm is a solution to finding the...

Please do not change the structure of the java files could you just solve the shortestChain , cliques, and connectors methods. shortestChain would use breath first search, cliques would use depth...

Consider the Markov Chain, Xn, on the states i = 0, 1, 2, . . . with transition matrix given by pi,i1 = p i = 1, 2, . . . pi,i+1 = 1 p i = 0, 1, . . . p0,0 = p where 0

As the XOR operation is not defined on the set {A, . . . , Z}, we replace it here during encryption with modulo-26 addition (e.g., C D = F and Y C = A). (i) Decrypt the following ciphertexts, which...

Define the contextual-equivalence relation ` M =ctx M0 : for pairs of PCF terms M, M0 , PCF types , and PCF type environments . [3 marks] (ii) For PCF terms M and N with respective typings ` M : and...

Honora Corp places in service a super computer on June 7, 2020 with a capitalized cost of $60,000. No other assets were placed in service during the year. Honora Corp. elects out of any potential...

A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a diamond, and let F be the event that the card drawn is a face card. In Problem, find the indicated...

The following table lists the Income statement and Balance sheet for First American Furniture Company Income Statement 2017 2018 Revenue $516 $630 Depreciation 30 35 Other operating costs 400 480...

True Green Nurseries Ltd. is a private company that follows ASPE. It is authorized to issue an unlimited number of both common and $6.50 cumulative preferred shares. On December 31, 2017, there were...

For the year ended December 31, 2017, Huron Lake Enterprises Ltd. had the following revenues and expenses: Sales, $745,000; Cost of Goods Sold, $450,000; Operating Expenses, $135,000; and Income Tax...

For the year ended December 31, 2017, Grayfair Inc. reported profit of $175,000. During the year, the company declared a total of $120,000 cash dividends and paid $85,000 of these dividends. Prepare...

On October 14, the board of directors of Celeria Corp. voted to declare the annual preferred share dividend to shareholders of record on November 1, payable on November 21. The company is authorized...

Refer to the information for Viceron Inc. and your answer in BE13-6. Prepare an income statement for Viceron Inc. for the year ended June 30, 2017. In exercise For the year ended June 30, 2017,...

Complete the stabements using the terms on the let.A melling glacier creates a tion that splita a population of squarels in hall. Resources, preditors, and other way interbine the the el the...

Suppose that we redefine the residual network to disallow edges into s. Argue that the procedure FORD-FULKERSON still correctly computes a maximum flow.

Explain how to implement two stacks in one array A[1 . . n] in such a way that neither stack overflows unless the total number of elements in both stacks together is n. The PUSH and POP operations...

Derive a point-value representation for A rev (x) = n 1 j = 0 a n - 1 j x j from a point value representation for A(x) = A (x) = n 1 j = 0 a j x j , assuming that none of the points is 0.

Take a sheet of paper and make six columns on it. Label the columns mere disagreements, overblown conflicts, competition, verbally abusive conflicts, and physically abusive conflicts. In each column,...

Can you think of examples where people either focused on the other person or tried to deal with the problem or issue instead? Discuss the outcomes.

For the above case, write out at least four statements that demonstrate fractionation, framing, reframing, and common ground.