Let G = (V, E) be a connected undirected graph. We define the risk factor of...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Let G = (V, E) be a connected undirected graph. We define the risk factor of a vertex u as the number of pairs of vertices that cannot reach one another after removing u from G; more formally, risk factor of u = {(x,y) EV-ux V-u : #x-y path in G[V – u]¹}|. For example, in the following graph u has risk factor 6 because removing u disconnects the graph into two connected components having 2 and 3 nodes respectively. U Design an algorithm that computes the risk factor of a given vertex u in O(n + m) time. Remember to: a) describe your algorithm in plain English, b) prove it correctness, and c) analyze its time complexity. To get full marks your algorithm must run in O(n + m) time. If you cannot make the stated bound, you can get partial credit by submitting a slower algorithm. Let G = (V, E) be a connected undirected graph. We define the risk factor of a vertex u as the number of pairs of vertices that cannot reach one another after removing u from G; more formally, risk factor of u = {(x,y) EV-ux V-u : #x-y path in G[V – u]¹}|. For example, in the following graph u has risk factor 6 because removing u disconnects the graph into two connected components having 2 and 3 nodes respectively. U Design an algorithm that computes the risk factor of a given vertex u in O(n + m) time. Remember to: a) describe your algorithm in plain English, b) prove it correctness, and c) analyze its time complexity. To get full marks your algorithm must run in O(n + m) time. If you cannot make the stated bound, you can get partial credit by submitting a slower algorithm.
Expert Answer:
Answer rating: 100% (QA)
a Algorithm in Plain English Create an empty set called unreachablepairs Traverse all vertices connected to the vertex u and remove each one of them f... View the full answer
Related Book For
Introduction to Algorithms
ISBN: 978-0262033848
3rd edition
Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
Posted Date:
Students also viewed these programming questions
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
Read the Comp & Ben Case Study and answer the following question: To the degree job growth (and increased car sales that come from m costs) is based on two tier-wage structures, how sustainable...
-
An object disintegrates into two fragments. One of the fragments has mass 1.00 MeV/c2 and momentum 1.75 MeV/c in the positive x direction. The other fragment has mass 1.50 MeV/c2 and momentum 2.00...
-
After door-to door canvassing, census workers determine the number of unoccupied homes. The table below lists the number of homes, in millions that were unoccupied in four census years. Year, x...
-
An investment is guaranteed to have a unique value of IRR if which of the following is true? a. Alternating positive and negative cash flows b. An initial negative cash flow followed by all positive...
-
Interact Systems, Inc., has developed software tools that help hotel chains solve application integration problems. Interacts application integration server (AIS) provides a two-way interface between...
-
A violet ray of light leaves a medium with refractive index of 6.46 at an angle of 0.07 radians to the normal and enters a second medium with refractive index of 22.04. At what angle to the normal...
-
What motivates a parent to bribe key people to get their kid admitted to a prestigious university? That is the ethical question of Operation Varsity Blues. In March 2019, the story broke of an...
-
After watching this video and considering what you learned about the IMA's Statement of Ethical Practice, think about what the auditors in this situation could have done to help catch Barry Minkow?...
-
A couple with three dependent children has an annual adjusted gross income (AGI) of $238,500. Calculate the total dollar amount of personal exemptions that they can claim for the 2011 tax year.
-
Save all of your sales receipts for 1 month. At the end of the month calculate the total sales tax paid and annualize the amount by multiplying it by 12. Compare this amount to your total state...
-
Assume you can save $4,000 a year (about $80 per week) after graduation. Set a financial goal for yourself and specify the time frame and cost. Calculate the interest rate required to achieve the...
-
Investigate a specific financial planning issue or decision that involves the use of the time va lue of money concepts. Describe why it is necessary to make a time value of money calculation....
-
Using a financial calculator, determine the future value of $5,000 invested at 12 percent for 40 years with annual compounding. What rate of interest would result in the same future value if the...
-
Heedo Co. reported the following information for 2021 in millions: Inventory, beg. - 5.0; Purchases - 26.0; Freight in -2.0; Purchase returns and allowances - 3.5; Purchase discounts -1.5; Sales -...
-
Stephen Schor, an accountant in New York City, advised his client, Andre Romanelli, Inc., to open an account at J. P. Morgan Chase Bank, N.A., to obtain a favorable interest rate on a line of credit....
-
Show that n k = 1 1/k 2 is bounded above by a constant.
-
Let G = (V, E) be a weighted, directed graph with weight function w : E and no negative-weight cycles. Let s V be the source vertex, and let G be initialized by INITIALIZE-SINGLE-SOURCE (G, s)....
-
Professor Karan measures her deterministic multi-threaded algorithm on 4, 10, and 64 processors of an ideal parallel computer using a greedy scheduler. She claims that the three runs yielded T 4 = 80...
-
Parents with a child in subsidized childcare in the province of Qubec, Canada, pay a basic amount and, depending on family income, may pay an additional amount. As of January 1, 2017, families with a...
-
A firm in the state of Karnataka in India can source one of its factors of production either within the state, \(F_{K}\), or from the neighboring state of Maharashtra, \(F_{M}\). Assume the quality...
-
A firm has the cost curve \(C(q)=25+q^{2}\). Show how the firm's average cost varies with output. Is there a minimum average cost and, if so, at what level of output is average cost minimized?
Study smarter with the SolutionInn App