Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 9.3, Problem 9E
Program Plan Intro
To describe the way to pick the optimal location of the main pipeline that minimizes the total length of the spurs and also shows the method to determine the optimal location in linear time.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A seven-story office building has 15 adjacent offices per floor. Each office contains a
wall socket for a terminal in the front wall, so the sockets form a rectangular grid in the
vertical plane, with a separation of 4 m between sockets, both horizontally and
vertically. Assuming that it is feasible to run a straight cable between any pair of
sockets, horizontally, vertically, or diagonally, how many meters of cable are needed to
connect all sockets using
a. (a) a star configuration with a single router in the middle?
b. (b) an 802.3 LAN?
Pakistan Railway has hired you for the task of repair of its rail networks of province SINDH, the cost of the repair of track between the different cities are presented in the given Table. For instance, the entry (KHI,HYD)= 10 in the table tells us the cost of building a rail connection between these two cities is 10 (in million rupees)
You are required to develop a rail network that connects all the cities by at least one path with the smallest cost by avoiding multiple paths to the same city. Hence the problem becomes the finding of Minimum spanning tree in a graph.
Your job is as follows;
a) Translate the given information in the form of Graph (Vertices & edges)
b) Use Greedy Algorithms (Kruskal’s , if the S5 is odd & Prim’s technique , if S5 is even) to build rail connections in this scenario. Apply this algorithm and show all steps up to the final routes.
c) What is the cost of repairing of resulting rail network?
A regional telephone company had 5.2 million subscribers. Each of their telephones is connected to a central office by a copper twisted pair. The average length of these twisted pairs is 3.5 km. How much is the copper in the local loops worth? Assume that the cross section of each strand is a circle 1.2 mm in diameter, the density of copper is 8.4 grams/cm3, and that copper sells for $15.00 per kilogram.
Chapter 9 Solutions
Introduction to Algorithms
Knowledge Booster
Similar questions
- API=(141.5/(SG))-131.5 SG=(141.5/(API+131.5)) The Characterization factor(Kw) for crude oil is given as; Kw=(∛TB)/SG where; TB=mean aberage boiling point, deg Rankine SG =specific gravity at 60 ℉ Crude oil are classified based on the following criteria; Kw =12.5-13.0→Paraffin based crude oil Kw =11.0-12.0→Napthenic based crude oil Kw =9.8-11.0→Aromatic based crude oil based on the above information,write php program for the classification of crude oilsarrow_forwardIn Figure, suppose that the wellheads can be divided into two groups depending on gas pressure: a high-pressure group that includes wells 2, 3, 4, and 6 and a low-pressure group that includes wells 5, 7, 8, and 9 . Because of pressure difference, it is not possible to link the wellheads from the two groups. At the same time, both groups must be connected to the delivery point through wellhead 1. Determine the minimum pipeline network for this situation. Choices: a.) Set length of arcs 3-5, 5-3, 4-5, 5-4, 4-7, 7-4, 5-6, and 6-5 to ∞ : Total length = 53 b.) Set length of arcs 3-5, 5-3, 4-5, 5-4, 4-7, 7-4, 5-6, and 6-5: Total length = 53 c.) Set length of arcs 3-5, 5-3, 4-5, 5-4, 4-7, 7-4, 5-6, and 6-7 to ∞ : Total length = 53 d.) Set length of arcs 3-5, 5-3, 4-5, 5-4, 4-7, 7-4, and 6-5 to ∞ : Total length = 53arrow_forwardFully developed flow moving a 40 cm diameter pipe has the following velocity profile: Radius r, cm 0.02.55.07.510.0 12.5 15.0 17.5 20.0 Velocity v, m/s 0.914 0.890 0.847 0.795 0.719 0.543 0.427 0.204 0 Find the volumetric flow rate Q integrate from 0 to R using the relationship Q = [_0^R_ 2rtrvdr. Where r is the radial axis of the pipe, R is the radius of the pipe and v is the velocity. Solve the problem using two steps. Fit a polynomial curve to the velocity data using polyfit. Integrate the equation using int.arrow_forward
- Coding problems: HW5_2 A thin square metal plate has uniform temperature of E1 4T, = E, + E2 + T, + T6 degrees on two opposite edges, a temperature of E2 on one edge, 4T, = E, + T1 + T3 + T5 and E3 on the final edge. Equations can be written for the 4T3 = E1 + E3 +T2+ T4 temperatures, Ti, at 6 uniformly spaced interior nodes. Solve for the 4T4 = E1 + E3 + T3 + T5 node temperatures when E1=80, E2=120 and E3=60. 4T5 = E1 + T2 + T4 + T6 Present the results in a complete sentence using fprintf 4T, = E1 + E2 + T, + T5arrow_forwardComputer Science Hand-execute the Ford-Fulkerson algorithm on the transport network. Find the maximum flow through the network. Identify the cut whose capacity equals the maximum flow. Your answer should include all the details of the execution clearly.arrow_forwardMajor Luna is sending military troops from his base (A) to the town of G. However, there is no direct route between A and G. Instead, the troops must pass through other places, namely: B, C, D, E, and F. The following routes are possible: A to B, A to C, B to F, C to D, C to E, D to G, E to G, and F to G. For some reason, such places can only accommodate a number of soldiers going through these places. B, C, D, E, and F has a capacity of 3, 3, 9, 6, and 4 soldiers. b. Solve the problem using the Ford-Fulkerson algorithm.arrow_forward
- A contractor owns three excavators of different capacity. He/she wants to dispatch these excavatorsinto three different jobs. The performance of the excavators is measured as the time consumed toperform each job. The data of the time tests are shown as given in the table below. (a) Draw a network flow diagram.(b) Formulate a mathematical model to obtain the minimum time.(c) Solve this model using the Vogel’s approximation model.arrow_forwardTN Communications provides cellular telephone services. The company is planning to expand into the Cincinnati area and is trying to determine the best location for its transmission tower. The tower transmits over a radius of 10 miles. The locations that must be reached by this tower are shown in the following figure. x y Florence 10 24 Covington 12 16 Hyde Park 16 18 Evendale 12 22 I was able to get the answer to question a, which was: x y Tower Location 12 22 Max Distance 6 And I almost got the answer to question b, but I'm missing the y, what is the answer? x y Tower Location 12.51 Max Distance 4.45arrow_forwardUsing MATLAParrow_forward
- Pipeline fluid flows are indicated below. Determine the maximum flow from Node 1 to Node 3. From To Pipeline Node Node Capacity 1 3 400 3 1 100 1 2 300 2 1 0 2 3 100 3 2 100 a. 700 b. 400 c. 100 d. none of the answers presented apply. e. 500arrow_forwardPipeline fluid flows are indicated below. Determine the maximum flow from Node 1 to Node 4. From To Pipeline Node Node Capacity 1 2 400 2 1 0 1 4 200 4 1 200 1 3 200 3 1 0 2 4 200 4 2 200 3 4 300 4 3 300 a. none of the answers presented apply. b. 600 c. 300 d. 700 e. 200arrow_forwardA uniform beam subject to a linearly increasing distributed load is shown below. The equation for the beam deflection (y) is Wo L Wo -(-x' + 2Ľ²X³ – L*x) y = 120EIL (а) (x = 0, y = 0) (x = L, y = 0) (b) where L = 600 cm, I = 30,000 cm*, and wo = 2.5 kN/cm. Write an m-file that uses the modified secant method with perturbation factor 8 = 0.1 to determine the location (xmax) of the maximum deflection in the beam, which occurs where dy/dx = 0. Use a stopping criterion of ɛa< 0.0001%.Your plot from problem 4 in homework 1 may help to provide an initial guess of the location. To evaluate the effect of material properties on the beam's deflection, the m-file must create a plot of the value of the maximum deflection for 100 equally spaced E values ranging from 30,000 kN/cm? to 70,000 kN/cm?. Label your axes appropriately. Turn in a printout of your code and a printout of the plot. Also state the x location of the point of maximum deflection.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole