DO LETTERS A & B FOR UPVOTE. PLEASE SKIP THIS IF YOU ALREADY DID THIS. THANK YOU SO MUCH. I REALLY NEED DIFFERENT ANSWERS. II. Read each problem carefully and present an algorithm with the required running-time to solve eachproblem.1. In class we discussed that directed acyclic graphs (DAG) can be used to representdependency/precedence relations. One example is modeling task dependency where tasks arerepresented as vertices and edges represents direct dependencies between tasks, e.g., if task Trequires task T, then there is an edge from vertex i to vertex j. Arranging tasks with respect to theirdependencies can easily be done by performing topological sort to the DAG.a. Describe an algorithm that runs in O(n + m) time that given two tasks, T, and I₁, determines iftask T, can be performed without performing task T₁. Note that I, is not required if it is not a director indirect dependency of T. Task I, is an indirect dependency of task T, if there is no edge fromT, to T, but I must appear before 7, in the topological order.b. Describe an algorithm that runs in O(n + m) time that given a task T₁, outputs the minimumpossible position of tasks T, in any topological order.

Answered: precedence relations. One exam as…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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II. Read each problem carefully and present an algorithm with the required running-time to solve each problem. 1. In class we discussed that directed acyclic graphs (DAG) can be used to represent dependency/precedence relations. One example is modeling task dependency where tasks are represented as vertices and edges represents direct dependencies between tasks, e.g., if task T requires task T, then there is an edge from vertex i to vertex j. Arranging tasks with respect to their dependencies can easily be done by performing topological sort to the DAG. b. Describe an algorithm that runs in O(n + m) time that given a task T₁, outputs the minimum possible position of tasks T, in any topological order.
Chess is a board game, where the board is made up of 64 squares arranged in an 8-by-8 grid. One of the pieces is a rook, which can move from its current square any number of spaces either vertically or horizontally (but not diagonally) in a single turn. Discuss how you could use graphs to show that a rook can get from its current square to any other square on the board in at most two turns. You’re encouraged to utilize relevant graph definitions, problems, and algorithms where appropriate.
Socaccio Pistachio, Inc. makes two types of pistachio nuts: Dazzling Red and Organic. Pistachio nuts require food color and salt, and the following table shows the amount of food color and salt required fo a 1-kilogram batch of pistachios as well as the total amount of these ingridients available each day: Use a graph to show the possible numbers of batches of each type of pistachio Socaccio can produce each day. Dazzling Red Organic Total Available Food color(grams) 2 1 20 Salt(grams) 10 20 220
Construct a niche overlap graph for six species of birds, where the hermit thrush competes with the robin and with the blue jay, the robin also competes with the mockingbird, the mockingbird also competes with the blue jay, and the nuthatch competes with the hairy woodpecker.
Consider the following graph. (Enter your answers as comma-separated lists.) A graph with 5 vertices and 7 edges is shown. Loop e1 connects vertex v1 and vertex v1. Edge e2 connects vertex v1 and vertex v2. Edge e7 connects vertex v1 and vertex v3. Loop e3 connects vertex v2 and vertex v2. Edge e6 connects vertex v2 and vertex v3. Edge e4 connects vertex v2 and vertex v5. Edge e5 connects vertex v2 and vertex v5. Vertex v4 is isolated. (a) Find all edges that are incident on v1. (b) Find all vertices that are adjacent to v3. (c) Find all edges that are adjacent to e1. (d) Find all loops. (e) Find all parallel edges. (f) Find all isolated vertices. (g) Find the degree of v3.
Among each pair of the CEOs of N companies there is (a) mutual like; (b) mutual dislike; (c) neutral feeling. A trade delegation of the maximum size needs to be formed such that it does not have any pair of members with mutual dislike. Transform this problem to a graph theoretic problem. What are the vertices of the graph? What are the edges of the graph? What do you have to find in the graph?
3. Can you think of a connected graph with four vertices, so that the span of the columns of the adjacency matrix is R¹? Can you generalize this to a graph with n vertices?
Vw QUESTION 10 9. Please use the graph below to show that Dijkstra's algorithm cannot be used if the graph has negative edges. Source = A 3. 1. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). Paragraph 10pt Arial 田国出田回 BIUS
Each vertex in the graph represents an animal that needs to be transported to the zoo. Two vertices are connected by an edge whenever the corresponding animals cannot be placed in the same cage (i.e., the edges represent pairs of animals that would harm each other if caged together). What is the fewest number of cages needed to transport these animals? Give a conflict-free way to assign them to cages. S V U W Y
What is the number of connected components for each of the following graphs?
4. Watch up to 1:00 minute of the following clip from Brooklyn 99 (feel free to keep watching because it is rather funny): https://www.youtube.com/watch?v=Ncl3n2f2uuU Boyle used an undirected graph to represent the different text chains at work. Sociologists also use graphs to model social relationships. A social network is a graph where the nodes represent "actors" (e.g., people, companies) and the edges represent relationships, or "ties," between actors (e.g., friendships, business partnerships). Consider the following social network. B TECHNIE) D A H EA a. A clique in a social network is a group of actors who all have ties to each other. What is the largest clique in this social network? 3 b. If you had to choose the most important actor in this social network, who would you pick? Why? c. Suppose the actors represent people and the ties represent acquaintances. If the people in this social network continue to interact, which two (currently unacquainted) actors would you most expect…
3. Use the training data of Gauss2 example (Gauss2.train). (a). Run the K-means algorithm with K = 2 clusters and make a plot identifying the clusters. Also label the points with their known classes. = 2 clusters and make (b). Multiple all the x1 by 10. Run the K-means algorithm with K a plot identifying the clusters. Also label the points with their known classes. (c). Compare the class and cluster groupings for both plots in (a) and (b). Explain any differences between them. (d). Use agglomerative hierarchical clustering (hclust in the MASS library) to cluster the data, and divide them into 2 groups. You can use the function cutree to divide the clusters into 2 groups. Report on how the predicted cluster labels compare with actual cluster labels for each of the three methods for measuring distance between clusters, i.e. single linkage, complete linkage and average linkage. (e). Plot the dendrograms for the three methods in (d). What does the shape of the the dendrograms suggest about…

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precedence relations. One exam as vertices and edges represents I, then there is an edge from ver can easily be done by performing