a) First, represent each problem by drawing a weighted graph. Label the vertices and indicate the weight of each edge. b) Then solve the problem. Recall: Greedy Algorithm 1. Choose a vertex to start at, then travel along the connected edge that has the smallest weight. (If two or more edges have the same weight, pick anyone.) 2. After arriving at the next vertex, travel along the edge of the smallest weight that connects to a vertex not yet visited. Continue this process until you have visited all vertices. 3. Return to the starting vertex. 1. Vincent needs to visit the pet store, the shopping mall, the local farmers market, and the pharmacy. His estimated driving times (in minutes) between locations are given in the table. a) Use the greedy algorithm to find two possible routes, starting and ending at home, that will help Vincent minimize his total travel time. (You need to find two answers for this problem.) Draw the weighted graph that represents each route (trace the route) and compute for the total travel time. Pharmacy home pet store shopping mall Farmer's market 18 0 14 22 20 0 home pet store 18 shopping mall 27 Farmer's market 15 pharmacy 8 27 14 0 30 32 15 22 30 0 25 8 20 32 25 0

a) First, represent each problem by drawing a weighted graph. Label the vertices and indicate the weight of each edge. b) Then solve the problem. Recall: Greedy Algorithm 1. Choose a vertex to start at, then travel along the connected edge that has the smallest weight. (If two or more edges have the same weight, pick anyone.) 2. After arriving at the next vertex, travel along the edge of the smallest weight that connects to a vertex not yet visited. Continue this process until you have visited all vertices. 3. Return to the starting vertex. 1. Vincent needs to visit the pet store, the shopping mall, the local farmers market, and the pharmacy. His estimated driving times (in minutes) between locations are given in the table. a) Use the greedy algorithm to find two possible routes, starting and ending at home, that will help Vincent minimize his total travel time. (You need to find two answers for this problem.) Draw the weighted graph that represents each route (trace the route) and compute for the total travel time. Pharmacy home pet store shopping mall Farmer's market 18 0 14 22 20 0 home pet store 18 shopping mall 27 Farmer's market 15 pharmacy 8 27 14 0 30 32 15 22 30 0 25 8 20 32 25 0

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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3. Kleinberg, Jon. Algorithm Design (p. 519, q. 28) Consider this version of the Independent Set Problem. You are given an undirected graph G and an integer k. We will call a set of nodes I "strongly independent" if, for any two nodes v, u € I, the edge (v, u) is not present in G, and neither is there a path of two edges from u to v. That is, there is no node w such that both (v, w) and (u, w) are present. The Strongly Independent Set problem is to decide whether G has a strongly independent set of size at least k. Show that the Strongly Independent Set Problem is NP-Complete.
.... Multiple choice: Consider a weighted graph where all the edges have weight=10. If we want to determine the shortest path between any two vertices, which algorithm can we use? Select all that applies: (select many) a. Bellman-Ford Algorithm b. Breadth First Search c. Dijkstra's Algorithm d. Floyd-Warshall Algorithm
Suppose you have a graph G with 6 vertices and 7 edges, and you are given the following information: The degree of vertex 1 is 3. The degree of vertex 2 is 4. The degree of vertex 3 is 2. The degree of vertex 4 is 3. The degree of vertex 5 is 2. The degree of vertex 6 is 2. What is the minimum possible number of cycles in the graph G?
Trees: a. Given a tree with 37 vertices. How many edges does the graph have? b. Given a tree with 45 vertices. How many edges does the graph have? c. Given a tree with 37 edges. How many vertices does the graph have? d. Given a tree with 45 edges. How many vertices does the graph have?
Given the following graph find all articulation points. If necessary, consider nodes and edges in alphabetical order. H. Display all articulation points alphabetically. Please, report only the list of vertices separated by a single space. No other symbols must be included in the response. This is an example of the response format: ABC etc. Computer Science Please not Calculus
: |: Section 3 - Random Forests Decision Trees on their own are effectiev classifiers. The true power, though, comes from a forest of trees -- multiple decision trees working together as an ensemble learner. We create multiple trees, each using a subset of the available attributes, let them each make a guess at the correct classification, and then take the majority vote as the predicted class. Sounds tricky, right? Once again, sklearn to the rescue. We are going to see if a random forest can improve on our decision tree accuracy for the bank data. To begin, we are going to create a Random Forest using the wheat training and test data from the previous section. First, reload our data. 1 # reload the wheat dataset from UCI 2 3 df = pd. read_csv ("seeds_dataset.txt", sep='\\t', engine='python') 4 6 7 df.columns = ['a', 'p', 'compactness', 'length', 'width', 'coeff', 'length_g', 'type'] print (f'Our data has {df.shape [0]} rows and {df.shape [1]} columns') 8 #Mark 70% of the data for…
A. Let G be a graph on 17 vertices. We know that G contains at most one cycle. How many edges can G contain at the most? B. The expression r is written in post-order notation (also referred to as RPN). What value does r evaluate to? r = 1 6 7 + - 5 3 + 2 * +
Please answer this question in 10 mins I will upvote your answer this question. Imagine a maze that consists of an n x n grid of cells. You can move from a cell to its neighbor provided there is no wall obstructing your path in that direction. Your goal is to find a path from the top right cell in the maze to the bottom left cell. a) Explain how finding a path through this maze can be represented as a graph problem. Clearly explain what the nodes and edges in your graph formulation correspond to in terms of the structure of the original maze. You may include a diagram or a sketch to explain your reasoning. b) using c++, implement an algorithm to find if a given maze has a solution (i.e., if it has a path that connects the top right cell to the bottom left cell). If it has a solution, the algorithm should return this path. If there is more than one possible solution, your algorithm should return any one of those possible paths. If there is no solution to the maze, return a special…
Consider navigating the maze shown below. N (М G 1. S 2. A 3. B 4. F 8. 5. H 6. D L 7. P (2 G 2 2 4 C E P 2 2 2 A S B FL The maze is represented as a graph with edge costs as shown on the edges. The edge cost is 1 for all edges where the cost is not shown. Let S be the initial state and G be the goal state. List the first 8 vertices expanded by Uniform Cost Search (enter the single letter label of a node). K 2 2 J 2 D H
Python Graph Algorithms: Minimum Spanning Trees Suppose you are an engineer working on designing a road network for a new town. The town has many residential areas and commercial centers that need to be connected efficiently. You decided to represent the town as a connected, undirected graph where each vertex represents a location, and each edge represents a road connecting two locations. The weight of each edge represents the distance between the two locations. To ensure the road network is efficient, you need to find the minimum spanning tree of the graph. However, due to budget constraints, you can only construct roads with a maximum distance limit. You need to determine for how many pairs of locations, the minimum spanning tree of the graph remains the same when the maximum distance limit of a road is increased by 2 units. To solve this, you write a program that takes as input the number of locations, the number of roads, and the weight of each road. Your program will also receive…
1. Use the graph below to answer the following questions. A B H 10 G 10 25 20 5 50 5 5 30 5 15 C 20 D F 15 E (a) Use Kruskal's Algorithm to produce a minimum spanning tree. Write down the edges that you choose in order of the algorithm. (b) Use Prim's Algorithm to produce a minimum spanning tree (assume A is the root/source). Write down the edges that you choose in order of the algorithm.
1. In the figure bellow, the nodes are laid out on a grid where each square has a size of 5x5 units. The node P is the start node, and the D node is goal node. List the order of nodes in which the A* algorithm explores the graph. Use the Manhattan Distances as a heuristic function. Note that if two nodes have the same value, select the nodes in alphabetical order. 31 33 24 31 25 40 21 22 25 25 21 start 13 35 35 45 21 Figure: graph with edge costs (z