7. Consider the following graph: A 9 14 D E C 12 10 17 B Apply Kruskal's algorithm to find the minimum spanning tree. Edges are sorted first by length, and in the event of a tie, by name, where the two letters are in alphabetical order. Use makeset (x), find (x), and union (x, y) to determine if there are cycles. a) Circle the edges that are part of the minimum spanning tree. AC, AD, AE, BC, BD, BE, DE b) What is the weight of the minimum spanning tree? c) Draw the tree that results from applying the union-find algorithm for cycle detection. When drawing the tree, put vertices with lower letters in the left subtrees so that all the vertices in a level are sorted alphabetically from left to right

7. Consider the following graph: A 9 14 D E C 12 10 17 B Apply Kruskal's algorithm to find the minimum spanning tree. Edges are sorted first by length, and in the event of a tie, by name, where the two letters are in alphabetical order. Use makeset (x), find (x), and union (x, y) to determine if there are cycles. a) Circle the edges that are part of the minimum spanning tree. AC, AD, AE, BC, BD, BE, DE b) What is the weight of the minimum spanning tree? c) Draw the tree that results from applying the union-find algorithm for cycle detection. When drawing the tree, put vertices with lower letters in the left subtrees so that all the vertices in a level are sorted alphabetically from left to right

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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9:17 Today Edit 9:17 AM Given a directed graph G=(V, E), design an algorithm to find out whether there is a route between two nodes, say, u and v. Your design should be based on depth first search and should be given in pseudo code.
max edge distance Simplification key Figure 4-1: A sample process for the Douglas-Peucker algorithm The Douglas-Peucker algorithm is for the selection of representative points to simplify a curve composed of line segments. It uses a point-to-edge distance tolerance. The algorithm starts with a crude simplification that is the single edge joining the first and last vertices of the original polyline. It then computes the perpendicular distance of all intermediate vertices to that edge. The vertex that is furthest away from that edge, and that has a computed distance that is larger than a specified tolerance, will be marked as a key and added to the simplification. This process will recurse for each edge in the current simplification until all vertices of the original polyline are within tolerance of the simplification results. This process is illustrated in Figure 4-1. (1) Given three points (xp, Yp), (Xa, Ya), (Xp,Yb), show a detailed process to compute the perpendicular distance from p…
b) Apply an algorithm to find the minimum spanning tree. To solve this problem, you need to transfer the unweighted graph into weighted graph and you can do it by using your mobile number (11 digits). Just assign the digits sequentially (left to right) to the edges of binary tree segment (means black color edges). And for rest of the edges, you may write 1 as their weights.
Minimum Spanning Trees (MST): Finding a Minimum Spanning Tree for the following graph based on each of the following algorithm. You need to show the procedures step-by-step. You could directly draw the final MST but indicate the sequence of your search by writing a series of letters, i.e. (a), (b), (c)… under the edges of the MST. This type of answer is preferred. Or else, you need to draw a graph for each step separately. Kruskal’s algorithm. Prim’s algorithm (start with the node ‘ORD).
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4-Clique Problem The clique problem is to find cliques in a graph. A clique is a set of vertices that are all adjacent - connected - to each other. A 4-clique is a set of 4 vertices that are all connected to each other. So in this example of the 4-Clique Problem, we have a 7-vertex graph. A brute-force algorithm has searched every possible combination of 4 vertices and found a set that forms a clique: https://en.wikipedia.org/wiki/Clique_problem You should read the Wikipedia page for the Clique Problem (and then read wider if need be) if you need to understand more about it. Note that the Clique Problem is NP-Complete and therefore when the graph size is large a deterministic search is impractical. That makes it an ideal candidate for an evolutionary search. For this assignment you must suppose that you have been tasked to implement the 4-clique problem as an evolutionary algorithm for any graph with any number of vertices (an n-vertex graph). The algorithm succeeds if it finds a…
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c) Given the following Graph and after applying Dijkstra algorithm, the final table looks as given below. 16 10 11 12 XXX H 4 18 Fr Vertex known d. T A 7 B T 0 15 H 19 C 41 M J B C D E F G I J JJ K L M T T T T T T T T T T T 6 2 20 5 7 14 31 P G 10 K 30 D G J K T 10 560 From this information, find out the shortest path from the source vertex B to vertex I, trace the path and also find out the shortest distance.
a) write the algorithm b) Briefly explain why the algorithm solves the problem, and the correctness c ) State and briefly explain the running time of your algorithm
A B. D H Suppose you run the topological sort algorithm on the graph above starting at vertex C. Use the rule that when there is a choice of vertices for the algorithm to visit, it visits them in alphabetic order. Which vertex would end up first in the eventual topologically sorted order? Which would end up being second? Which would end up being third? Which would end up being fourth? Which would end up being fifth? Which would end up being sixth?
Exercise # 2 - Detecting Cycle between List of N Airports The following graph is an example from Rosen (2011). It shows the flights and distances between some of the major airports in the United States. Dallas 200 1300 200 Austin Washington Denver 1400 Atlanta 160 800 800 Chicago Houston Write a function that takes a list of N airports and checks if they form a cycle of size N. {A cycle is a directed path that starts and ends at the same vertex. Before writing code, make sure you can identify cycles yourself} >> check_cycles (G, ['Austin','Houston', 'Atlanta','Washington','Dallas'l) Yes >>> check_cycles (G, ['Austin', 'Houston','Atlanta','Washington']) No 600 600 780 0000 000L 006