ply Prims algorithm to the graph below, starting with vertex a. Construct a table that shows the vertices added to the spanning tree in one column, and the priority queue containing the remaining vertices in a second column, as Levitin does in Figure 9.3. (It is not necessary to illustrate the graph at each step.) Label each vertex with (1) the nearest vertex in the spanning tree so far, and (2) the weight of the edge to that vertex. 4 9 a d 6 C 12 7 5 b e 10 Tree vertices Priority queue of remaining vertices When the algorithm is complete, show how to construct the list of edges that makes up the spanning tree from the information in your table, and write down this list.

ply Prims algorithm to the graph below, starting with vertex a. Construct a table that shows the vertices added to the spanning tree in one column, and the priority queue containing the remaining vertices in a second column, as Levitin does in Figure 9.3. (It is not necessary to illustrate the graph at each step.) Label each vertex with (1) the nearest vertex in the spanning tree so far, and (2) the weight of the edge to that vertex. 4 9 a d 6 C 12 7 5 b e 10 Tree vertices Priority queue of remaining vertices When the algorithm is complete, show how to construct the list of edges that makes up the spanning tree from the information in your table, and write down this list.

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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2. Consider the graph G2(V2, E2) below. 2a. Find the MST of this graph with Kruskal’s algorithm. Draw the MST, and show the table [edge] [w(u, v)] [mark]. 2b. Find the MST of this graph with Prim’s algorithm starting at vertex 'a'. Draw the MST and list the vertices in order you added them to the MST. 2c. Would you get a different MST if you repeat 2b starting at vertex 'e'? Why or why not?
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A mathematician applies Prim’s Algorithm to find a minimum spanning tree for the weighted graph starting at vertex D. The order of the edges picked so far is AD, AB, BE, and EF. The next edge selected when applying Prim’s Algorithm should be BF FG CG CE What is the total weight of the tree that uses the edges DE, CE, CG, FG and BF? 93 92 91 90 The tree described in problem #8 is a spanning True False
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1 A spanning tree for an undirected graph is a sub-graph which includes all vertices but has no cycles. There can be several spanning trees for a graph. A weighted undirected graph can have several spanning trees One of the spanning trees has smallest sum of all the weights associated with the edges. This tree is called minimum spanning tree (MST). Find the MST in the following graph using Kruskal?s Algorithm. V={a, b, c, d, e, f, g, h, i, j} and E={(a, b, 12), (a, b, 3), (a, j, 13), (b, c, 12), (b, d, 2), (b, h, 4), (b, i, 25), (c, d, 7), (c, j, 5), (e, f, 11), (e, j, 9), (f, g, 15), (f, h, 14), (g, h, 6), (h, d, 20), (h, i, 1) }. Note: Numeric value is the weight of the corresponding edge.