Explanation Algorithm used: Kruskal’s Algorithm The procedure for Kruskal’s Algorithm to construct a minimum spanning tree: Step 1: Select the overall lowest weight and mark it in color. Step 2: Select the edge with lowest weight from the remaining edges which should not form a circuit with the colored edges and mark it in color. Step 3: Proceed this process till all the vertices are covered. Nearest neighbor method The procedure for the nearest neighbor method: Step 1: Draw the complete, weighted graph. Step 2: Select a vertex and choose an edge with shortest distance or lowest cost (smallest weight) and travel along the next vertex with second smallest weight. Step 3: From the second vertex repeat the step 2. Step 4: Continue this process till the entire vertex are covered and return back to the initial vertex. This procedure gives an approximate solution instead of optimal solution. The minimum spanning tree: By the use of Google map, the distance in miles from Pittsburgh to Cleveland is 134, Pittsburgh to Columbus is 186, Pittsburgh to Cincinnati is 287, Pittsburgh to Detroit is 285, Cleveland to Columbus is 143, Cleveland to Cincinnati is 249, Cleveland to Detroit is 168, Columbus to Cincinnati is 108, Columbus to Detroit is 200, Cincinnati to Detroit is 263. Each city is represented as vertices and the route between them as edges. The complete graph has edges between each pair of vertices and the weighted graph has the weights marked near each edge. The complete and weighted graph for the given information is drawn below in Figure 1. From Figure 1, the distance in miles is marked over each edge and there exists edges between each pair of vertices...

3rd Edition

ISBN: 9780073519678

Author: David Sobecki Professor, Allan G. Bluman

Publisher: McGraw-Hill Education

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Chapter 14.4, Problem 36E

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To find: The minimum spanning tree and approximate optimal solution.

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The minimum spanning tree and approximate optimal solution.

Solution Summary: The author explains Kruskal's algorithm to construct a minimum spanning tree and approximate optimal solution.

To find: The minimum spanning tree and approximate optimal solution.

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Chapter 14 Solutions