Explanation 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. Calculation: Let A be the initial vertex. Notice that the edge with minimum weight from the vertex A is AC and its weight is 8. Then from the vertex C , there are two possible shortest edges CB and CE . Case (i): Choose the edge CB and its weight is 12. Now from the vertex B , the next shortest edge is BF whose weight is 13. Then from the vertex F , the edge with next minimum weight whose vertex are not covered is FE and its weight is 13...

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ISBN: 9780073519678

Author: David Sobecki Professor, Allan G. Bluman

Publisher: McGraw-Hill Education

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Chapter 14.3, Problem 34E

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The approximate optimal solution for the given weighted graph by the use of nearest neighbor method.

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