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HW9Sol - Fall 2009 IEOR 160 Industrial Engineering...

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Fall 2009 IEOR 160 November 16, 2009 Page 1 of 1 HOMEWORK 9 SOLUTIONS Section 8.6 1. Prim’s algorithm: We begin at Gary and include the Gary-South Bend arc. Then we add the South Bend-Fort Wayne arc. Next we add the Gary-Terre Haute arc. Finally we add the Terre Haute-Evansville arc. This minimum spanning tree has a total length of 58 + 79 + 164 + 113 = 414 miles. Kruskal’s algorithm: We first add the Gary-South Bend arc. Then we add the South Bend-Fort Wayne arc. Next we add the Terre Haute-Evansville arc. Finally we add the Gary-Terre Haute arc. Reverse algorithm: We start with the whole graph and then we remove the Fort Wayne-Evansville arc. Next we remove the Gary-Evansville arc. Finally we remove the Terre Haute-South Bend arc. 2. Prim’s algorithm: We begin at node 1 with arc (1,3). Then we add (in turn) arc (3,5), arc (3,4), and arc (3,2). Total length of the tree is 15.
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