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hw5 - ENGRI 115 Engineering Applications of OR Fall 2007...

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ENGRI 115 Engineering Applications of OR Fall 2007 Maximum Matchings in Bipartite Graphs Homework 5 Due date: Thursday, October 25 in class. References: Lecture notes; Lab 6; The first two problems are practice problems, DO NOT hand them in. The TAs will be glad to help you if you have any questions. 1. G is a bipartite graph, V 1 = { a, b, c, d, e, f, g, h, } and V 2 = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 } . Neighbors for the nodes in V 1 are listed below. Find a maximum matching using the Alternating Path Algorithm. What is the size of a maximum matching? Indicate a minimum node cover for this graph. a: 3, 5, 6; b: 2, 3, 4, 7; c: 3, 5; d: 1, 4, 8; e: 3, 6; f: 1, 2, 7, 8; g: 1, 3, 5, 8; h: 5, 6. 2. Seven students (A, B, C, D, E, F, G) have applied for six on-campus jobs (1, 2, 3, 4, 5, 6); A for 1; B for 1 and 6; C for 2, 3, and 4; D for 2 and 5; E for 3, 4, 5; F for 1 and 6; G for 6. Can all the six jobs be filled? Does it make any difference if F changes his mind and decides to apply for job 2 as well? 3. The foreman at the Duffield Hall construction site has to assign six workers (A, B, C, D, E, F) to the following six machines: a crane, a bulldozer, two dump-trucks, a piledriver and a cement mixer.
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