Unformatted text preview: w i are capable of performing jobs t j as shown in the following table. Worker capable of these jobs w 1 t 1 , t 2 , t 3 w 2 t 1 , t 2 , t 5 w 3 t 2 , t 4 , t 6 w 4 t 3 , t 4 , t 5 w 5 t 4 , t 6 w 6 t 2 , t 6 (a) Draw the bipartite graph G whose vertices are the the w i and t j and whose edges represent which workers are capable of which jobs. (b) Starting with the matching M = {{ w 1 ,t 1 } , { w 2 ,t 2 } , { w 3 ,t 4 } , { w 4 ,t 5 } , { w 6 ,t 6 }} use the bipartite matching algorithm to ﬁnd a maximum matching for G . (c) Does G have a perfect matching? (d) Worker w 2 becomes partially incapacitated and can no longer perform tasks t 1 or t 5 . Let H be the resulting bipartite graph. Starting with the matching M given above, use the bipartite matching algorithm to ﬁnd a minimum covering and a maximum matching in H . (e) Does H have a perfect matching?...
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 Spring '08
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 Math, WI, Bipartite graph, Dulmage–Mendelsohn decomposition, maximum matching, bipartite matching algorithm

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