# 45 65 a b d f g 215 235 215 215 255 i j k l m g has

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4.5 6.5 12.5 3.5 17.5 a b d f g 21.5 23.5 21.5 21.5 25.5 i j k l m G * has no perfect matching. A deficient set is { a, b, d, f, g } with N G * ( S ) = { j, m } . So ǫ = min { y i + y j w ij , i S, j W \ N G * ( S ) } = 6. Page 12

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CO 227 - Homework assignment 6 Fall ‘10 Page 13 -1.5 0.5 6.5 -2.5 11.5 a b d f g 21.5 29.5 21.5 21.5 31.5 i j k l m G * has no perfect matching. A deficient set is { a, b, d, f, g } with N G * ( S ) = { j, k, m } . So ǫ = min { y i + y j w ij , i S, j W \ N G * ( S ) } = 6. -7.5 -5.5 0.5 -8.5 5.5 a b d f g 21.5 35.5 27.5 21.5 37.5 i j k l m G * has no perfect matching. A deficient set is { a, b, d, f, g } with N G * ( S ) = { i, j, k, m } . So ǫ = min { y i + y j w ij , i S, j W \ N G * ( S ) } = 6. Page 13
CO 227 - Homework assignment 6 Fall ‘10 Page 14 -13.5 -11.5 -5.5 -14.5 -0.5 a b d f g 27.5 41.5 33.5 21.5 43.5 i j k l m G * has no perfect matching. A deficient set is { a, b, d, g } with N G * ( S ) = { j, k, m } . So ǫ = min { y i + y j w ij , i S, j W \ N G * ( S ) } = 1. -14.5 -12.5 -6.5 -14.5 -1.5 a b d f g 27.5 42.5 34.5 21.5 44.5 i j k l m G * has a perfect matching: { a, k } , { b, j } , { d, i } , { f, l } , { g, m } , which is therefore a maximum weight perfect matching of weight 121. Page 14
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