https://youtu.be/QIChleSVMqo

1. ήʔϜཧ࿦#4*$ԋश
ίΞΛ‫ٻ‬ΊΔ

2. ༏Ճ๏ੑΛຬͨ͢ήʔϜʹ͓͚ΔίΞ
લճͷ໰୊

3. ༏Ճ๏ੑΛຬͨ͢ήʔϜʹ͓͚ΔίΞ
ఆཧ
ಛੑؔ਺‫ܗ‬ήʔϜ ʹ͓͍ͯ
͕༏Ճ๏ੑΛຬͨ͢ͱ͖
ίΞ͸
ఆٛɿఏ‫ܞ‬ ͷෆຬ
ಛੑؔ਺‫ܗ‬ήʔϜ ʹ͓͍ͯ
഑෼ ͱఏ‫ܞ‬ ΛͱΔͱ͖
Λ഑෼ ʹର͢Δఏ‫ܞ‬ ͷෆຬͱ͍͏
ίΞʹ‫·ؚ‬ΕΔ഑෼͸ ͱͳΔͨΊ
͢΂ͯͷఏ‫ܞ‬ ʹ͍ͭͯෆຬ͕ͳ͍ঢ়ଶͱ΋‫͑ݴ‬Δ
(N, v) v
C(v) = {x ∈
𝒜
(v)|
∑
i∈S
xi ≥ v(S), ∀S ⊂ N, S ≠ ∅, N}
S
(N, v) x ∈
𝒜
(v) S ⊆ N
e(S, x) = v(S) −
∑
i∈S
xi x S
e(S, x) ≤ 0
S ⊆ N
ఏ‫߹ܞ‬ཧੑ

4.
͜ͷಛੑؔ਺Λ༻͍ͯ
ίΞΛ‫ٻ‬ΊͯΈΑ͏
v({1,2,3}) = 6 v({1,2}) = 1 v({1,3}) = 3 v({2,3}) = 2
v({1}) = v({2}) = v({3}) = 0
લճͷ໰୊ ͕७ઓུD
1ʘ2 C C
B
B
͕७ઓུD
1ʘ2 C C
B
B
φογϡ‫ߧۉ‬
φογϡ‫ߧۉ‬

5.
͜ͷಛੑؔ਺Λ༻͍ͯ
ίΞΛ‫ٻ‬ΊͯΈΑ͏
഑෼Λ ͱ͢Δͱ
શମ߹ཧੑ
‫ݸ‬ਓ߹ཧੑ
ఏ‫߹ܞ‬ཧੑΛຬͨ͢ͷͰ
શମ߹ཧੑ
‫ݸ‬ਓ߹ཧੑ
ఏ‫߹ܞ‬ཧੑ
v({1,2,3}) = 6 v({1,2}) = 1 v({1,3}) = 3 v({2,3}) = 2
v({1}) = v({2}) = v({3}) = 0
x = (x1, x2, x3)
x1 + x2 + x3 = 6
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0
x1 + x2 ≥ 1, x1 + x3 ≥ 3, x2 + x3 ≥ 2
લճͷ໰୊ ͕७ઓུD
1ʘ2 C C
B
B
͕७ઓུD
1ʘ2 C C
B
B
φογϡ‫ߧۉ‬
φογϡ‫ߧۉ‬

6.
͜ͷಛੑؔ਺Λ༻͍ͯ
ίΞΛ‫ٻ‬ΊͯΈΑ͏
഑෼Λ ͱ͢Δͱ
શମ߹ཧੑ
‫ݸ‬ਓ߹ཧੑ
ఏ‫߹ܞ‬ཧੑΛຬͨ͢ͷͰ
શମ߹ཧੑ
‫ݸ‬ਓ߹ཧੑ
ఏ‫߹ܞ‬ཧੑ
v({1,2,3}) = 6 v({1,2}) = 1 v({1,3}) = 3 v({2,3}) = 2
v({1}) = v({2}) = v({3}) = 0
x = (x1, x2, x3)
x1 + x2 + x3 = 6
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0
x1 + x2 ≥ 1, x1 + x3 ≥ 3, x2 + x3 ≥ 2
⇒ 5 ≥ x3, 3 ≥ x2, 4 ≥ x1
C(v) = {x ∈
𝒜
(v)|5 ≥ x3, 3 ≥ x2, 4 ≥ x1}
લճͷ໰୊ ͕७ઓུD
1ʘ2 C C
B
B
͕७ઓུD
1ʘ2 C C
B
B
φογϡ‫ߧۉ‬
φογϡ‫ߧۉ‬
1
2 3
x1 ≤ 4
x2 ≤ 3
x3 ≤ 5
ίΞ

7. ήʔϜཧ࿦#4*$ԋश
ίΞΛ‫ٻ‬ΊΔ
࣍ճɿԋश