F = 0.1
tildeV = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
opening hub costs
1:12.0 2:12.0 3:12.0 4:12.0 5:12.0 6:12.0 7:12.0 8:12.0 9:12.0 10:12.0 11:12.0 12:12.0
c =
1 2 3 4 5 6 7 8 9 10 11 12
1 . 171.0 144.0 248.0 45.0 232.0 106.0 141.0 156.0 45.0 42.0 90.0
2 . . 70.0 236.0 209.0 301.0 67.0 115.0 47.0 204.0 177.0 108.0
3 . . . 171.0 171.0 232.0 61.0 45.0 24.0 164.0 165.0 58.0
4 . . . . 242.0 124.0 223.0 133.0 190.0 233.0 286.0 180.0
5 . . . . . 205.0 144.0 156.0 187.0 9.0 78.0 113.0
6 . . . . . . 261.0 187.0 255.0 199.0 274.0 207.0
7 . . . . . . . 90.0 60.0 139.0 115.0 55.0
8 . . . . . . . . 69.0 148.0 172.0 55.0
9 . . . . . . . . . 181.0 172.0 76.0
10 . . . . . . . . . . 81.0 107.0
11 . . . . . . . . . . . 118.0
12 . . . . . . . . . . . .
d =
1 2 3 4 5 6 7 8 9 10 11 12
1 . 399.0 336.0 577.0 105.0 542.0 246.0 328.0 364.0 105.0 98.0 208.0
2 399.0 . 162.0 550.0 488.0 701.0 155.0 267.0 110.0 476.0 411.0 251.0
3 336.0 162.0 . 399.0 399.0 541.0 141.0 105.0 55.0 383.0 385.0 135.0
4 577.0 550.0 399.0 . 564.0 288.0 519.0 309.0 442.0 544.0 667.0 418.0
5 105.0 488.0 399.0 564.0 . 478.0 334.0 364.0 436.0 20.0 182.0 264.0
6 542.0 701.0 541.0 288.0 478.0 . 608.0 437.0 595.0 463.0 639.0 483.0
7 246.0 155.0 141.0 519.0 334.0 608.0 . 210.0 139.0 323.0 267.0 127.0
8 328.0 267.0 105.0 309.0 364.0 437.0 210.0 . 159.0 345.0 400.0 127.0
9 364.0 110.0 55.0 442.0 436.0 595.0 139.0 159.0 . 421.0 402.0 176.0
10 105.0 476.0 383.0 544.0 20.0 463.0 323.0 345.0 421.0 . 189.0 248.0
11 98.0 411.0 385.0 667.0 182.0 639.0 267.0 400.0 402.0 189.0 . 274.0
12 208.0 251.0 135.0 418.0 264.0 483.0 127.0 127.0 176.0 248.0 274.0 .
c'=c and d'=d
RING NODES 1 10 11 12 RING 1 --- 12 | cost [90.0] 1 --- 13 | cost [0.0] 10 --- 11 | cost [81.0] 10 --- 13 | cost [45.0] 11 --- 12 | cost [118.0] STAR 2 --> 12 | cost [251.0] 3 --> 12 | cost [135.0] 4 --> 12 | cost [418.0] 5 --> 12 | cost [264.0] 6 --> 12 | cost [483.0] 7 --> 12 | cost [127.0] 8 --> 12 | cost [127.0] 9 --> 12 | cost [176.0] ring = [(1, 12), (10, 11), (10, 13), (11, 12)] BACKUP RING 1 --- 11 | cost [42.0] 10 --- 12 | cost [107.0] 11 --- 13 | cost [42.0] BACKUP STAR 2 --> 1 | cost [399.0] 3 --> 1 | cost [336.0] 4 --> 10 | cost [544.0] 5 --> 10 | cost [20.0] 6 --> 10 | cost [463.0] 7 --> 1 | cost [246.0] 8 --> 1 | cost [328.0] 9 --> 1 | cost [364.0]
α[2] = 41.1, α_poly[2] = 39.9
α[3] = 38.3, α_poly[3] = 33.6
α[4] = 54.4, α_poly[4] = 54.4
α[5] = 2.0, α_poly[5] = 2.0
α[6] = 46.3, α_poly[6] = 46.3
α[7] = 26.7, α_poly[7] = 24.6
α[8] = 34.5, α_poly[8] = 32.8
α[9] = 42.1, α_poly[9] = 36.4
β[1, 12, 11] = 4.2, β_poly[1, 12, 11] = 4.2
γ[2, 12] = 0.1, γ_poly[2,12] = 0.1
γ[3, 12] = 0.1, γ_poly[3,12] = 0.1
γ[4, 12] = 0.1, γ_poly[4,12] = 0.1
γ[5, 12] = 0.1, γ_poly[5,12] = 0.1
γ[6, 12] = 0.1, γ_poly[6,12] = 0.1
γ[7, 12] = 0.1, γ_poly[7,12] = 0.1
γ[8, 12] = 0.1, γ_poly[8,12] = 0.1
γ[9, 12] = 0.1, γ_poly[9,12] = 0.1
δ[1, 12, 11] = 0.1, δ_poly[1, 12, 11] = 0.1 cost[98.0]
ζ[2, 1] = 0.0, ζ_poly[2,1] = 39.9
ζ[2, 3] = 24.9, ζ_poly[2,3] = 0.0
ζ[2, 7] = 25.6, ζ_poly[2,7] = 0.0
ζ[2, 8] = 14.4, ζ_poly[2,8] = 0.0
ζ[2, 9] = 30.1, ζ_poly[2,9] = 0.0
ζ[2, 12] = 41.1, ζ_poly[2,12] = 0.0
ζ[3, 1] = 0.0, ζ_poly[3,1] = 33.6
ζ[3, 2] = 22.1, ζ_poly[3,2] = 0.0
ζ[3, 7] = 24.2, ζ_poly[3,7] = 0.0
ζ[3, 8] = 27.8, ζ_poly[3,8] = 0.0
ζ[3, 9] = 32.8, ζ_poly[3,9] = 0.0
ζ[3, 12] = 38.3, ζ_poly[3,12] = 0.0
ζ[4, 1] = 0.0, ζ_poly[4,1] = 54.4
ζ[4, 3] = 14.5, ζ_poly[4,3] = 0.0
ζ[4, 6] = 25.6, ζ_poly[4,6] = 0.0
ζ[4, 7] = 2.5, ζ_poly[4,7] = 0.0
ζ[4, 8] = 23.5, ζ_poly[4,8] = 0.0
ζ[4, 9] = 10.2, ζ_poly[4,9] = 0.0
ζ[4, 12] = 54.4, ζ_poly[4,12] = 0.0
ζ[5, 1] = 0.0, ζ_poly[5,1] = 2.0
ζ[5, 12] = 2.0, ζ_poly[5,12] = 0.0
ζ[6, 1] = 0.0, ζ_poly[6,1] = 46.3
ζ[6, 4] = 17.5, ζ_poly[6,4] = 0.0
ζ[6, 8] = 2.64, ζ_poly[6,8] = 0.0
ζ[6, 12] = 46.3, ζ_poly[6,12] = 0.0
ζ[7, 1] = 0.0, ζ_poly[7,1] = 24.6
ζ[7, 2] = 11.2, ζ_poly[7,2] = 0.0
ζ[7, 3] = 12.6, ζ_poly[7,3] = 0.0
ζ[7, 8] = 5.7, ζ_poly[7,8] = 0.0
ζ[7, 9] = 12.8, ζ_poly[7,9] = 0.0
ζ[7, 12] = 26.7, ζ_poly[7,12] = 0.0
ζ[8, 1] = 0.0, ζ_poly[8,1] = 32.8
ζ[8, 2] = 7.8, ζ_poly[8,2] = 0.0
ζ[8, 3] = 24.0, ζ_poly[8,3] = 0.0
ζ[8, 4] = 3.6, ζ_poly[8,4] = 0.0
ζ[8, 7] = 13.5, ζ_poly[8,7] = 0.0
ζ[8, 9] = 18.6, ζ_poly[8,9] = 0.0
ζ[8, 12] = 34.5, ζ_poly[8,12] = 0.0
ζ[9, 1] = 0.0, ζ_poly[9,1] = 36.4
ζ[9, 2] = 31.1, ζ_poly[9,2] = 0.0
ζ[9, 3] = 36.6, ζ_poly[9,3] = 0.0
ζ[9, 7] = 28.2, ζ_poly[9,7] = 0.0
ζ[9, 8] = 26.2, ζ_poly[9,8] = 0.0
ζ[9, 11] = 1.9, ζ_poly[9,11] = 0.0
ζ[9, 12] = 42.1, ζ_poly[9,12] = 0.0
ζ[12, 1] = 0.0, ζ_poly[12,1] = 20.8
(B_computed, B_primal, B_val, B_dual_poly) = (274.2, 274.2, 287.7, 274.2)