This page lists all instances currently available. Click on any block to (un)collapse. Then click any header column to sort the table.

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Legend:
  • |V|: Number of nodes in the graph (MaxCut, .mc) representation of the instance.
  • |E|: Number of edges in the graph (MaxCut, .mc) representation of the instance.
  • dim(Q): Row/Column dimension of the matrix Q in the unconstrained BQP (.bq) representation of the instance.
  • nz(Q>): Number of non-zero entries in the strict upper triangle of a symmetrized matrix Q in the unconstrained BQP (.bq) representation of the instance.
  • nz(Diag(Q)): Number of non-zero entries on the diagonal of the matrix Q in the unconstrained BQP (.bq) representation of the instance.
  • OSV: The optimal solution value of the instance (or a lower/upper bound if marked by an asterisk).
Sparse unconstrained BQP instances (density 10%) generated by John E. Beasley as part of the OR Library (1990) where they can be retrieved with weights assuming a maximization objective.
There are ten instances bqpn-i with dimension n=50,100,250,500. These instances are also part of the Biq Mac Library (2007).
Instance |V| |E| dim(Q) nz(Q>) nz(Diag(Q)) OSV
bqp100-1 (.mc, .bq) 101 563 100 464 11 -7970
bqp100-10 (.mc, .bq) 101 584 100 485 12 -12565
bqp100-2 (.mc, .bq) 101 582 100 482 12 -11036
bqp100-3 (.mc, .bq) 101 590 100 490 15 -12723
bqp100-4 (.mc, .bq) 101 575 100 475 12 -10368
bqp100-5 (.mc, .bq) 101 558 100 459 12 -9083
bqp100-6 (.mc, .bq) 101 610 100 510 18 -10210
bqp100-7 (.mc, .bq) 101 567 100 469 9 -10125
bqp100-8 (.mc, .bq) 101 591 100 492 7 -11435
bqp100-9 (.mc, .bq) 101 602 100 502 9 -11455
bqp250-1 (.mc, .bq) 251 3339 250 3089 31 -45607
bqp250-10 (.mc, .bq) 251 3294 250 3045 24 -40442
bqp250-2 (.mc, .bq) 251 3285 250 3035 29 -44810
bqp250-3 (.mc, .bq) 251 3313 250 3063 29 -49037
bqp250-4 (.mc, .bq) 251 3397 250 3147 26 -41274
bqp250-5 (.mc, .bq) 251 3364 250 3114 20 -47961
bqp250-6 (.mc, .bq) 251 3433 250 3183 25 -41014
bqp250-7 (.mc, .bq) 251 3337 250 3087 24 -46757
bqp250-8 (.mc, .bq) 251 3265 250 3015 24 -35726
bqp250-9 (.mc, .bq) 251 3395 250 3145 22 -48916
bqp50-1 (.mc, .bq) 51 158 50 108 3 -2098
bqp50-10 (.mc, .bq) 51 158 50 108 3 -3507
bqp50-2 (.mc, .bq) 51 168 50 120 3 -3702
bqp50-3 (.mc, .bq) 51 182 50 132 4 -4626
bqp50-4 (.mc, .bq) 51 160 50 111 4 -3544
bqp50-5 (.mc, .bq) 51 181 50 131 7 -4012
bqp50-6 (.mc, .bq) 51 150 50 101 14 -3693
bqp50-7 (.mc, .bq) 51 174 50 124 3 -4520
bqp50-8 (.mc, .bq) 51 187 50 137 10 -4216
bqp50-9 (.mc, .bq) 51 172 50 122 7 -3780
bqp500-1 (.mc, .bq) 501 12871 500 12372 49 n/a
bqp500-10 (.mc, .bq) 501 12908 500 12408 48 n/a
bqp500-2 (.mc, .bq) 501 12778 500 12278 39 n/a
bqp500-3 (.mc, .bq) 501 13021 500 12522 34 n/a
bqp500-4 (.mc, .bq) 501 12779 500 12280 52 n/a
bqp500-5 (.mc, .bq) 501 12830 500 12330 47 n/a
bqp500-6 (.mc, .bq) 501 12817 500 12318 52 n/a
bqp500-7 (.mc, .bq) 501 12907 500 12407 51 n/a
bqp500-8 (.mc, .bq) 501 12776 500 12276 38 n/a
bqp500-9 (.mc, .bq) 501 12857 500 12358 42 n/a
Unconstrained BQP instances generated by Alain Billionnet and Sourour Elloumi (2007) using the generator proposed by P. M. Pardalos and G. P. Rodgers (1990). The precise calls to the generator can be obtained from here.
  • be100.i Ten instances with dimension n=100 and density 1.
  • ben.3.i Ten instances with dimension n=120,150,200 and density 0.3.
  • ben.8.i Ten instances with dimension n=120,150,200 and density 0.8.
  • be250.i Ten instances with dimension n=250 and density 0.1.
These instances are also part of the Biq Mac Library (2007), and part of the OR Library (1990) where they can be retrieved with weights assuming a maximization objective.
Instance |V| |E| dim(Q) nz(Q>) nz(Diag(Q)) OSV
be100.1 (.mc, .bq) 101 5003 100 4903 100 -19412
be100.10 (.mc, .bq) 101 5006 100 4906 98 -15352
be100.2 (.mc, .bq) 101 5006 100 4906 98 -17290
be100.3 (.mc, .bq) 101 5000 100 4900 99 -17565
be100.4 (.mc, .bq) 101 5004 100 4905 100 -19125
be100.5 (.mc, .bq) 101 5005 100 4905 100 -15868
be100.6 (.mc, .bq) 101 4992 100 4892 99 -17368
be100.7 (.mc, .bq) 101 5015 100 4915 100 -18629
be100.8 (.mc, .bq) 101 5009 100 4909 100 -18649
be100.9 (.mc, .bq) 101 4997 100 4898 99 -13294
be120.3.1 (.mc, .bq) 121 2242 120 2123 120 -13067
be120.3.10 (.mc, .bq) 121 2248 120 2128 119 -12201
be120.3.2 (.mc, .bq) 121 2253 120 2133 120 -13046
be120.3.3 (.mc, .bq) 121 2176 120 2056 120 -12418
be120.3.4 (.mc, .bq) 121 2224 120 2105 120 -13867
be120.3.5 (.mc, .bq) 121 2248 120 2128 120 -11403
be120.3.6 (.mc, .bq) 121 2240 120 2120 119 -12915
be120.3.7 (.mc, .bq) 121 2192 120 2072 120 -14068
be120.3.8 (.mc, .bq) 121 2249 120 2130 119 -14701
be120.3.9 (.mc, .bq) 121 2184 120 2064 120 -10458
be120.8.1 (.mc, .bq) 121 5764 120 5644 120 -18691
be120.8.10 (.mc, .bq) 121 5768 120 5648 120 -19049
be120.8.2 (.mc, .bq) 121 5747 120 5627 120 -18827
be120.8.3 (.mc, .bq) 121 5791 120 5672 120 -19302
be120.8.4 (.mc, .bq) 121 5764 120 5644 119 -20765
be120.8.5 (.mc, .bq) 121 5753 120 5633 120 -20417
be120.8.6 (.mc, .bq) 121 5720 120 5600 120 -18482
be120.8.7 (.mc, .bq) 121 5795 120 5675 119 -22194
be120.8.8 (.mc, .bq) 121 5743 120 5624 120 -19534
be120.8.9 (.mc, .bq) 121 5736 120 5616 120 -18195
be150.3.1 (.mc, .bq) 151 3500 150 3350 150 -18889
be150.3.10 (.mc, .bq) 151 3452 150 3303 149 -17963
be150.3.2 (.mc, .bq) 151 3535 150 3385 149 -17816
be150.3.3 (.mc, .bq) 151 3400 150 3250 149 -17314
be150.3.4 (.mc, .bq) 151 3446 150 3296 150 -19884
be150.3.5 (.mc, .bq) 151 3490 150 3340 147 -16817
be150.3.6 (.mc, .bq) 151 3516 150 3366 150 -16780
be150.3.7 (.mc, .bq) 151 3464 150 3315 148 -18001
be150.3.8 (.mc, .bq) 151 3465 150 3316 148 -18303
be150.3.9 (.mc, .bq) 151 3377 150 3227 150 -12838
be150.8.1 (.mc, .bq) 151 8981 150 8831 147 -27089
be150.8.10 (.mc, .bq) 151 8992 150 8842 148 -28374
be150.8.2 (.mc, .bq) 151 9021 150 8872 150 -26779
be150.8.3 (.mc, .bq) 151 8994 150 8844 150 -29438
be150.8.4 (.mc, .bq) 151 8977 150 8827 149 -26911
be150.8.5 (.mc, .bq) 151 8939 150 8789 150 -28017
be150.8.6 (.mc, .bq) 151 8937 150 8788 150 -29221
be150.8.7 (.mc, .bq) 151 9009 150 8859 150 -31209
be150.8.8 (.mc, .bq) 151 8967 150 8817 148 -29730
be150.8.9 (.mc, .bq) 151 8941 150 8791 149 -25388
be200.3.1 (.mc, .bq) 201 6123 200 5923 199 -25453
be200.3.10 (.mc, .bq) 201 6143 200 5943 197 -23842
be200.3.2 (.mc, .bq) 201 6176 200 5976 199 -25027
be200.3.3 (.mc, .bq) 201 5994 200 5794 198 -28023
be200.3.4 (.mc, .bq) 201 6077 200 5877 200 -27434
be200.3.5 (.mc, .bq) 201 6080 200 5880 198 -26355
be200.3.6 (.mc, .bq) 201 6113 200 5916 199 -26146
be200.3.7 (.mc, .bq) 201 6107 200 5908 200 -30483
be200.3.8 (.mc, .bq) 201 6130 200 5930 200 -27355
be200.3.9 (.mc, .bq) 201 6088 200 5888 199 -24683
be200.8.1 (.mc, .bq) 201 15971 200 15771 198 -48534
be200.8.10 (.mc, .bq) 201 15963 200 15763 199 -42832
be200.8.2 (.mc, .bq) 201 15957 200 15757 199 -40821
be200.8.3 (.mc, .bq) 201 15945 200 15745 200 -43207
be200.8.4 (.mc, .bq) 201 15971 200 15771 200 -43757
be200.8.5 (.mc, .bq) 201 15859 200 15659 199 -41482
be200.8.6 (.mc, .bq) 201 15877 200 15677 200 -49492
be200.8.7 (.mc, .bq) 201 15971 200 15771 200 -46828
be200.8.8 (.mc, .bq) 201 15923 200 15723 200 -44502
be200.8.9 (.mc, .bq) 201 15921 200 15721 199 -43241
be250.1 (.mc, .bq) 251 3269 250 3019 249 -24076
be250.10 (.mc, .bq) 251 3349 250 3099 250 -23159
be250.2 (.mc, .bq) 251 3343 250 3093 250 -22540
be250.3 (.mc, .bq) 251 3279 250 3029 248 -22923
be250.4 (.mc, .bq) 251 3326 250 3078 249 -24649
be250.5 (.mc, .bq) 251 3348 250 3098 250 -21057
be250.6 (.mc, .bq) 251 3309 250 3059 245 -22735
be250.7 (.mc, .bq) 251 3389 250 3140 248 -24095
be250.8 (.mc, .bq) 251 3283 250 3036 248 -23801
be250.9 (.mc, .bq) 251 3280 250 3032 249 -20051
Ising Spinglass instances generated by Samuel Burer, Renato D. C. Monteiro, and Yin Zhang (2002).
More precisely: 20 regular cubic lattices having randomly generated interaction magnitudes, ten with base length 10 (1000 nodes), and ten with base length 14 (2744 nodes). Like the problems considered by Hartmann (1997), the weights are from {-1, 0, 1} such that the total weight sum is zero. Notice that here, due to the format specifications, the zero-weight edges are not included.
Instance |V| |E| dim(Q) nz(Q>) nz(Diag(Q)) OSV
sg3dl101000 (.mc, .bq) 1000 3000 1000 3000 697 n/a
sg3dl1010000 (.mc, .bq) 1000 3000 1000 3000 701 n/a
sg3dl102000 (.mc, .bq) 1000 3000 1000 3000 688 n/a
sg3dl103000 (.mc, .bq) 1000 3000 1000 3000 686 n/a
sg3dl104000 (.mc, .bq) 1000 3000 1000 3000 675 n/a
sg3dl105000 (.mc, .bq) 1000 3000 1000 3000 680 n/a
sg3dl106000 (.mc, .bq) 1000 3000 1000 3000 683 n/a
sg3dl107000 (.mc, .bq) 1000 3000 1000 3000 697 n/a
sg3dl108000 (.mc, .bq) 1000 3000 1000 3000 679 n/a
sg3dl109000 (.mc, .bq) 1000 3000 1000 3000 683 n/a
sg3dl141000 (.mc, .bq) 2744 8232 2744 8232 1884 n/a
sg3dl1410000 (.mc, .bq) 2744 8232 2744 8232 1901 n/a
sg3dl142000 (.mc, .bq) 2744 8232 2744 8232 1885 n/a
sg3dl143000 (.mc, .bq) 2744 8232 2744 8232 1911 n/a
sg3dl144000 (.mc, .bq) 2744 8232 2744 8232 1857 n/a
sg3dl145000 (.mc, .bq) 2744 8232 2744 8232 1892 n/a
sg3dl146000 (.mc, .bq) 2744 8232 2744 8232 1891 n/a
sg3dl147000 (.mc, .bq) 2744 8232 2744 8232 1938 n/a
sg3dl148000 (.mc, .bq) 2744 8232 2744 8232 1920 n/a
sg3dl149000 (.mc, .bq) 2744 8232 2744 8232 1872 n/a
Unconstrained BQP instances generated by Fred Glover, Gary A. Kochenberger and Bahram Alidaee using the generator proposed by P. M. Pardalos and G. P. Rodgers (1990). The precise calls to the generator can be obtained from here.
  • gkaia: Eight instances with dimensions from 30 to 100, densities from 0.0625 to 0.5. Diagonal coefficients from [-100,100], off-diagonal coefficients from [-100,100].
  • gkaib: Ten instances with dimensions from 20 to 125, density 1. Diagonal coefficients from [-63,0], off-diagonal coefficients from [0,100].
  • gkaic: Seven instances with dimensions from 40 to 100, densities from 0.1 to 0.8. Diagonal coefficients from [-100,100], off-diagonal coefficients from [-50,50].
  • gkaid: Ten instances with dimension 100, densities from 0.1 to 1. Diagonal coefficients from [-75,75], off-diagonal coefficients from [-50,50].
  • gkaie: Five instances with dimension 200, densities from 0.1 to 0.5. Diagonal coefficients from [-100,100], off-diagonal coefficients from [-50,50].
  • gkaif: Five instances with dimension 500, densities from 0.1 to 1. Diagonal coefficients from [-75,75], off-diagonal coefficients from [-50,50].
These instances are also part of the Biq Mac Library (2007), and part of the OR Library (1990) where they can be retrieved with weights assuming a maximization objective.
Instance |V| |E| dim(Q) nz(Q>) nz(Diag(Q)) OSV
gka10b (.mc, .bq) 126 7791 125 7666 122 -154
gka10d (.mc, .bq) 101 4997 100 4897 99 -19102
gka1a (.mc, .bq) 51 156 50 106 50 -3414
gka1b (.mc, .bq) 21 207 20 187 20 -133
gka1c (.mc, .bq) 41 665 40 625 40 -5058
gka1d (.mc, .bq) 101 593 100 494 99 -6333
gka1e (.mc, .bq) 201 2124 200 1924 200 -16464
gka1f (.mc, .bq) 501 12921 500 12421 496 n/a
gka2a (.mc, .bq) 61 222 60 163 59 -6063
gka2b (.mc, .bq) 31 459 30 429 30 -121
gka2c (.mc, .bq) 51 813 50 763 50 -6213
gka2d (.mc, .bq) 101 1116 100 1016 100 -6579
gka2e (.mc, .bq) 201 4127 200 3927 200 -23395
gka2f (.mc, .bq) 501 31518 500 31018 496 n/a
gka3a (.mc, .bq) 71 292 70 223 69 -6037
gka3b (.mc, .bq) 41 812 40 772 39 -118
gka3c (.mc, .bq) 61 761 60 701 60 -6665
gka3d (.mc, .bq) 101 1524 100 1425 100 -9261
gka3e (.mc, .bq) 201 6049 200 5850 198 -25243
gka3f (.mc, .bq) 501 62405 500 61906 494 n/a
gka4a (.mc, .bq) 81 384 80 304 79 -8598
gka4b (.mc, .bq) 51 1259 50 1209 49 -129
gka4c (.mc, .bq) 71 790 70 720 69 -7398
gka4d (.mc, .bq) 101 2100 100 2000 100 -10727
gka4e (.mc, .bq) 201 8117 200 7917 200 -35594
gka4f (.mc, .bq) 501 93253 500 92753 495 n/a
gka5a (.mc, .bq) 51 281 50 231 50 -5737
gka5b (.mc, .bq) 61 1811 60 1751 60 -150
gka5c (.mc, .bq) 81 721 80 641 80 -7362
gka5d (.mc, .bq) 101 2514 100 2414 99 -11626
gka5e (.mc, .bq) 201 10057 200 9857 198 -35154
gka5f (.mc, .bq) 501 124021 500 123521 498 n/a
gka6a (.mc, .bq) 31 204 30 174 30 -3980
gka6b (.mc, .bq) 71 2458 70 2388 70 -146
gka6c (.mc, .bq) 91 490 90 400 89 -5824
gka6d (.mc, .bq) 101 3048 100 2948 100 -14207
gka7a (.mc, .bq) 31 241 30 211 30 -4541
gka7b (.mc, .bq) 81 3205 80 3125 80 -160
gka7c (.mc, .bq) 101 595 100 495 100 -7225
gka7d (.mc, .bq) 101 3532 100 3434 98 -14476
gka8a (.mc, .bq) 101 404 100 304 99 -11109
gka8b (.mc, .bq) 91 4053 90 3963 89 -145
gka8d (.mc, .bq) 101 4007 100 3907 100 -16352
gka9b (.mc, .bq) 101 5003 100 4903 99 -137
gka9d (.mc, .bq) 101 4446 100 4346 99 -15656
MaxCut instances generated by Christoph Helmberg and Franz Rendl (2000) using the machine independent graph generator ``rudy'' written by G. Rinaldi. The precise calls to ``rudy'' can be obtained from the original article.
The first 21 graphs have 800 nodes. More precisely:
  • Graphs G1 to G5 are random graphs with unit weights and a density of 6%.
  • G6 to G10 are the same graphs with random edge weights from {-1, 1}.
  • G11 to G13 are toroidal grids with random edge weights from {-1, 1}.
  • G14 to G17 are composed from the union of two (almost maximal) planar graphs with unit weights.
  • G18 to G21 are the same graphs with random edge weights from {-1, 1}.
The next 21 graphs, G22 to G42, have the analogous types but with 2000 nodes.
G43 to G54 are again constructed using the same types.
Instance |V| |E| dim(Q) nz(Q>) nz(Diag(Q)) OSV
G_1 (.mc, .bq) 800 19176 800 19176 800 n/a
G_10 (.mc, .bq) 800 19176 800 19176 757 n/a
G_11 (.mc, .bq) 800 1600 800 1600 519 n/a
G_12 (.mc, .bq) 800 1600 800 1600 498 n/a
G_13 (.mc, .bq) 800 1600 800 1600 486 n/a
G_14 (.mc, .bq) 800 4694 800 4694 800 n/a
G_15 (.mc, .bq) 800 4661 800 4661 800 n/a
G_16 (.mc, .bq) 800 4672 800 4672 800 n/a
G_17 (.mc, .bq) 800 4667 800 4667 800 n/a
G_18 (.mc, .bq) 800 4694 800 4694 668 n/a
G_19 (.mc, .bq) 800 4661 800 4661 686 n/a
G_2 (.mc, .bq) 800 19176 800 19176 800 n/a
G_20 (.mc, .bq) 800 4672 800 4672 701 n/a
G_21 (.mc, .bq) 800 4667 800 4667 670 n/a
G_22 (.mc, .bq) 2000 19990 2000 19990 2000 n/a
G_23 (.mc, .bq) 2000 19990 2000 19990 2000 n/a
G_24 (.mc, .bq) 2000 19990 2000 19990 2000 n/a
G_25 (.mc, .bq) 2000 19990 2000 19990 2000 n/a
G_26 (.mc, .bq) 2000 19990 2000 19990 2000 n/a
G_27 (.mc, .bq) 2000 19990 2000 19990 1840 n/a
G_28 (.mc, .bq) 2000 19990 2000 19990 1813 n/a
G_29 (.mc, .bq) 2000 19990 2000 19990 1820 n/a
G_3 (.mc, .bq) 800 19176 800 19176 800 n/a
G_30 (.mc, .bq) 2000 19990 2000 19990 1811 n/a
G_31 (.mc, .bq) 2000 19990 2000 19990 1829 n/a
G_32 (.mc, .bq) 2000 4000 2000 4000 1281 n/a
G_33 (.mc, .bq) 2000 4000 2000 4000 1215 n/a
G_34 (.mc, .bq) 2000 4000 2000 4000 1267 n/a
G_35 (.mc, .bq) 2000 11778 2000 11778 2000 n/a
G_36 (.mc, .bq) 2000 11766 2000 11766 2000 n/a
G_37 (.mc, .bq) 2000 11785 2000 11785 2000 n/a
G_38 (.mc, .bq) 2000 11779 2000 11779 2000 n/a
G_39 (.mc, .bq) 2000 11778 2000 11778 1698 n/a
G_4 (.mc, .bq) 800 19176 800 19176 800 n/a
G_40 (.mc, .bq) 2000 11766 2000 11766 1708 n/a
G_41 (.mc, .bq) 2000 11785 2000 11785 1676 n/a
G_42 (.mc, .bq) 2000 11779 2000 11779 1685 n/a
G_43 (.mc, .bq) 1000 9990 1000 9990 1000 n/a
G_44 (.mc, .bq) 1000 9990 1000 9990 1000 n/a
G_45 (.mc, .bq) 1000 9990 1000 9990 1000 n/a
G_46 (.mc, .bq) 1000 9990 1000 9990 1000 n/a
G_47 (.mc, .bq) 1000 9990 1000 9990 1000 n/a
G_48 (.mc, .bq) 3000 6000 3000 6000 3000 n/a
G_49 (.mc, .bq) 3000 6000 3000 6000 3000 n/a
G_5 (.mc, .bq) 800 19176 800 19176 800 n/a
G_50 (.mc, .bq) 3000 6000 3000 6000 3000 n/a
G_51 (.mc, .bq) 1000 5909 1000 5909 1000 n/a
G_52 (.mc, .bq) 1000 5916 1000 5916 1000 n/a
G_53 (.mc, .bq) 1000 5914 1000 5914 1000 n/a
G_54 (.mc, .bq) 1000 5916 1000 5916 1000 n/a
G_6 (.mc, .bq) 800 19176 800 19176 752 n/a
G_7 (.mc, .bq) 800 19176 800 19176 759 n/a
G_8 (.mc, .bq) 800 19176 800 19176 743 n/a
G_9 (.mc, .bq) 800 19176 800 19176 757 n/a
Ising Spinglass instances generated by Frauke Liers (2004).
  • ising2.5-n_seed: For each dimension three one-dimensional Ising chain instances. n=100,150,200,250,300.
  • ising3.0-n_seed: For each dimension three one-dimensional Ising chain instances. n=100,150,200,250,300.
  • t2gn_seed: For each dimension three two-dimensional toroidal grid graphs with gaussian distributed weights and dimension n times n, n=10,15,20.
  • t3gn_seed: For each dimension three three-dimensional toroidal grid graphs with gaussian distributed weights and dimension n times n times n, n=5,6,7.
These instances are also part of the Biq Mac Library (2007).
Attention: As opposed to other representations of some of these instances, ours do not contain zero-weight edges or coeffcients in accordance with our format specifications.
Instance |V| |E| dim(Q) nz(Q>) nz(Diag(Q)) OSV
ising2.5-100_5555 (.mc, .bq) 100 4881 100 4881 100 2460049
ising2.5-100_6666 (.mc, .bq) 100 4877 100 4877 100 2031217
ising2.5-100_7777 (.mc, .bq) 100 4869 100 4869 100 3363230
ising2.5-150_5555 (.mc, .bq) 150 10711 150 10711 150 4363532
ising2.5-150_6666 (.mc, .bq) 150 10722 150 10722 150 4057153
ising2.5-150_7777 (.mc, .bq) 150 10698 150 10698 150 4243269
ising2.5-200_5555 (.mc, .bq) 200 18237 200 18237 200 6294701
ising2.5-200_6666 (.mc, .bq) 200 18246 200 18246 200 6795365
ising2.5-200_7777 (.mc, .bq) 200 18230 200 18230 200 5568272
ising2.5-250_5555 (.mc, .bq) 250 26522 250 26522 250 7919449
ising2.5-250_6666 (.mc, .bq) 250 26533 250 26533 250 6925717
ising2.5-250_7777 (.mc, .bq) 250 26534 250 26534 250 6596797
ising2.5-300_5555 (.mc, .bq) 300 34576 300 34576 300 8579363
ising2.5-300_6666 (.mc, .bq) 300 34753 300 34753 300 9102033
ising2.5-300_7777 (.mc, .bq) 300 34717 300 34717 300 8323804
ising3.0-100_5555 (.mc, .bq) 100 4575 100 4575 100 2448189
ising3.0-100_6666 (.mc, .bq) 100 4543 100 4543 100 1984099
ising3.0-100_7777 (.mc, .bq) 100 4546 100 4546 100 3335814
ising3.0-150_5555 (.mc, .bq) 150 8390 150 8390 150 4279261
ising3.0-150_6666 (.mc, .bq) 150 8432 150 8432 150 3949317
ising3.0-150_7777 (.mc, .bq) 150 8413 150 8413 150 4211158
ising3.0-200_5555 (.mc, .bq) 200 10459 200 10459 200 6215531
ising3.0-200_6666 (.mc, .bq) 200 10474 200 10474 200 6756263
ising3.0-200_7777 (.mc, .bq) 200 10492 200 10492 200 5560824
ising3.0-250_5555 (.mc, .bq) 250 12039 250 12039 250 7823791
ising3.0-250_6666 (.mc, .bq) 250 12008 250 12008 250 6903351
ising3.0-250_7777 (.mc, .bq) 250 12031 250 12031 250 6418276
ising3.0-300_5555 (.mc, .bq) 300 14011 300 14011 300 8493173
ising3.0-300_6666 (.mc, .bq) 300 13882 300 13882 300 8915110
ising3.0-300_7777 (.mc, .bq) 300 13983 300 13983 300 8242904
t2g10_5555 (.mc, .bq) 100 200 100 200 100 6049461
t2g10_6666 (.mc, .bq) 100 200 100 200 100 5757868
t2g10_7777 (.mc, .bq) 100 200 100 200 100 6509837
t2g15_5555 (.mc, .bq) 225 450 225 450 225 15051133
t2g15_6666 (.mc, .bq) 225 450 225 450 225 15763716
t2g15_7777 (.mc, .bq) 225 450 225 450 225 15269399
t2g20_5555 (.mc, .bq) 400 800 400 800 400 24838942
t2g20_6666 (.mc, .bq) 400 800 400 800 400 29290570
t2g20_7777 (.mc, .bq) 400 800 400 800 400 28349398
t3g5_5555 (.mc, .bq) 125 375 125 375 125 10933215
t3g5_6666 (.mc, .bq) 125 375 125 375 125 11582216
t3g5_7777 (.mc, .bq) 125 375 125 375 125 11552046
t3g6_5555 (.mc, .bq) 216 648 216 648 216 17434469
t3g6_6666 (.mc, .bq) 216 648 216 648 216 20217380
t3g6_7777 (.mc, .bq) 216 648 216 648 216 19475011
t3g7_5555 (.mc, .bq) 343 1029 343 1029 343 28302918
t3g7_6666 (.mc, .bq) 343 1029 343 1029 343 33611981
t3g7_7777 (.mc, .bq) 343 1029 343 1029 343 29118445
These instances were generated from real-world data on radio frequency interferences between major Italian cities in the context of a frequency assignment problem. They have been made available by Carlo Mannino and have been first used in a MaxCut context in this paper.
Instance |V| |E| dim(Q) nz(Q>) nz(Diag(Q)) OSV
mannino_k48 (.mc, .bq) 48 1128 48 1128 48 252518838
mannino_k487a (.mc, .bq) 487 1435 487 1435 412 1110926
mannino_k487b (.mc, .bq) 487 5391 487 5391 487 3655475
mannino_k487c (.mc, .bq) 487 8511 487 8511 487 8640860
MaxCut instances generated by Angelika Wiegele as part of the Biq Mac Library (2007) using the machine independent graph generator ``rudy'' written by G. Rinaldi. The precise calls to ``rudy'' can be obtained from here.
Attention: As opposed to other representations of some of these instances, ours do not contain zero-weight edges or coeffcients in accordance with our format specifications.
  • g05_n.i: For each dimension ten unweighted graphs with edge probability 0.5. n=60,80,100
  • pm1s_n.i: For each dimension ten weighted graphs with edge weights chosen uniformly from {-1,0,1} and density 0.1. n=80,100
  • pm1d_n.i: For each dimension ten weighted graphs with edge weights chosen uniformly from {-1,0,1} and density 0.99. n=80,100
  • wd_100.i: For each density ten graphs with integer edge weights chosen from [-10,10] and density d=0.1,0.5,0.9, n=100
  • pwd_100.i: For each density ten graphs with integer edge weights chosen from [0,10] and density d=0.1,0.5,0.9, n=100
Instance |V| |E| dim(Q) nz(Q>) nz(Diag(Q)) OSV
g05_100.0 (.mc, .bq) 100 2475 100 2475 100 1430
g05_100.1 (.mc, .bq) 100 2475 100 2475 100 1425
g05_100.2 (.mc, .bq) 100 2475 100 2475 100 1432
g05_100.3 (.mc, .bq) 100 2475 100 2475 100 1424
g05_100.4 (.mc, .bq) 100 2475 100 2475 100 1440
g05_100.5 (.mc, .bq) 100 2475 100 2475 100 1436
g05_100.6 (.mc, .bq) 100 2475 100 2475 100 1434
g05_100.7 (.mc, .bq) 100 2475 100 2475 100 1431
g05_100.8 (.mc, .bq) 100 2475 100 2475 100 1432
g05_100.9 (.mc, .bq) 100 2475 100 2475 100 1430
g05_60.0 (.mc, .bq) 60 885 60 885 60 536
g05_60.1 (.mc, .bq) 60 885 60 885 60 532
g05_60.2 (.mc, .bq) 60 885 60 885 60 529
g05_60.3 (.mc, .bq) 60 885 60 885 60 538
g05_60.4 (.mc, .bq) 60 885 60 885 60 527
g05_60.5 (.mc, .bq) 60 885 60 885 60 533
g05_60.6 (.mc, .bq) 60 885 60 885 60 531
g05_60.7 (.mc, .bq) 60 885 60 885 60 535
g05_60.8 (.mc, .bq) 60 885 60 885 60 530
g05_60.9 (.mc, .bq) 60 885 60 885 60 533
g05_80.0 (.mc, .bq) 80 1580 80 1580 80 929
g05_80.1 (.mc, .bq) 80 1580 80 1580 80 941
g05_80.2 (.mc, .bq) 80 1580 80 1580 80 934
g05_80.3 (.mc, .bq) 80 1580 80 1580 80 923
g05_80.4 (.mc, .bq) 80 1580 80 1580 80 932
g05_80.5 (.mc, .bq) 80 1580 80 1580 80 926
g05_80.6 (.mc, .bq) 80 1580 80 1580 80 929
g05_80.7 (.mc, .bq) 80 1580 80 1580 80 929
g05_80.8 (.mc, .bq) 80 1580 80 1580 80 925
g05_80.9 (.mc, .bq) 80 1580 80 1580 80 923
pm1d_100.0 (.mc, .bq) 100 4901 100 4901 97 340
pm1d_100.1 (.mc, .bq) 100 4901 100 4901 99 324
pm1d_100.2 (.mc, .bq) 100 4901 100 4901 99 389
pm1d_100.3 (.mc, .bq) 100 4901 100 4901 94 400
pm1d_100.4 (.mc, .bq) 100 4901 100 4901 100 363
pm1d_100.5 (.mc, .bq) 100 4901 100 4901 97 441
pm1d_100.6 (.mc, .bq) 100 4901 100 4901 97 367
pm1d_100.7 (.mc, .bq) 100 4901 100 4901 98 361
pm1d_100.8 (.mc, .bq) 100 4901 100 4901 94 385
pm1d_100.9 (.mc, .bq) 100 4901 100 4901 97 405
pm1d_80.0 (.mc, .bq) 80 3128 80 3128 75 227
pm1d_80.1 (.mc, .bq) 80 3128 80 3128 75 245
pm1d_80.2 (.mc, .bq) 80 3128 80 3128 78 284
pm1d_80.3 (.mc, .bq) 80 3128 80 3128 78 291
pm1d_80.4 (.mc, .bq) 80 3128 80 3128 79 251
pm1d_80.5 (.mc, .bq) 80 3128 80 3128 78 242
pm1d_80.6 (.mc, .bq) 80 3128 80 3128 75 205
pm1d_80.7 (.mc, .bq) 80 3128 80 3128 76 249
pm1d_80.8 (.mc, .bq) 80 3128 80 3128 74 293
pm1d_80.9 (.mc, .bq) 80 3128 80 3128 77 258
pm1s_100.0 (.mc, .bq) 100 495 100 495 88 127
pm1s_100.1 (.mc, .bq) 100 495 100 495 92 126
pm1s_100.2 (.mc, .bq) 100 495 100 495 87 125
pm1s_100.3 (.mc, .bq) 100 495 100 495 87 111
pm1s_100.4 (.mc, .bq) 100 495 100 495 86 128
pm1s_100.5 (.mc, .bq) 100 495 100 495 81 128
pm1s_100.6 (.mc, .bq) 100 495 100 495 90 122
pm1s_100.7 (.mc, .bq) 100 495 100 495 90 112
pm1s_100.8 (.mc, .bq) 100 495 100 495 91 120
pm1s_100.9 (.mc, .bq) 100 495 100 495 86 127
pm1s_80.0 (.mc, .bq) 80 316 80 316 70 79
pm1s_80.1 (.mc, .bq) 80 316 80 316 69 85
pm1s_80.2 (.mc, .bq) 80 316 80 316 67 82
pm1s_80.3 (.mc, .bq) 80 316 80 316 66 81
pm1s_80.4 (.mc, .bq) 80 316 80 316 69 70
pm1s_80.5 (.mc, .bq) 80 316 80 316 66 87
pm1s_80.6 (.mc, .bq) 80 316 80 316 71 73
pm1s_80.7 (.mc, .bq) 80 316 80 316 69 83
pm1s_80.8 (.mc, .bq) 80 316 80 316 68 81
pm1s_80.9 (.mc, .bq) 80 316 80 316 67 70
pw01_100.0 (.mc, .bq) 100 495 100 495 100 2019
pw01_100.1 (.mc, .bq) 100 495 100 495 100 2060
pw01_100.2 (.mc, .bq) 100 495 100 495 100 2032
pw01_100.3 (.mc, .bq) 100 495 100 495 100 2067
pw01_100.4 (.mc, .bq) 100 495 100 495 100 2039
pw01_100.5 (.mc, .bq) 100 495 100 495 100 2108
pw01_100.6 (.mc, .bq) 100 495 100 495 100 2032
pw01_100.7 (.mc, .bq) 100 495 100 495 100 2074
pw01_100.8 (.mc, .bq) 100 495 100 495 100 2022
pw01_100.9 (.mc, .bq) 100 495 100 495 100 2005
pw05_100.0 (.mc, .bq) 100 2475 100 2475 100 8190
pw05_100.1 (.mc, .bq) 100 2475 100 2475 100 8045
pw05_100.2 (.mc, .bq) 100 2475 100 2475 100 8039
pw05_100.3 (.mc, .bq) 100 2475 100 2475 100 8139
pw05_100.4 (.mc, .bq) 100 2475 100 2475 100 8125
pw05_100.5 (.mc, .bq) 100 2475 100 2475 100 8169
pw05_100.6 (.mc, .bq) 100 2475 100 2475 100 8217
pw05_100.7 (.mc, .bq) 100 2475 100 2475 100 8249
pw05_100.8 (.mc, .bq) 100 2475 100 2475 100 8199
pw05_100.9 (.mc, .bq) 100 2475 100 2475 100 8099
pw09_100.0 (.mc, .bq) 100 4455 100 4455 100 13585
pw09_100.1 (.mc, .bq) 100 4455 100 4455 100 13417
pw09_100.2 (.mc, .bq) 100 4455 100 4455 100 13461
pw09_100.3 (.mc, .bq) 100 4455 100 4455 100 13656
pw09_100.4 (.mc, .bq) 100 4455 100 4455 100 13514
pw09_100.5 (.mc, .bq) 100 4455 100 4455 100 13574
pw09_100.6 (.mc, .bq) 100 4455 100 4455 100 13640
pw09_100.7 (.mc, .bq) 100 4455 100 4455 100 13501
pw09_100.8 (.mc, .bq) 100 4455 100 4455 100 13593
pw09_100.9 (.mc, .bq) 100 4455 100 4455 100 13658
w01_100.0 (.mc, .bq) 100 466 100 466 98 651
w01_100.1 (.mc, .bq) 100 468 100 468 97 719
w01_100.2 (.mc, .bq) 100 460 100 460 99 676
w01_100.3 (.mc, .bq) 100 475 100 475 98 813
w01_100.4 (.mc, .bq) 100 464 100 464 97 668
w01_100.5 (.mc, .bq) 100 473 100 473 99 643
w01_100.6 (.mc, .bq) 100 474 100 474 97 654
w01_100.7 (.mc, .bq) 100 476 100 476 97 725
w01_100.8 (.mc, .bq) 100 473 100 473 98 721
w01_100.9 (.mc, .bq) 100 475 100 475 100 729
w05_100.0 (.mc, .bq) 100 2343 100 2343 100 1646
w05_100.1 (.mc, .bq) 100 2357 100 2357 99 1606
w05_100.2 (.mc, .bq) 100 2352 100 2352 97 1902
w05_100.3 (.mc, .bq) 100 2365 100 2365 98 1627
w05_100.4 (.mc, .bq) 100 2348 100 2348 98 1546
w05_100.5 (.mc, .bq) 100 2360 100 2360 100 1581
w05_100.6 (.mc, .bq) 100 2355 100 2355 97 1479
w05_100.7 (.mc, .bq) 100 2365 100 2365 99 1987
w05_100.8 (.mc, .bq) 100 2364 100 2364 100 1311
w05_100.9 (.mc, .bq) 100 2355 100 2355 99 1752
w09_100.0 (.mc, .bq) 100 4223 100 4223 98 2121
w09_100.1 (.mc, .bq) 100 4222 100 4222 99 2096
w09_100.2 (.mc, .bq) 100 4252 100 4252 100 2738
w09_100.3 (.mc, .bq) 100 4254 100 4254 99 1990
w09_100.4 (.mc, .bq) 100 4222 100 4222 100 2033
w09_100.5 (.mc, .bq) 100 4258 100 4258 99 2433
w09_100.6 (.mc, .bq) 100 4245 100 4245 98 2220
w09_100.7 (.mc, .bq) 100 4258 100 4258 98 2252
w09_100.8 (.mc, .bq) 100 4258 100 4258 99 1843
w09_100.9 (.mc, .bq) 100 4258 100 4258 99 2043

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