This file contains the results of running dmclique on the DIMACS benchmark graphs for clique, as well as selected random graphs with N from 100 to 8000. (For the most part, only one graph for each N,p pair; this is not intended as a statistically valid study, merely a quick survey of about what to expect from the code.) For each graph, we report the results of 1000 runs of the heuristic, giving a frequency count for the largest cliques found by each run. (We also list the true maximum clique size, when known, and the time to find it if it was found by dfmax. For random graphs, if we do not know the true optimal, we provide an estimate of the expected maximum clique size.) Times reported are the overall running time for the 1000 runs. From this data, readers can guage the kind of quality of solution and running time one would obtain by running the heuristic K times and taking the best result (at least for K <= 100 or so). Dmclique has two adjustable parameters and , and for some graphs we report the results for more than one setting, although it is possible that better results may be obtainable with other settings. The computer was an SGI Challenge, which has 8 MIPS R4400 processors. The processors on this machine are in the same class as SPARC 10's and DEC Alphas, perhaps 2-4 times faster than a SPARC 2. CLIQUE BENCHMARKS: User Time GRAPH NAME setlim candnum Read Run brock200_1.clq.b 50 30 0.05 26.56 (1000) [OPT = 21] [Note: optimally solved by dfmax in 381.22 seconds] 16 1 17 62 18 370 19 432 20 129 21 6 brock200_1.clq.b 50 50 0.05 30.79 (1000) 16 1 17 40 18 321 19 490 20 143 21 5 brock200_1.clq.b 75 30 0.05 87.77 (1000) 17 4 18 196 19 574 20 220 21 6 brock200_2.clq.b 100 30 0.03 30.81 (1000) [OPT = 12] [Note: optimally solved by dfmax in 0.72 seconds] 9 292 10 650 11 29 12 29 brock200_2.clq.b 100 50 0.03 31.48 (1000) 9 274 10 659 11 34 12 33 brock200_3.clq.b 100 30 0.05 53.20 (1000) [OPT = 15] [Note: optimally solved by dfmax in 4.95 seconds] 11 1 12 234 13 682 14 73 15 10 brock200_4.clq.b 100 30 0.05 148.92 (1000) [OPT = 17] [Note: optimally solved by dfmax in 21.18 seconds] 13 2 14 389 15 504 16 87 17 18 brock400_1.clq.b 100 50 0.18 629.72 (1000) [OPT = 27] 21 63 22 473 23 412 24 52 brock400_1.clq.b 100 100 0.18 589.18 (1000) 21 28 22 407 23 493 24 72 brock400_2.clq.b 100 100 0.18 590.17 (1000) [OPT = 29] 21 46 22 412 23 446 24 88 25 8 brock400_3.clq.b 100 50 0.18 654.02 (1000) [OPT = 31] 21 94 22 495 23 353 24 55 25 3 brock400_3.clq.b 100 100 0.18 598.13 (1000) 21 72 22 474 23 397 24 57 brock400_4.clq.b 100 50 0.18 586.44 (1000) [OPT = 33] 20 2 21 61 22 450 23 424 24 63 brock400_4.clq.b 100 100 0.18 575.34 (1000) 21 45 22 425 23 446 24 80 25 4 brock800_1.clq.b 100 100 0.72 374.31 (1000) [OPT = 23] 17 10 18 497 19 457 20 34 21 2 brock800_1.clq.b 100 200 0.72 411.89 (1000) 17 9 18 501 19 447 20 41 21 2 brock800_1.clq.b 100 300 0.73 452.61 (1000) 17 10 18 442 19 504 20 42 21 2 brock800_2.clq.b 100 200 0.72 397.33 (1000) [OPT = 24] 17 7 18 406 19 537 20 49 21 1 brock800_2.clq.b 100 300 0.72 442.77 (1000) 17 4 18 407 19 534 20 54 21 1 brock800_3.clq.b 100 100 0.72 370.51 (1000) [OPT = 25] 17 12 18 478 19 481 20 29 brock800_3.clq.b 100 200 0.72 400.92 (1000) 17 5 18 491 19 469 20 33 21 2 brock800_3.clq.b 100 300 0.72 454.71 (1000) 17 5 18 459 19 490 20 43 21 3 brock800_4.clq.b 100 100 0.72 372.93 (1000) [OPT = 26] 17 14 18 498 19 449 20 38 21 1 brock800_4.clq.b 100 200 0.72 404.26 (1000) 17 7 18 471 19 480 20 42 brock800_4.clq.b 100 300 0.72 452.22 (1000) 17 3 18 480 19 476 20 39 21 2 c-fat200-1.clq.b 100 50 0.03 13.66 (1000) [OPT = 12] [Note: optimally solved by dfmax in 0.06 seconds] 10 495 11 49 12 456 c-fat200-2.clq.b 100 50 0.03 14.35 (1000) [OPT = 24] [Note: optimally solved by dfmax in 0.07 seconds] 22 800 23 104 24 96 c-fat200-5.clq.b 100 50 0.05 20.35 (1000) [OPT = 58] [Note: optimally solved by dfmax in 24238.52 seconds] 56 151 57 259 58 590 c-fat500-1.clq.b 100 100 0.22 81.94 (1000) [OPT = 14] [Note: optimally solved by dfmax in 0.34 seconds] 12 707 13 27 14 266 c-fat500-1.clq.b 100 50 0.22 82.07 (1000) 12 701 13 22 14 277 c-fat500-2.clq.b 100 100 0.22 82.48 (1000) [OPT = 26] [Note: optimally solved by dfmax in 0.35 seconds] 24 444 25 43 26 513 c-fat500-5.clq.b 100 100 0.23 89.08 (1000) [OPT = 64] [Note: optimally solved by dfmax in 75.85 seconds] 62 609 63 128 64 263 c-fat500-10.clq.b 100 100 0.25 408.46 (1000) [OPT = ??] 124 263 125 253 126 484 hamming6-2.clq.b 30 16 0.00 5.36 (1000) [OPT = 32] [Note: optimally solved by dfmax in 0.40 seconds] 22 1 27 8 32 991 hamming6-4.clq.b 30 16 0.00 2.41 (1000) [OPT = 4] [Note: optimally solved by dfmax in 0.05 seconds] 4 1000 hamming8-2.clq.b 50 50 0.08 210.25 (1000) [OPT = 128] 128 1000 hamming8-4.clq.b 50 50 0.07 29.02 (1000) [OPT = 16] [Note: optimally solved by dfmax in 44.72 seconds] 16 1000 hamming10-2.clq.b 1 10 1.33 943.23 (1000) [OPT = 512] 330-399 98 400-450 164 451-475 148 476 5 477 9 478 11 479 10 480 9 481 7 482 9 483 6 484 14 485 5 487 17 489 21 490 26 494 18 496 80 503 130 512 213 hamming10-4.clq.b 50 50 1.27 439.94 (1000) [OPT = ??] 29 8 30 61 31 142 32 227 33 223 34 132 35 104 36 97 37 3 38 2 40 1 johnson8-2-4.clq.b 30 50 0.00 2.22 (1000) [OPT = 4] [Note: optimally solved by dfmax in 0.03 seconds] 4 1000 johnson8-4-4.clq.b 30 50 0.02 5.89 (1000) [OPT = 14] [Note: optimally solved by dfmax in 0.14 seconds] 14 1000 johnson16-2-4.clq.b 30 50 0.05 9.87 (1000) [OPT = 8] [Note: optimally solved by dfmax in 18.61 seconds] 8 1000 johnson32-2-4.clq.b 50 50 0.28 116.85 (1000) [OPT = 16] 16 1000 keller4.clq.b 50 50 0.05 16.77 (1000) [OPT = 11] [Note: optimally solved by dfmax in 9.05 seconds] 8 69 9 350 10 127 11 454 keller5.clq.b 100 200 0.92 572.95 (1000) [OPT = 27] 19 9 20 27 21 93 22 226 23 218 24 266 25 105 26 20 27 36 keller6.clq.b 50 400 17.65 11366.83 (1000) [OPT >= 59] 40 4 41 33 42 79 43 132 44 174 45 193 46 176 47 117 48 49 49 28 50 8 51 7 keller6.clq.b 100 800 17.65 19802.28 (1000) 41 1 42 9 43 29 44 69 45 96 46 163 47 193 48 177 49 135 50 76 51 30 52 16 53 6 keller6.clq.b 100 2000 17.20 52208.01 (1000) 42 2 43 2 44 17 45 33 46 65 47 128 48 169 49 192 50 190 51 124 52 55 53 19 54 3 55 1 MANN_a9.clq.b 30 10 0.00 9.39 (1000) [OPT = 16] [Note: optimally solved by dfmax in 3.96 seconds] 16 1000 MANN_a27.clq.b 30 75 0.20 667.85 (1000) [OPT = 126] 123 1 124 47 125 720 126 232 MANN_a45.clq.b 30 250 1.53 20452.38 (1000) [OPT = 345] 339 4 340 71 341 444 342 411 343 69 344 1 MANN_a81.clq.b 30 750 17.53 33581.55 (41) [OPT = ???] 1093 1 1094 1 1095 8 1096 21 1097 10 p_hat300-1.clq.b 75 75 0.10 33.59 (1000) [OPT = 8] [Note: optimally solved by dfmax in 0.42 seconds] 5 3 6 253 7 668 8 76 p_hat300-2.clq.b 75 75 0.10 79.52 (1000) [OPT = 25] [Note: optimally solved by dfmax in 18.19 seconds] 16 25 17 33 18 104 19 108 20 120 21 125 22 159 23 170 24 77 25 79 p_hat300-3.clq.b 75 75 0.12 371.44 (1000) [OPT = 36] [Note: optimally solved by dfmax in 26036.40 seconds] 27 3 28 18 29 39 30 105 31 198 32 263 33 238 34 118 35 15 36 3 p_hat500-1.clq.b 100 100 0.27 104.69 (1000) [OPT = 9] [Note: optimally solved by dfmax in 1.67 seconds] 6 5 7 198 8 636 9 161 p_hat500-2.clq.b 100 100 0.30 690.07 (1000) [OPT = 36] [Note: optimally solved by dfmax in 4341.69 seconds] 21 1 22 10 23 29 24 46 25 45 26 86 27 90 28 91 29 90 30 123 31 117 32 87 33 79 34 72 35 29 36 5 p_hat500-3.clq.b 50 100 0.35 300.54 (1000) [OPT = ???] 37 4 38 7 39 27 40 43 41 73 42 104 43 128 44 138 45 159 46 150 47 107 48 56 49 4 p_hat700-1.clq.b 100 150 0.55 210.52 (1000) [OPT = 11] [Note: optimally solved by dfmax in 5.37 seconds] 7 35 8 559 9 389 10 8 11 9 p_hat700-2.clq.b 100 150 0.60 2324.38 (1000) [OPT = ???] 26 5 27 5 28 17 29 37 30 38 31 54 32 69 33 65 34 46 35 63 36 92 37 88 38 73 39 64 40 57 41 86 42 55 43 50 44 36 p_hat700-3.clq.b 50 150 0.63 758.36 (1000) [OPT = ???] 45 1 46 4 47 4 48 14 49 25 50 44 51 55 52 68 53 79 54 100 55 96 56 81 57 106 58 105 59 83 60 96 61 34 62 5 p_hat1000-1.clq.b 100 200 1.10 434.81 (1000) [OPT = 10] [Note: optimally solved by dfmax in 25.01 seconds] 7 6 8 302 9 587 10 105 p_hat1000-2.clq.b 100 200 1.22 4033.64 (1000) [OPT = ??] 27 1 28 1 29 9 30 12 31 19 32 46 33 40 34 63 35 69 36 68 37 77 38 65 39 71 40 70 41 103 42 79 43 80 44 77 45 43 46 7 p_hat1000-3.clq.b 50 200 1.32 1477.85 (1000) [OPT = ??] 51 2 52 6 53 16 54 41 55 52 56 95 57 87 58 117 59 138 60 124 61 122 62 119 63 65 64 14 65 2 p_hat1500-1.clq.b 100 300 2.58 987.09 (1000) [OPT = 12] [Note: optimally solved by dfmax in 235.54 seconds] 8 11 9 380 10 558 11 51 p_hat1500-2.clq.b 100 300 2.85 18509.44 (1000) [OPT = ??] 38 1 39 3 40 4 41 7 42 11 43 22 44 24 45 40 46 26 47 39 48 48 49 48 50 57 51 42 52 54 53 52 54 53 55 51 56 51 57 62 58 63 59 68 60 55 61 57 62 29 63 24 64 9 p_hat1500-3.clq.b 50 300 3.07 4088.19 (1000) [OPT = ??] 68 3 69 4 70 7 71 4 72 18 73 17 74 39 75 47 76 49 77 63 78 59 79 86 80 84 81 85 82 79 83 78 84 69 85 76 86 42 87 40 88 25 89 16 90 6 91 4 san200_0.7_1.clq.b 50 50 0.05 169.31 (1000) [OPT = 30] 15 3 16 374 17 439 18 10 19 11 20 7 21 7 22 8 23 12 24 10 25 5 26 3 30 111 san200_0.7_2.clq.b 50 50 0.05 94.09 (1000) [OPT = 18] 13 95 14 668 15 226 16 4 17 4 18 3 san200_0.9_1.clq.b 30 50 0.05 75.69 (1000) [OPT = 70] 44 4 45 18 46 115 47 377 48 259 49 22 50 8 51 7 52 8 53 7 54 7 55 2 56 3 57 5 58 2 59 6 60 6 61 6 62 10 63 7 64 15 65 2 66 19 67 3 68 33 70 49 san200_0.9_2.clq.b 30 50 0.05 57.00 (1000) [OPT = 60] 31 1 33 1 34 9 35 13 36 12 37 18 38 102 39 323 40 288 41 87 42 13 43 7 44 7 45 5 46 8 47 7 48 11 49 9 50 11 51 6 52 9 53 6 54 9 55 14 56 3 57 9 58 2 59 2 60 8 san200_0.9_3.clq.b 30 50 0.05 48.35 (1000) [OPT = 44] 30 1 31 15 32 98 33 247 34 339 35 224 36 51 37 15 38 3 39 2 40 2 41 1 42 2 san200_0.9_3.clq.b 60 50 0.05 345.60 (1000) 31 1 32 21 33 142 34 336 35 360 36 119 37 14 38 3 39 1 40 2 41 1 san400_0.5_1.clq.b 100 100 0.17 130.29 (1000) [OPT = 13] [Note: optimally solved by dfmax in 14660.59 seconds] 7 218 8 678 9 81 10 5 13 18 san400_0.5_1.clq.b 150 100 0.17 1507.78 (1000) 7 56 8 684 9 241 10 2 13 17 san400_0.7_1.clq.b 50 100 0.17 128.22 (1000) [OPT = 40] 21 442 22 440 23 16 24 1 25 3 26 1 27 6 28 4 29 3 30 9 31 5 32 1 33 7 34 3 40 59 san400_0.7_2.clq.b 50 100 0.18 111.74 (1000) [OPT = 30] 16 23 17 559 18 359 19 11 20 2 21 2 22 3 23 5 24 4 25 1 26 2 27 2 30 27 san400_0.7_3.clq.b 50 100 0.17 91.16 (1000) [OPT = 22] 13 33 14 222 15 411 16 295 17 33 18 1 19 1 21 1 22 3 san400_0.7_3.clq.b 100 100 0.18 817.50 (1000) 14 54 15 311 16 526 17 101 18 3 19 3 22 2 san400_0.9_1.clq.b 30 100 0.18 278.49 (1000) [OPT = 100] 52 19 53 213 54 294 55 129 56 38 57 10 58 7 59 8 60 6 61 3 62 4 63 7 64 5 65 6 66 6 67 7 68 4 69 3 70 4 71 2 72 4 73 9 74 9 75 5 76 11 77 5 78 6 79 7 80 7 81 5 82 8 83 6 84 5 85 3 86 6 87 6 88 3 89 3 90 7 91 4 92 21 93 25 94 6 95 3 100 51 san1000.clq.b 100 250 1.23 616.48 (1000) [OPT = 15] 8 250 9 585 10 157 12 1 13 2 15 5 sanr200_0.7.clq.b 50 50 0.05 25.24 (1000) [OPT = 18] [Note: optimally solved by dfmax in 76.71 seconds] 14 14 15 287 16 501 17 170 18 28 sanr200_0.7.clq.b 75 50 0.05 51.32 (1000) 15 139 16 542 17 270 18 49 sanr200_0.9.clq.b 30 50 0.07 53.82 (1000) [OPT = ??] 33 1 34 8 35 45 36 145 37 206 38 258 39 188 40 109 41 39 42 1 sanr200_0.9.clq.b 50 50 0.07 96.13 (1000) 34 8 35 27 36 88 37 177 38 285 39 223 40 145 41 44 42 3 sanr400_0.5.clq.b 100 100 0.17 71.36 (1000) [OPT = 13] [Note: optimally solved by dfmax in 45.94 seconds] 10 18 11 654 12 316 13 12 sanr400_0.5.clq.b 150 100 0.17 129.42 (1000) 11 347 12 637 13 16 sanr400_0.7.clq.b 50 100 0.18 88.99 (1000) [OPT = ??] 16 1 17 34 18 415 19 464 20 84 21 2 RANDOM GRAPHS: N=100,p=0.4 50 25 0.02 5.73 (1000) [OPT = 8] [Note: optimally solved by dfmax in 0.07 seconds] 6 474 7 452 8 74 N=100,p=0.5 50 25 0.02 6.47 (1000) [OPT = 9] [Note: optimally solved by dfmax in 0.09 seconds] 7 11 8 367 9 622 N=100,p=0.6 50 25 0.02 7.66 (1000) [OPT = 12] [Note: optimally solved by dfmax in 0.16 seconds] 9 6 10 335 11 503 12 156 N=100,p=0.7 50 25 0.02 10.07 (1000) [OPT = 15] [Note: optimally solved by dfmax in 0.54 seconds] 11 1 12 98 13 404 14 460 15 37 N=100,p=0.8 40 25 0.02 11.03 (1000) [OPT = 20] [Note: optimally solved by dfmax in 3.33 seconds] 15 1 16 21 17 221 18 406 19 247 20 104 N=100,p=.85 30 25 0.02 10.38 (1000) [OPT = 24] [Note: optimally solved by dfmax in 14.34 seconds] 19 1 20 46 21 163 22 365 23 420 24 5 N=100,p=0.9 30 25 0.02 13.91 (1000) [OPT = 31] [Note: optimally solved by dfmax in 77.84 seconds] 26 5 27 30 28 160 29 296 30 348 31 161 N=100,p=0.9 30 25 0.02 13.49 (1000) [OPT = 30] [Note: optimally solved by dfmax in 95.23 seconds] 26 11 27 92 28 323 29 331 30 243 N=100,p=0.95 30 25 0.02 21.29 (1000) [OPT = 42] [Note: optimally solved by dfmax in 402.77 seconds] 37 8 38 80 39 212 40 251 41 325 42 124 N=100,p=0.99 30 25 0.02 42.19 (1000) [OPT = 71] [Note: optimally solved by dfmax in 48.09 seconds] 68 6 69 13 70 55 71 926 N=200,p=0.4 100 50 0.05 24.10 (1000) [OPT = 9] [Note: optimally solved by dfmax in 0.33 seconds] 7 17 8 816 9 167 N=200,p=0.5 100 50 0.05 33.45 (1000) [OPT = 11] [Note: optimally solved by dfmax in 1.04 seconds] 9 49 10 764 11 187 N=200,p=0.6 75 50 0.05 26.52 (1000) [OPT = 14] [Note: optimally solved by dfmax in 7.56 seconds] 11 11 12 526 13 441 14 22 N=200,p=0.7 50 50 0.05 25.52 (1000) [OPT = 18] [Note: optimally solved by dfmax in 79.91 seconds] 14 2 15 137 16 473 17 359 18 29 N=200,p=0.8 40 50 0.05 33.34 (1000) [OPT = 26] [Note: optimally solved by dfmax in 4437.68 seconds] 20 5 21 75 22 250 23 417 24 192 25 57 26 4 N=200,p=0.9 30 50 0.07 50.62 (1000) [EXP OPT ~ 44] 33 1 34 15 35 102 36 279 37 319 38 203 39 72 40 9 N=300,p=0.4 100 50 0.12 35.82 (1000) [OPT = 9] [Note: optimally solved by dfmax in 1.55 seconds] 8 604 9 396 N=300,p=0.5 100 75 0.12 53.44 (1000) [OPT = 12] [Note: optimally solved by dfmax in 7.95 seconds] 10 166 11 805 12 29 N=300,p=0.6 75 75 0.13 52.44 (1000) [OPT = 15] [Note: optimally solved by dfmax in 106.82 seconds] 12 17 13 533 14 417 15 33 N=300,p=0.7 50 50 0.13 45.24 (1000) [OPT = 20] [Note: optimally solved by dfmax in 4552.65 seconds] 16 107 17 533 18 331 19 29 N=300,p=0.8 40 50 0.13 55.04 (1000) [EXP OPT ~ 29] 22 2 23 77 24 312 25 416 26 171 27 20 28 2 N=300,p=0.9 30 100 0.13 142.27 (1000) [EXP OPT ~ 50] 38 2 39 28 40 130 41 262 42 326 43 162 44 73 45 15 46 2 N=400,p=0.4 100 100 0.23 65.08 (1000) [OPT = 10] [Note: optimally solved by dfmax in 1.55 seconds] 8 119 9 783 10 98 N=400,p=0.5 100 100 0.23 72.38 (1000) [OPT = 13] [Note: optimally solved by dfmax in 47.82 seconds] 10 20 11 657 12 313 13 10 N=400,p=0.6 75 100 0.22 81.63 (1000) [OPT = 16] [Note: optimally solved by dfmax in 896.13 seconds] 13 57 14 666 15 259 16 18 N=400,p=0.7 50 100 0.23 89.15 (1000) [EXP OPT ~ 22] 17 26 18 333 19 520 20 116 21 5 N=400,p=0.8 40 100 0.23 117.50 (1000) [EXP OPT ~ 31] 24 3 25 76 26 338 27 399 28 168 29 14 30 2 N=400,p=0.9 30 100 0.27 209.28 (1000) [EXP OPT ~ 55] 41 1 42 3 43 19 44 87 45 175 46 267 47 248 48 141 49 52 50 7 N=500,p=0.3 100 125 0.33 91.44 (1000) [OPT = 9] [Note: optimally solved by dfmax in 2.64 seconds] 6 1 7 627 8 369 9 3 N=500,p=0.4 100 125 0.33 101.44 (1000) [OPT = 11] [Note: optimally solved by dfmax in 14.34 seconds] 8 2 9 713 10 280 11 5 N=500,p=0.5 100 100 0.68 110.92 (1000) [OPT = 13] [Note: optimally solved by dfmax in 180.18 seconds] 10 1 11 280 12 669 13 50 N=500,p=0.6 75 125 0.35 119.75 (1000) [OPT = 17] [Note: optimally solved by dfmax in 5379.38 seconds] 13 7 14 427 15 527 16 39 N=500,p=0.7 50 125 0.37 138.07 (1000) [EXP OPT ~ 23] 18 56 19 438 20 421 21 80 22 5 N=500,p=0.8 40 125 0.37 182.91 (1000) [EXP OPT ~ 33] 25 3 26 47 27 276 28 437 29 195 30 36 31 5 32 1 N=500,p=0.9 30 125 0.38 329.55 (1000) [EXP OPT ~ 58] 45 5 46 27 47 104 48 227 49 290 50 205 51 104 52 30 53 7 54 1 N=600,p=0.5 100 150 0.50 162.08 (1000) [OPT = 14] [Note: optimally solved by dfmax in 625.83 seconds] 11 67 12 832 13 101 N=700,p=0.5 100 150 0.68 211.88 (1000) [OPT = 14] [Note: optimally solved by dfmax in 1819.55 seconds] 11 13 12 691 13 288 14 8 N=800,p=0.5 100 200 0.88 292.77 (1000) [OPT = 14] [Note: optimally solved by dfmax in 4845.32 seconds] 11 2 12 460 13 513 14 25 N=900,p=0.5 100 200 1.15 367.25 (1000) [OPT = 15] [Note: optimally solved by dfmax in 11344.77 seconds] 12 238 13 723 14 39 N=1000,p=0.3 100 250 1.33 399.72 (1000) [OPT = 9] [Note: optimally solved by dfmax in 52.80 seconds] 7 63 8 831 9 106 N=1000,p=0.4 100 250 1.37 432.48 (1000) [OPT = 12] [Note: optimally solved by dfmax in 753.87 seconds] 9 2 10 687 11 302 12 9 N=1000,p=0.5 100 250 1.43 476.46 (1000) [OPT = 15] [Note: optimally solved by dfmax in 23932.15 seconds] 12 80 13 810 14 109 15 1 N=1000,p=0.6 75 250 1.47 526.24 (1000) [EXP OPT ~ 19] 15 22 16 505 17 437 18 36 N=1000,p=0.7 50 250 1.50 645.47 (1000) [EXP OPT ~ 26] 20 22 21 319 22 513 23 134 24 11 25 1 N=1000,p=0.8 40 250 1.62 909.54 (1000) [EXP OPT ~ 38] 29 1 30 66 31 344 32 383 33 172 34 28 35 6 N=1000,p=0.9 30 250 1.58 1767.13 (1000) [EXP OPT ~ 69] 54 1 55 9 56 51 57 167 58 263 59 260 60 176 61 52 62 15 63 6 N=1500,p=0.3 100 375 2.98 1269.84 (1000) [OPT = 10] [Note: optimally solved by dfmax in 370.34 seconds] 8 521 9 476 10 3 N=1500,p=0.4 100 375 3.08 987.61 (1000) [EXP OPT ~ 13] 10 336 11 643 12 21 N=1500,p=0.5 100 375 3.18 1085.19 (1000) [EXP OPT ~ 16] 13 375 14 593 15 32 N=1500,p=0.6 75 375 3.28 1244.50 (1000) [EXP OPT ~ 21] 16 35 17 585 18 363 19 17 N=1500,p=0.7 50 375 3.38 1529.33 (1000) [EXP OPT ~ 28] 21 3 22 158 23 512 24 301 25 23 26 3 N=1500,p=0.8 40 375 3.95 2150.09 (1000) [EXP OPT ~ 41] 31 1 32 50 33 233 34 419 35 242 36 49 37 6 N=1500,p=0.9 30 375 3.57 4244.96 (1000) [EXP OPT ~ 75] 58 2 59 4 60 52 61 125 62 268 63 240 64 187 65 89 66 27 67 6 N=2000,p=0.3 100 500 5.32 1651.72 (1000) [OPT = 10] [Note: optimally solved by dfmax in 1796.45 seconds] 8 124 9 851 10 25 N=2000,p=0.4 100 500 5.53 1766.24 (1000) [EXP OPT ~ 13] 10 13 11 817 12 168 13 2 N=2000,p=0.5.b 100 500 5.23 2227.56 (1000) [EXP OPT ~ 17] 13 87 14 764 15 145 16 4 N=2000,p=0.6 75 500 5.90 2254.87 (1000) [EXP OPT ~ 22] 17 95 18 691 19 207 20 7 N=2000,p=0.7 50 500 6.07 2825.65 (1000) [EXP OPT ~ 29] 22 6 23 162 24 521 25 280 26 29 27 2 N=2000,p=0.8 40 500 6.20 3999.66 (1000) [EXP OPT ~ 43] 33 3 34 92 35 327 36 366 37 172 38 37 39 3 N=2000,p=0.9 30 500 6.35 7881.31 (1000) [EXP OPT ~ 79] 63 17 64 91 65 188 66 264 67 211 68 160 69 50 70 13 71 6 N=4000,p=0.5 100 1000 23.73 9730.28 (1000) [EXP OPT ~ 18] 14 55 15 762 16 183 N=6000,p=0.5 100 1500 60.92 23588.89 (1000) [EXP OPT ~ 19] 15 99 16 821 17 80 N=8000,p=0.5 100 2000 119.32 43233.51 (1000) [EXP OPT ~ 20] 15 26 16 718 17 246 18 10