
Euclidean Instances in 10**7 by 10**7 Square
Sample Size = 10,000

OPT - optimal tour length
SUB - subtour relaxation lower bound
GAP - 100 * (OPT - SUB) / SUB

Mean and Standard Deviation

----------------------------------------------------------------------
   n   OPT       Stdev       SUB       Stdev       GAP       Stdev
----------------------------------------------------------------------
 100   0.776469  0.023001    0.770554  0.022989    0.769293  0.468819
 110   0.773085  0.021682    0.767132  0.021662    0.777509  0.448874
 120   0.770532  0.020582    0.764527  0.020646    0.787151  0.428988
 130   0.768130  0.019705    0.762087  0.019718    0.794383  0.411938
 140   0.765833  0.018951    0.759812  0.019022    0.793927  0.390224
 150   0.763660  0.017895    0.757665  0.017973    0.792673  0.373635
 160   0.762260  0.017347    0.756220  0.017414    0.799932  0.361457
 170   0.760623  0.016990    0.754582  0.017031    0.801656  0.350326
 180   0.759100  0.016052    0.753069  0.016105    0.801815  0.333207
 190   0.757604  0.015734    0.751580  0.015849    0.802644  0.324448
 200   0.756354  0.015257    0.750346  0.015344    0.801847  0.323111
 210   0.755384  0.014950    0.749387  0.015061    0.801355  0.306051
 220   0.754279  0.014519    0.748308  0.014601    0.798929  0.299757
 230   0.753442  0.013998    0.747456  0.014089    0.801821  0.286937
 240   0.752484  0.013593    0.746518  0.013680    0.799999  0.286031
 250   0.751430  0.013399    0.745456  0.013512    0.802316  0.275796
 260   0.750734  0.012929    0.744761  0.013030    0.802875  0.273061
 270   0.749983  0.012920    0.744080  0.013059    0.794294  0.263246
 280   0.749418  0.012576    0.743505  0.012697    0.796210  0.261176
 290   0.748538  0.012364    0.742642  0.012452    0.794571  0.255062
 300   0.747763  0.012152    0.741872  0.012255    0.794748  0.247436
 310   0.747142  0.011985    0.741272  0.012084    0.792654  0.242922
 320   0.746716  0.011537    0.740868  0.011623    0.790041  0.238375
 330   0.746141  0.011536    0.740296  0.011674    0.790363  0.234012
 340   0.745499  0.011363    0.739658  0.011462    0.790281  0.228080
 350   0.744947  0.011118    0.739096  0.011240    0.792427  0.227764
 360   0.744602  0.010966    0.738775  0.011085    0.789495  0.225497
 370   0.744283  0.010841    0.738500  0.010930    0.783743  0.218718
 380   0.743686  0.010605    0.737883  0.010703    0.786962  0.210646
 390   0.743194  0.010437    0.737402  0.010531    0.785936  0.210361
 400   0.742844  0.010377    0.737088  0.010509    0.781647  0.208415
 410   0.742430  0.010218    0.736675  0.010316    0.781783  0.203678
 420   0.742087  0.010188    0.736354  0.010277    0.779056  0.201800
 430   0.741840  0.009957    0.736124  0.010057    0.776955  0.198173
 440   0.741354  0.009842    0.735616  0.009933    0.780591  0.195461
 450   0.741119  0.009721    0.735384  0.009819    0.780483  0.192814
 460   0.740631  0.009581    0.734909  0.009698    0.779108  0.191026
 470   0.740203  0.009517    0.734496  0.009600    0.777343  0.186416
 480   0.739940  0.009441    0.734259  0.009528    0.774238  0.183864
 490   0.739776  0.009366    0.734089  0.009457    0.775157  0.183119
 500   0.739454  0.009135    0.733800  0.009249    0.771098  0.180584
 510   0.739001  0.009120    0.733328  0.009217    0.773984  0.179398
 520   0.738942  0.008984    0.733267  0.009105    0.774381  0.177809
 530   0.738671  0.008790    0.732982  0.008891    0.776516  0.177546
 540   0.738426  0.008786    0.732777  0.008901    0.771308  0.172671
 550   0.738228  0.008594    0.732593  0.008713    0.769600  0.171794
 560   0.737927  0.008618    0.732304  0.008733    0.768310  0.169973
 570   0.737550  0.008609    0.731929  0.008693    0.768349  0.165706
 580   0.737309  0.008469    0.731704  0.008554    0.766389  0.166086
 590   0.737176  0.008447    0.731568  0.008534    0.766898  0.164831
 600   0.736941  0.008316    0.731332  0.008421    0.767305  0.161523
 610   0.736722  0.008266    0.731119  0.008354    0.766696  0.162250
 600   0.736941  0.008316    0.731332  0.008421    0.767305  0.161523
 610   0.736722  0.008266    0.731119  0.008354    0.766696  0.162250
 620   0.736622  0.008162    0.731024  0.008257    0.766247  0.159258
 630   0.736276  0.008114    0.730706  0.008226    0.762649  0.158331
 640   0.736087  0.008029    0.730517  0.008137    0.762905  0.158187
 650   0.736006  0.007959    0.730433  0.008047    0.763248  0.154498
 660   0.735840  0.007934    0.730280  0.008024    0.761692  0.151777
 670   0.735643  0.007947    0.730095  0.008043    0.760231  0.150690
 680   0.735440  0.007807    0.729907  0.007886    0.758289  0.150989
 690   0.735132  0.007696    0.729597  0.007808    0.759038  0.149818
 700   0.734990  0.007623    0.729461  0.007718    0.758251  0.148447
 710   0.734886  0.007658    0.729361  0.007750    0.757834  0.144645
 720   0.734792  0.007470    0.729275  0.007565    0.756718  0.144493
 730   0.734597  0.007384    0.729078  0.007488    0.757202  0.146766
 740   0.734470  0.007399    0.728969  0.007485    0.754901  0.143379
 750   0.734292  0.007410    0.728792  0.007510    0.755056  0.140195
 760   0.734076  0.007265    0.728576  0.007359    0.755164  0.141414
 770   0.733928  0.007185    0.728422  0.007252    0.756193  0.141882
 780   0.733840  0.007140    0.728368  0.007221    0.751526  0.139232
 790   0.733802  0.007078    0.728324  0.007175    0.752418  0.138078
 800   0.733575  0.007164    0.728103  0.007272    0.751828  0.135943
 810   0.733376  0.007096    0.727927  0.007178    0.748934  0.136392
 820   0.733355  0.007093    0.727886  0.007182    0.751644  0.135936
 830   0.733174  0.006972    0.727730  0.007043    0.748246  0.132655
 840   0.733071  0.006873    0.727626  0.006946    0.748575  0.134804
 850   0.732928  0.006901    0.727490  0.006988    0.747756  0.132372
 860   0.732743  0.006765    0.727307  0.006865    0.747754  0.132363
 870   0.732640  0.006794    0.727195  0.006878    0.748965  0.128861
 880   0.732512  0.006716    0.727091  0.006804    0.745795  0.130124
 890   0.732338  0.006705    0.726917  0.006788    0.745921  0.127026
 900   0.732111  0.006694    0.726686  0.006779    0.746794  0.126363
 910   0.732156  0.006613    0.726746  0.006691    0.744639  0.126666
 920   0.732046  0.006609    0.726623  0.006695    0.746626  0.126674
 930   0.731916  0.006551    0.726521  0.006645    0.742767  0.125800
 940   0.731890  0.006559    0.726485  0.006641    0.744227  0.124628
 950   0.731660  0.006492    0.726268  0.006565    0.742605  0.123865
 960   0.731708  0.006443    0.726314  0.006526    0.742819  0.123972
 970   0.731506  0.006461    0.726120  0.006550    0.741996  0.122688
 980   0.731474  0.006347    0.726086  0.006420    0.742391  0.122212
 990   0.731362  0.006407    0.725964  0.006470    0.743800  0.120841
1000   0.731223  0.006317    0.725865  0.006392    0.738381  0.120503
1100                         0.724960  0.006156
1200                         0.724105  0.005854
1300                         0.723625  0.005555
1400                         0.722846  0.005329
1500                         0.722444  0.005128
1600                         0.721884  0.005021
1700                         0.721517  0.004801
1800                         0.721110  0.004668
1900                         0.720691  0.004542
2000                         0.720421  0.004437
2100                         0.720064  0.004369
2200                         0.719812  0.004164
2300                         0.719559  0.004130
2400                         0.719266  0.004059
2500                         0.719035  0.003945
2600                         0.718799  0.003910
2700                         0.718640  0.003791
2800                         0.718470  0.003747
2900                         0.718217  0.003684
3000                         0.718123  0.003601
3100                         0.717903  0.003557
3200                         0.717790  0.003484 
3300                         0.717545  0.003418 
3400                         0.717363  0.003382
3500                         0.717334  0.003285
3600                         0.717139  0.003288
3700                         0.717075  0.003227
3800                         0.716909  0.003191
3900                         0.716716  0.003147
4000                         0.716660  0.003128
4100                         0.716553  0.003079
4200                         0.716463  0.002996
4300                         0.716424  0.003016
4400                         0.716210  0.002948
4500                         0.716132  0.002925
4600                         0.716059  0.002899
4700                         0.715956  0.002876
4800                         0.715849  0.002858
4900                         0.715759  0.002837
5000                         0.715720  0.002778
5100                         0.715588  0.002741
5200                         0.715563  0.002686
5300                         0.715466  0.002669
5400                         0.715426  0.002637
5500                         0.715330  0.002630
5600                         0.715248  0.002625
5700                         0.715173  0.002619
5800                         0.715180  0.002581
5900                         0.715102  0.002559
6000                         0.715036  0.002523
6100                         0.714957  0.002513
6200                         0.714950  0.002466
6300                         0.714848  0.002450
6400                         0.714835  0.002449
6500                         0.714742  0.002423
6600                         0.714697  0.002430
6700                         0.714627  0.002425
6800                         0.714612  0.002357
6900                         0.714562  0.002364
7000                         0.714467  0.002303 
7100                         0.714444  0.002312
7200                         0.714422  0.002312
7300                         0.714356  0.002241
7400                         0.714298  0.002264
7500                         0.714299  0.002270
7600                         0.714218  0.002246
7700                         0.714139  0.002248
7800                         0.714158  0.002206
7900                         0.714127  0.002171
8000                         0.714049  0.002203
8100                         0.714062  0.002183
8200                         0.714005  0.002140
8300                         0.713974  0.002153
8400                         0.713901  0.002089
8500                         0.713902  0.002098
8600                         0.713820  0.002103
8700                         0.713786  0.002072
8800                         0.713758  0.002084
8900                         0.713722  0.002055
9000                         0.713720  0.002014
9100                         0.713719  0.002034
9200                         0.713674  0.002020
9300                         0.713604  0.002016
9400                         0.713612  0.002033
9500                         0.713542  0.001994
9600                         0.713525  0.001980
9700                         0.713491  0.001944
9800                         0.713475  0.001960
9900                         0.713444  0.001935
10000                        0.713420  0.001945
20000                        0.711816  0.001367
30000                        0.711083  0.001110
40000                        0.710672  0.000961
50000                        0.710376  0.000869
60000                        0.710175  0.000789
70000                        0.710002  0.000718
80000                        0.709890  0.000684
90000                        0.709769  0.000637
100000                       0.709670  0.000607

----------------------------------------------------------------------
----------------------------------------------------------------------

Sample size = 1,000 for million-city instances

1000000                      0.708511  0.000198


