Last updated: 2012 February 20 Monday 07:35:02.656 Central Standard Time = GMT/UTC-06:00
2012 February 20 Monday 13:35:02.656 Greenwich Mean Time = GMT/UTC
JULIAN DATE= 2455978
This is a very difficult math problem to get the ultimate "perfect" answer - that is, the absolute minimum distance sum. The technique used is "simulated annealing". I'll be continually running it and trying to improve the answer.
College Basketball Sectionals[ Monte Carlo Landmark Papers ]
The 1-64 listing of the sectionals is in a rough east-west order. The combining of the sectionals into regionals will be done in the next stage. So don't read anything into the 1-64 ordering now. The goal is to minimize the total mileage - that is, have the teams as close together as possible. Actually, to minimize the product of the average distance times the root-mean-square distance. By mileage, I'm referring to the sum of the mileages from the 64 sectionals. The mileage for a given sectional is the sum of the distances between all possible pairs of teams in a sectional. In a 5-team sectional (which 37 are),there are 5*4 / 2 = 10 possible pairs of teams. In a 6-team sectional (which 27 are) there are 6*5 / 2 = 15 possible pairs of teams. 39 sectionals with 5 teams = 195 teams 39 * 10 = 390 pairs 25 sectionals with 6 teams = 150 teams 25 * 15 = 375 pairs ------------- ----------- 345 teams 765 pairs And the numbers to the left of each team's name are simply the code numbers used by the program for each team. They have no other significance. The suggestion here is that the host role of the sectionals would rotate among the teams so that each team gets to host its sectional every 5(6) years.
total golden miles=104532.2207 total pairs=765 average golden miles between pairs of teams=136.64 suggested T0=.396067901 total linear miles=69890.1079 total pairs=765 average linear miles between pairs of teams=91.36 suggested T0=.264810488 total miles squared=31952721.2063 total pairs=765 square root(mean miles squared) between pairs of teams=204.37 suggested T0=121.067429028 ____________________________________________________________________________________________________ SECTIONAL# 1 total miles=980 average distance between teams=98 pairs=10 teams=5 4 Boston U. 42.333987 -71.104774 $ 5 Harvard 42.378430 -71.116441 $ 1 Maine 44.899236 -68.669199 $ 2 New Hampshire 43.135641 -70.932837 $ 3 Northeastern 42.339820 -71.087552 $ ____________________________________________________________________________________________________ SECTIONAL# 2 total miles=451 average distance between teams=30 pairs=15 teams=6 6 Boston College 42.335653 -71.171165 $ 7 Brown 41.826211 -71.397556 $ 9 Bryant College 41.921264 -71.537983 $ 11 Holy Cross 42.238982 -71.807849 $ 8 Providence 41.843711 -71.437836 $ 10 Rhode Island 41.486212 -71.548116 $ ____________________________________________________________________________________________________ SECTIONAL# 3 total miles=269 average distance between teams=27 pairs=10 teams=5 16 Cent. Connecticut State 41.690100 -72.768152 $ 12 Connecticut 41.809265 -72.253690 $ 15 Hartford 41.795655 -72.715094 $ 17 Quinnipiac 41.418986 -72.894268 $ 18 Yale 41.311208 -72.926491 $ ____________________________________________________________________________________________________ SECTIONAL# 4 total miles=904 average distance between teams=90 pairs=10 teams=5 25 Albany-NY 42.660016 -73.771364 $ 13 Dartmouth 43.704793 -72.292591 $ 14 Massachusetts 42.388979 -72.528699 $ 24 Siena 42.718412 -73.753731 $ 20 Vermont 44.477549 -73.193183 $ ____________________________________________________________________________________________________ SECTIONAL# 5 total miles=599 average distance between teams=40 pairs=15 teams=6 32 Army 41.387872 -73.964306 $ 22 Fairfield 41.160652 -73.257615 $ 23 Hofstra 40.714546 -73.600684 $ 30 Marist 41.722038 -73.934304 $ 21 Sacred Heart 41.221485 -73.241504 $ 19 Stony Brook-NY 40.917321 -73.124554 $ ____________________________________________________________________________________________________ SECTIONAL# 6 total miles=139 average distance between teams=9 pairs=15 teams=6 31 Columbia 40.808990 -73.961249 $ 36 Fairleigh Dickinson 40.898432 -74.028195 $ 28 Fordham 40.861211 -73.885969 $ 26 Iona 40.925932 -73.787077 $ 29 Manhattan 40.889544 -73.901525 $ 27 St. John's 40.722047 -73.795134 $ ____________________________________________________________________________________________________ SECTIONAL# 7 total miles=124 average distance between teams=8 pairs=15 teams=6 33 Long Island U. 40.690000 -73.981667 $ 39 NJIT(New Jersey Tech) 40.742323 -74.178756 $ 37 Saint Peter's 40.727324 -74.071253 $ 40 Seton Hall 40.742601 -74.247369 $ 34 St. Francis-NY 40.693294 -73.991535 $ 38 Wagner 40.614548 -74.094308 $ ____________________________________________________________________________________________________ SECTIONAL# 8 total miles=552 average distance between teams=37 pairs=15 teams=6 48 Lafayette 40.698154 -75.207399 $ 51 Lehigh 40.606487 -75.380180 $ 35 Monmouth-NJ 40.278167 -74.006527 $ 42 Princeton 40.342885 -74.656825 $ 43 Rider 40.279275 -74.739327 $ 41 Rutgers 40.499549 -74.444319 $ ____________________________________________________________________________________________________ SECTIONAL# 9 total miles=88 average distance between teams=6 pairs=15 teams=6 46 Drexel 39.954002 -75.192957 $ 45 La Salle 40.038723 -75.154065 $ 47 Pennsylvania 39.950946 -75.193513 $ 49 Saint Joseph's 39.995371 -75.239062 $ 44 Temple 39.980946 -75.152955 $ 50 Villanova 40.038166 -75.344632 $ ____________________________________________________________________________________________________ SECTIONAL#10 total miles=613 average distance between teams=61 pairs=10 teams=5 55 Delaware 39.679556 -75.752991 $ 53 Delaware State 39.185668 -75.544091 $ 54 Md.-Eastern Shore 38.207344 -75.686038 $ 63 Morgan State 39.345940 -76.583022 $ 62 Navy 38.982056 -76.483016 $ ____________________________________________________________________________________________________ SECTIONAL#11 total miles=782 average distance between teams=78 pairs=10 teams=5 56 Binghamton-NY 42.089797 -75.968254 $ 69 Bucknell 40.955363 -76.884133 $ 52 Colgate 42.817292 -75.535735 $ 61 Cornell 42.447017 -76.482996 $ 57 Syracuse 43.037844 -76.134646 $ ____________________________________________________________________________________________________ SECTIONAL#12 total miles=702 average distance between teams=47 pairs=15 teams=6 60 Hampton 37.019869 -76.338833 $ 58 Norfolk State 36.849592 -76.262717 $ 59 Old Dominion 36.890148 -76.304386 $ 79 Richmond 37.576257 -77.537487 $ 78 Va. Commonwealth 37.547646 -77.456095 $ 67 William & Mary 37.271536 -76.711624 $ ____________________________________________________________________________________________________ SECTIONAL#13 total miles=217 average distance between teams=22 pairs=10 teams=5 66 Coppin State 39.310384 -76.658303 $ 65 Loyola-Maryland 39.346496 -76.619135 $ 76 Mount St. Mary's 39.681764 -77.353042 $ 64 Towson 39.392329 -76.605801 $ 68 UMBC(Md-Balt) 39.255384 -76.711637 $ ____________________________________________________________________________________________________ SECTIONAL#14 total miles=130 average distance between teams=9 pairs=15 teams=6 74 American U. 38.937055 -77.086922 $ 75 George Mason 38.834002 -77.308596 $ 72 George Washington 38.898723 -77.045810 $ 73 Georgetown 38.907334 -77.072200 $ 71 Howard 38.923722 -77.021366 $ 70 Maryland 38.985944 -76.938586 $ ____________________________________________________________________________________________________ SECTIONAL#15 total miles=969 average distance between teams=97 pairs=10 teams=5 87 Campbell 35.409883 -78.740295 $ 93 Coastal Carolina 33.793782 -79.011979 $ 77 East Carolina 35.600439 -77.364409 $ 86 NC State 35.786589 -78.670735 $ 81 NC Wilmington 34.226837 -77.876930 $ ____________________________________________________________________________________________________ SECTIONAL#16 total miles=817 average distance between teams=82 pairs=10 teams=5 88 Buffalo 42.953113 -78.820868 $ 89 Canisius 42.925336 -78.852535 $ 94 Niagara 43.138666 -79.038933 $ 80 Penn State 40.803950 -77.857224 $ 83 St. Bonaventure 42.079787 -78.482522 $ ____________________________________________________________________________________________________ SECTIONAL#17 total miles=556 average distance between teams=56 pairs=10 teams=5 90 James Madison 38.438180 -78.873360 $ 96 Liberty 37.350977 -79.180579 $ 82 Longwood 37.300430 -78.395551 $ 97 VMI 37.789576 -79.439482 $ 84 Virginia 38.035417 -78.503346 $ ____________________________________________________________________________________________________ SECTIONAL#18 total miles=438 average distance between teams=29 pairs=15 teams=6 92 Duke 35.997527 -78.942317 $ 98 Elon 36.107080 -79.505856 $ 99 N.C. A&T 36.073746 -79.776419 $ 91 NC Central 35.974276 -78.898605 $ 100 NC Greensboro 36.070969 -79.811143 $ 95 North Carolina 35.899514 -79.043930 $ ____________________________________________________________________________________________________ SECTIONAL#19 total miles=476 average distance between teams=48 pairs=10 teams=5 105 Duquesne 40.436180 -79.992831 $ 103 Pittsburgh 40.442847 -79.959219 $ 107 Robert Morris 40.438958 -79.993664 $ 85 St. Francis-Pa. 40.504237 -78.637518 $ 102 West Virginia 39.634248 -79.954508 $ ____________________________________________________________________________________________________ SECTIONAL#20 total miles=1058 average distance between teams=71 pairs=15 teams=6 108 Charleston Southern 32.977127 -80.069864 $ 104 Citadel 32.796010 -79.959256 $ 101 College of Charleston 32.784065 -79.937033 $ 133 Georgia Southern 32.425456 -81.783445 $ 122 Savannah State 32.022434 -81.055112 $ 118 South Carolina State 33.498444 -80.848123 $ ____________________________________________________________________________________________________ SECTIONAL#21 total miles=1247 average distance between teams=83 pairs=15 teams=6 131 Appalachian State 36.214573 -81.680385 $ 139 East Tennessee State 36.303440 -82.369029 $ 106 High Point 35.972081 -79.993650 $ 114 Radford 37.139015 -80.549502 $ 113 Virginia Tech 37.228740 -80.423662 $ 110 Wake Forest 36.133471 -80.277273 $ ____________________________________________________________________________________________________ SECTIONAL#22 total miles=1118 average distance between teams=112 pairs=10 teams=5 109 Florida Atlantic 26.371188 -80.102543 $ 132 Florida Gulf Coast 26.471045 -81.764672 $ 112 Florida International 25.754267 -80.381998 $ 111 Miami-Florida 25.719546 -80.278662 $ 141 South Florida 28.062795 -82.412315 $ ____________________________________________________________________________________________________ SECTIONAL#23 total miles=934 average distance between teams=62 pairs=15 teams=6 116 Charlotte 35.305142 -80.732014 $ 117 Davidson 35.500136 -80.845073 $ 129 Gardner-Webb 35.247625 -81.670374 $ 134 Presbyterian College 34.465072 -81.868978 $ 119 South Carolina 33.999044 -81.026481 $ 120 Winthrop 34.940700 -81.028411 $ ____________________________________________________________________________________________________ SECTIONAL#24 total miles=1077 average distance between teams=72 pairs=15 teams=6 121 Bethune-Cookman 29.210259 -81.035056 $ 123 Central Florida(UCF) 28.600277 -81.202010 $ 138 Florida 29.648579 -82.349271 $ 128 Jacksonville 30.352462 -81.605371 $ 126 North Florida(UNF) 30.269963 -81.507033 $ 124 Stetson 29.035540 -81.303396 $ ____________________________________________________________________________________________________ SECTIONAL#25 total miles=712 average distance between teams=71 pairs=10 teams=5 127 Akron 41.076167 -81.511505 $ 130 Cleveland State 41.503107 -81.672908 $ 125 Kent State 41.147834 -81.338441 $ 145 Ohio State 39.996175 -83.018795 $ 115 Youngstown State 41.104225 -80.647019 $ ____________________________________________________________________________________________________ SECTIONAL#26 total miles=717 average distance between teams=48 pairs=15 teams=6 144 Clemson 34.677049 -82.838754 $ 140 Furman 34.841784 -82.401789 $ 143 NC Asheville 35.618167 -82.565683 $ 136 USC Upstate 34.995684 -81.968813 $ 147 Western Carolina 35.310933 -83.181811 $ 135 Wofford 34.959011 -81.935382 $ ____________________________________________________________________________________________________ SECTIONAL#27 total miles=691 average distance between teams=46 pairs=15 teams=6 153 Bowling Green 41.375886 -83.639656 $ 146 Detroit 42.332260 -83.037976 $ 152 Eastern Michigan 42.246983 -83.622716 $ 155 Michigan 42.275872 -83.736052 $ 148 Oakland-Mich. 42.675866 -83.217713 $ 151 Toledo 41.661994 -83.614380 $ ____________________________________________________________________________________________________ SECTIONAL#28 total miles=978 average distance between teams=98 pairs=10 teams=5 167 Cincinnati 39.131448 -84.516332 $ 166 Kentucky 38.030355 -84.499383 $ 142 Marshall 38.423139 -82.430431 $ 150 Morehead State 38.186748 -83.433240 $ 137 Ohio U. 39.323129 -82.095422 $ ____________________________________________________________________________________________________ SECTIONAL#29 total miles=567 average distance between teams=57 pairs=10 teams=5 149 Georgia 33.951226 -83.373769 $ 162 Georgia State 33.752884 -84.386038 $ 163 Georgia Tech 33.772884 -84.393816 $ 168 Kennesaw State 34.037600 -84.585211 $ 154 Mercer 32.831806 -83.649903 $ ____________________________________________________________________________________________________ SECTIONAL#30 total miles=500 average distance between teams=50 pairs=10 teams=5 173 Ball State 40.199488 -85.412471 $ 158 Dayton 39.739781 -84.178273 $ 169 Miami-Ohio 39.509220 -84.734120 $ 157 Wright State 39.783670 -84.063547 $ 164 Xavier-Ohio 39.149782 -84.477998 $ ____________________________________________________________________________________________________ SECTIONAL#31 total miles=1346 average distance between teams=135 pairs=10 teams=5 172 Chattanooga 35.046185 -85.300235 $ 161 Eastern Kentucky 37.738135 -84.301599 $ 177 Louisville 38.215071 -85.759129 $ 156 Tennessee 35.954249 -83.930740 $ 175 Tennessee Tech 36.174505 -85.503865 $ ____________________________________________________________________________________________________ SECTIONAL#32 total miles=987 average distance between teams=99 pairs=10 teams=5 170 Central Michigan 43.591419 -84.775014 $ 171 IPFW 41.116715 -85.097192 $ 165 Michigan State 42.730868 -84.478587 $ 182 Notre Dame 41.703104 -86.239173 $ 176 Western Michigan 42.283651 -85.611951 $ ____________________________________________________________________________________________________ SECTIONAL#33 total miles=1490 average distance between teams=149 pairs=10 teams=5 174 Auburn 32.602079 -85.484949 $ 159 Florida A&M 30.426867 -84.285177 $ 160 Florida State 30.440756 -84.291844 $ 209 South Alabama 30.694912 -88.179725 $ 179 Troy 31.800713 -85.957173 $ ____________________________________________________________________________________________________ SECTIONAL#34 total miles=699 average distance between teams=70 pairs=10 teams=5 199 Alabama 33.215118 -87.546673 $ 183 Alabama State 32.364027 -86.295524 $ 178 Jacksonville State 33.822323 -85.766632 $ 188 Samford 33.465107 -86.793323 $ 191 UAB 33.504828 -86.799990 $ ____________________________________________________________________________________________________ SECTIONAL#35 total miles=593 average distance between teams=40 pairs=15 teams=6 187 Alabama A&M 34.785646 -86.569159 $ 189 Belmont 36.135613 -86.794721 $ 190 Lipscomb 36.105614 -86.799444 $ 184 Middle Tennessee 35.852288 -86.369992 $ 193 Tennessee State 36.167279 -86.830555 $ 192 Vanderbilt 36.148113 -86.803055 $ ____________________________________________________________________________________________________ SECTIONAL#36 total miles=1011 average distance between teams=67 pairs=15 teams=6 180 Butler 39.838930 -86.172488 $ 208 Eastern Illinois 39.480590 -88.175596 $ 181 IUPUI 39.776432 -86.185265 $ 186 Indiana 39.166158 -86.526386 $ 197 Indiana State 39.468648 -87.408631 $ 194 Purdue 40.428091 -86.922510 $ ____________________________________________________________________________________________________ SECTIONAL#37 total miles=910 average distance between teams=91 pairs=10 teams=5 196 Austin Peay 36.533382 -87.353897 $ 198 Evansville 37.971709 -87.531681 $ 211 Murray State 36.611445 -88.322261 $ 214 Tennessee-Martin 36.341452 -88.864227 $ 185 Western Kentucky 36.987542 -86.451658 $ ____________________________________________________________________________________________________ SECTIONAL#38 total miles=334 average distance between teams=22 pairs=15 teams=6 200 Chicago State 41.718090 -87.608659 $ 202 DePaul 41.922810 -87.653110 $ 201 Illinois-Chicago 41.871977 -87.649220 $ 203 Loyola-Chicago 42.000587 -87.658112 $ 204 Northwestern 42.055586 -87.674503 $ 195 Valparaiso 41.462539 -87.043641 $ ____________________________________________________________________________________________________ SECTIONAL#39 total miles=932 average distance between teams=93 pairs=10 teams=5 207 Marquette 43.037514 -87.929807 $ 212 Northern Illinois 41.937529 -88.775921 $ 206 Wis.-Green Bay 44.529993 -87.920934 $ 205 Wis.-Milwaukee 43.075568 -87.878973 $ 218 Wisconsin 43.073885 -89.410953 $ ____________________________________________________________________________________________________ SECTIONAL#40 total miles=1194 average distance between teams=119 pairs=10 teams=5 225 Jackson State 32.295980 -90.207866 $ 227 MVSU(Mississippi Valley St.) 33.515120 -90.338696 $ 220 Mississippi 34.366773 -89.535360 $ 213 Mississippi State 33.454844 -88.788664 $ 217 Southern Mississippi 31.326563 -89.332285 $ ____________________________________________________________________________________________________ SECTIONAL#41 total miles=1019 average distance between teams=102 pairs=10 teams=5 221 Bradley 40.698093 -89.617043 $ 210 Illinois 40.108643 -88.228382 $ 215 Illinois State 40.512536 -88.997576 $ 235 Iowa 41.661683 -91.536280 $ 230 Western Illinois 40.464208 -90.683742 $ ____________________________________________________________________________________________________ SECTIONAL#42 total miles=1044 average distance between teams=104 pairs=10 teams=5 239 Missouri 38.945872 -92.327684 $ 219 SE Missouri State 37.312551 -89.530926 $ 223 SIU-Edwardsville 38.796333 -89.999826 $ 226 Saint Louis 38.635329 -90.233723 $ 216 Southern Illinois 37.713106 -89.218695 $ ____________________________________________________________________________________________________ SECTIONAL#43 total miles=879 average distance between teams=59 pairs=15 teams=6 233 LSU 30.414636 -91.176218 $ 236 Louisiana-Lafayette 30.215479 -92.019009 $ 231 Nicholls State 29.794375 -90.802037 $ 228 SE Louisiana 30.515191 -90.471200 $ 234 Southern University 30.523522 -91.190386 $ 224 Tulane 29.939927 -90.119518 $ ____________________________________________________________________________________________________ SECTIONAL#44 total miles=975 average distance between teams=98 pairs=10 teams=5 240 Ark.-Little Rock 34.721759 -92.341264 $ 237 Ark.-Pine Bluff 34.242320 -92.019585 $ 229 Arkansas State 35.843130 -90.677056 $ 241 Central Arkansas 35.079252 -92.457102 $ 222 Memphis 35.118701 -89.937311 $ ____________________________________________________________________________________________________ SECTIONAL#45 total miles=660 average distance between teams=66 pairs=10 teams=5 232 Alcorn State 31.877105 -91.141220 $ 244 Grambling 32.525428 -92.715152 $ 243 Louisiana Tech 32.527372 -92.646260 $ 238 Louisiana-Monroe 32.526532 -92.074578 $ 245 Northwestern State 31.753220 -93.097664 $ ____________________________________________________________________________________________________ SECTIONAL#46 total miles=1102 average distance between teams=110 pairs=10 teams=5 262 Creighton 41.265276 -95.947514 $ 250 Drake 41.601378 -93.651886 $ 249 Iowa State 42.026097 -93.648552 $ 265 Nebraska-Omaha 41.257087 -96.008717 $ 242 Northern Iowa 42.515818 -92.457410 $ ____________________________________________________________________________________________________ SECTIONAL#47 total miles=980 average distance between teams=65 pairs=15 teams=6 256 Houston 29.720507 -95.343549 $ 259 Houston Baptist 29.694786 -95.517220 $ 251 Lamar 29.879382 -93.926837 $ 246 McNeese State 30.180485 -93.217376 $ 258 Rice 29.719118 -95.397439 $ 257 Texas Southern 29.722729 -95.360772 $ ____________________________________________________________________________________________________ SECTIONAL#48 total miles=1143 average distance between teams=114 pairs=10 teams=5 252 Arkansas 36.068691 -94.172149 $ 248 Missouri State 37.198382 -93.278520 $ 273 Oklahoma State 36.121995 -97.070313 $ 263 Oral Roberts 36.049262 -95.951105 $ 261 Tulsa 36.152316 -95.946106 $ ____________________________________________________________________________________________________ SECTIONAL#49 total miles=930 average distance between teams=93 pairs=10 teams=5 275 Baylor 31.544889 -97.119446 $ 264 Prairie View A&M 30.092163 -95.989678 $ 260 Sam Houston State 30.714360 -95.549388 $ 254 Stephen F. Austin 31.621568 -94.649376 $ 266 Texas A&M 30.617700 -96.338296 $ ____________________________________________________________________________________________________ SECTIONAL#50 total miles=1286 average distance between teams=129 pairs=10 teams=5 255 Kansas 38.958058 -95.247750 $ 267 Kansas State 39.200400 -96.588400 $ 268 Nebraska 40.817779 -96.701683 $ 253 UMKC 39.035005 -94.577178 $ 278 Wichita State 37.719180 -97.293378 $ ____________________________________________________________________________________________________ SECTIONAL#51 total miles=2156 average distance between teams=216 pairs=10 teams=5 247 Minnesota 44.974410 -93.233002 $ 274 North Dakota 47.927668 -97.071444 $ 271 North Dakota State 46.894687 -96.803415 $ 272 South Dakota 42.783118 -96.924328 $ 269 South Dakota State 44.319431 -96.783275 $ ____________________________________________________________________________________________________ SECTIONAL#52 total miles=822 average distance between teams=82 pairs=10 teams=5 277 North Texas 33.211508 -97.150013 $ 281 Oklahoma 35.203956 -97.444478 $ 270 SMU 32.845127 -96.784167 $ 280 TCU 32.709298 -97.361684 $ 276 Texas-Arlington 32.729298 -97.126677 $ ____________________________________________________________________________________________________ SECTIONAL#53 total miles=1491 average distance between teams=149 pairs=10 teams=5 282 Texas 30.286041 -97.738894 $ 279 Texas A&M-CorpusChristi 27.714198 -97.324713 $ 283 Texas State 29.889941 -97.939450 $ 284 Texas-Pan American 26.309793 -98.174177 $ 285 Texas-San Antonio 29.577172 -98.622799 $ ____________________________________________________________________________________________________ SECTIONAL#54 total miles=1085 average distance between teams=72 pairs=15 teams=6 288 Air Force 38.990270 -104.858313 $ 291 Colorado 40.005541 -105.264434 $ 290 Colorado State 40.574982 -105.083867 $ 289 Denver 39.676654 -104.962203 $ 287 Northern Colorado 40.409981 -104.693021 $ 292 Wyoming 41.311923 -105.576378 $ ____________________________________________________________________________________________________ SECTIONAL#55 total miles=2707 average distance between teams=271 pairs=10 teams=5 296 Arizona 32.231187 -110.952591 $ 294 New Mexico 35.083936 -106.619191 $ 295 New Mexico State 32.283428 -106.753336 $ 286 Texas Tech 33.585918 -101.871834 $ 293 UTEP 31.777608 -106.506099 $ ____________________________________________________________________________________________________ SECTIONAL#56 total miles=1264 average distance between teams=84 pairs=15 teams=6 298 BYU 40.245788 -111.651033 $ 305 Idaho State 42.866859 -112.433312 $ 302 Utah 40.764946 -111.848546 $ 301 Utah State 41.741042 -111.812721 $ 300 Utah Valley State 40.289398 -111.706315 $ 304 Weber State 41.211055 -111.944385 $ ____________________________________________________________________________________________________ SECTIONAL#57 total miles=2426 average distance between teams=243 pairs=10 teams=5 303 Arizona State 33.417268 -111.935421 $ 299 Northern Arizona 35.190012 -111.658217 $ 306 Southern Utah 37.676088 -113.068560 $ 314 UC Riverside 33.973349 -117.330877 $ 308 UNLV 36.107750 -115.141665 $ ____________________________________________________________________________________________________ SECTIONAL#58 total miles=2337 average distance between teams=156 pairs=15 teams=6 316 Eastern Washington 47.489889 -117.582985 $ 315 Gonzaga 47.665725 -117.402435 $ 310 Idaho 46.725721 -117.011276 $ 307 Montana 46.860202 -113.983720 $ 297 Montana State 45.669652 -111.053003 $ 312 Washington State 46.730997 -117.158226 $ ____________________________________________________________________________________________________ SECTIONAL#59 total miles=855 average distance between teams=57 pairs=15 teams=6 318 CS Fullerton 33.880292 -117.885615 $ 319 Long Beach State 33.776406 -118.114232 $ 313 San Diego 32.771994 -117.191701 $ 311 San Diego State 32.776717 -117.070864 $ 320 Southern California 34.020846 -118.285630 $ 317 UC Irvine 33.646132 -117.842833 $ ____________________________________________________________________________________________________ SECTIONAL#60 total miles=863 average distance between teams=58 pairs=15 teams=6 325 CS Bakersfield 35.372504 -119.012900 $ 323 CS Northridge 34.238615 -118.531197 $ 321 Loyola Marymount 33.970846 -118.416744 $ 324 Pepperdine 34.040563 -118.709253 $ 328 UC Santa Barbara 34.416107 -119.849027 $ 322 UCLA 34.071398 -118.438413 $ ____________________________________________________________________________________________________ SECTIONAL#61 total miles=2956 average distance between teams=296 pairs=10 teams=5 309 Boise State 43.602945 -116.198450 $ 327 Nevada 39.541577 -119.814914 $ 343 Oregon 44.035125 -123.084531 $ 331 Sacramento State 38.562684 -121.424120 $ 332 UC Davis 38.540184 -121.749128 $ ____________________________________________________________________________________________________ SECTIONAL#62 total miles=1100 average distance between teams=110 pairs=10 teams=5 329 Cal Poly-SLO 35.300808 -120.660727 $ 326 Fresno State 36.812450 -119.746533 $ 330 Pacific 37.979645 -121.311336 $ 333 San Jose State 37.334386 -121.881066 $ 334 Santa Clara 37.349108 -121.939957 $ ____________________________________________________________________________________________________ SECTIONAL#63 total miles=9741 average distance between teams=974 pairs=10 teams=5 337 California 37.869648 -122.258858 $ 345 Hawaii 21.300278 -157.823056 $ 335 Saint Mary's-Cal. 37.841037 -122.108020 $ 340 San Francisco 37.775485 -122.450805 $ 336 Stanford 37.427161 -122.170242 $ ____________________________________________________________________________________________________ SECTIONAL#64 total miles=1170 average distance between teams=117 pairs=10 teams=5 344 Oregon State 44.567344 -123.278155 $ 342 Portland 45.572062 -122.724265 $ 341 Portland State 45.512063 -122.683707 $ 339 Seattle 47.607629 -122.313223 $ 338 Washington 47.656209 -122.306515 $ ____________________________________________________________________________________________________ ________________________________________________________________________________ Explanation of Data It's really hard to get the exact solution other than literally checking every possible combination but with 402 Indiana high school(345 in NCAA division I) teams, you can see that the factorial issue soon makes that impossible on even the best PC's and in fact for even the fastest super-computers. In fact, for the Indiana High Schools, based on there being 46 sectionals with 6 teams and 18 sectionals with 7 teams, I think it would be: 402! ____________________________________ (6!)^46 * (7!)^18 * 64! And the natural logarithm of the answer is 1351.224517650 and thus the logbase10 of the answer is 586.8293232143 which means the number of possible combinations is 10^586.8293232143 which is an amazingly large number! It would be actually be an exact integer, but I don't have access to a computer that can handle such large integers. I think only the latest "super computers" can. For college basketball, it would be 345! ____________________________________ ˜ 485.7592980235 which is also a number beyond the capacity to (5!)^39 * (6!)^25 * 64! simply "try all the possibilities". Remember, there are 31.5576 million seconds in an average year or ˜ 3.16 * 10^7 seconds. Thus for even a super-computer to check every possibility in one-year, it would have to evaluate about more than 10^578 possibilities per second for the high schools and 10^478 per second for the colleges. So the simulated annealing technique is used to avoid the impossible task of literally checking every possibility. It was first developed in the early 1950s at Los Alamos by guys like Edward Teller when they (Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M.; Teller, A. H.; and Teller, E. "Equation of State Calculations by Fast Computing Machines." J. Chem. Phys. 21, 1087-1092, 1953. ) were working on the hydrogen bomb. I was in my early oughts then and so was only consulting with them on an informal basis :-) (just kidding!) at that time.
[ Equation of State Calculations by Fast Computing Machines ]
> Equation of State Calculations by Fast Computing Machines > N. Metropolis, A.W.Rosenbluth, M.N.Rosenbluth, A.H.Teller and E. Teller 1953 > The Journal of Chemical Physics, 21, 1087 (1953) > THE paper. Probably THE most important algorithm of the 20th century, often called the M(RT)2 algorith from the names of the authors. (the paper begins in the middle of page 1087) The exact same technique could be used to redistrict for congressional and state districts if you were to treat each voter as a "team". And each district would end up with very close to the same number of voters and those voters would all be close to each other geographically. No more ludicrously shaped districts created totally for the purpose of giving an advantage to the party drawing the lines. Of course you'd need to use the supercomputers at the major universities because even using simulated annealing would take a very long time with several million "teams(voters)" in each state :-D But the neat thing about is that each party could have a mathematician who liked them run the program and they'd either both get the same answer, or the one with the lower total distance would have the better answer. The fact that this would literally "take politics out of the equation", is probably the reason that it wouldn't be adopted; each party would worry that an honest redistricting could take away "their" safe seats. Enjoy! Jeff Sagarin Top of Pageend of file