multilevel heuristic algorithm for graph partitioning

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� £6������xb¥ �V\J^doM±��}\�zNjJ©Np k�ci²2r�gNrx\`lu^io�\�~MkMvwg6k�^i\�oMgNcº]Ncio!j�\�lNgNci\M_Graph |V| |E| max min avg File Size (KB)add20 2395 7462 123 1 6.23 63add32 4960 9462 31 1 3.82 90

wingnod al 10937 75488 28 5 13.80 768fe4elt2 11143 32818 12 3 5.89 341

vibrobox 12328 165250 120 8 26.81 1679memplus 17758 54196 573 1 6.10 536

cs4 22499 43858 2 4 3.90 506bcsstk32 44609 985046 1 215 44.16 11368brack2 62631 366559 3 32 11.71 4358fetooth 78136 452591 39 3 11.58 5413ferotor 99617 662431 5 125 13.3 7894feocean 143437 409593 6 1 5.71 5242

wave 156317 1059331 44 3 13.55 13479

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Impact of using different parameters in SA (vibrobox , 8 partitions)

2500030000

3500040000

45000

500005500060000

6500070000

75000

800008500090000

95000

100000

1 501 1001 1501 2001 2501 3001 3501 4001

tfactor=0,95 tfactor=0,99 tfactor=0,995

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K=2 K=4 K=8 K=16 K=32Graph algorithm

cuts imb. cuts imb. cuts imb. cuts imb. cuts imb.

pMetis 725 0 1292 0 1907 0 2504 1 3008 3

kMetis 719 3 1257 3 1857 5 2442 5 3073 74add20

MLrMSATS 696 5 1193 5 1757 5 2186 5 2793 4

pMetis 21 0 42 0 81 0 128 0 288 1

kMetis 28 2 44 3 102 3 206 3 352 15add32

MLrMSATS 10 0 35 3 133 5 184 4 294 5

pMetis 1820 0 4000 0 6070 0 9290 0 13237 0

kMetis 1855 0 4355 2 6337 3 9465 3 12678 3wingnodal

MLrMSATS 1670 5 3596 5 5387 5 8425 5 11812 6

pMetis 130 0 359 0 654 0 1152 0 1787 0

kMetis 132 0 398 3 684 3 1149 3 1770 3fe4elt2

MLrMSATS 130 0 350 2 632 5 1054 5 1662 6

pMetis 12427 0 21471 0 28177 0 37441 0 46112 0

kMetis 11952 1 23141 2 29640 3 38673 3 45613 3vibrobox

MLrMSATS 12096 3 20391 5 26147 5 34791 5 42530 5

pMetis 6337 0 10559 0 13110 0 14942 0 17303 0

kMetis 6453 3 10483 3 12615 3 14604 6 16821 6memplus

MLrMSATS 5662 5 9427 5 12283 5 14176 5 15661 5

pMetis 414 0 1154 0 1746 0 2538 0 3579 0

kMetis 410 0 1173 3 1677 3 2521 3 3396 3cs4

MLrMSATS 418 4 1103 4 1696 5 2430 5 3371 5

pMetis 5672 0 12225 0 23601 0 43371 0 70020 0

kMetis 5374 0 11561 3 27311 3 42581 3 82864 3bcsstk

32MLrMSATS 5193 5 18821 5 34596 5 51341 5 78260 7

pMetis 738 0 3250 0 7844 0 12655 0 19786 0

kMetis 769 0 3458 1 8776 3 13652 3 19888 3brack2

MLrMSATS 668 4 2808 5 8582 5 13770 5 18245 5

pMetis 4292 0 8577 0 13653 0 19346 0 29215 0

kMetis 4262 2 7835 3 13544 3 20455 3 28572 3fetooth

MLrMSATS 4436 5 7152 4 14081 5 19201 5 26016 5

pMetis 2190 0 8564 0 15712 0 23863 0 36225 0

kMetis 2294 0 8829 3 14929 3 24477 3 36159 3ferotor

MLrMSATS 1974 3 8143 5 14495 4 23807 5 33900 5

pMetis 505 0 2039 0 4516 0 9613 0 14613 0

kMetis 536 0 2194 2 5627 2 10253 3 16604 3feocean

MLrMSATS 317 3 3035 5 6023 5 8699 5 13954 5

pMetis 9493 0 23032 0 34795 0 48106 0 72404 0

kMetis 9655 0 21682 2 33146 3 48183 3 67860 3wave

MLrMSATS 8868 5 18246 5 30583 5 44625 5 63809 5

�m5">�I�Ú�0VUÃÔ;Kª5fÒD3!ï�UøSÅÝ+HWSÃÞL�ÂÑ�ÞÃ>�ÕÀÓ4HW3!îVKq5m>AU«ÕR365iI 3V׺IWÒ4KªÚ�0N5fKq5?IJÒ4K®HWKM5JÛ4@�IW5�3VÔ4çIW02>AU4KqدÔbXøH�S¹ÞL�ÂÑ�Þ�.�Ñ�Ò4Kq5fK½HJKq5fÛ4@�IW5M8�0V@�3NU4LÅï�>�IJÒ¯IWÒ4K(Ú3VUEÚ@AÛD5f>A3VUE5"3VÔ}I�02>AU4KMØ 32×�IJÒDKIW02ÔD@�K�ã484Ø}K�ÕÀ3VUE5iIWHW02IJK<IJÒ4K"LN363}Ø�ÔEKMÒD09îb>�3NÛ4H�32×�IJÒ4K 0V@�LN3VHW>�IWÒ4Õ Ò4KMHJK�Ó4HW3VÓ;3N5JKMØ�.

� £6����� �D¥ n�oqp"]6k�cihwrxoqzR�}\W^�§�\�\�z ¦ � c ¦ �Na+�d�ukMz6l�c ¦ �Va��d�}_

K=2 K=4 K=8 K=16 K=32Graph algorithm

cuts time cuts time cuts time cuts time cuts time

rMSATS 843 10 1349 14 1791 29 2159 71 2637 174add20

MLrMSATS 696 29 1193 31 1757 45 2186 104 2793 329

rMSATS 51 9 84 16 154 27 165 49 279 188add32

MLrMSATS 10 5 35 13 133 29 184 83 294 293

rMSATS 1674 99 3626 124 5485 148 8370 218 11905 469wingnodal MLrMSATS 1670 163 3596 196 5387 254 8425 447 11812 1174

rMSATS 206 20 385 43 752 65 1223 141 1805 488fe4elt2

MLrMSATS 130 34 350 68 632 104 1054 208 1662 693

rMSATS 12229 192 20777 246 31092 294 34460 396 42118 964vibrobox MLrMSATS 12096 439 20391 434 26147 543 34791 851 42530 1864

rMSATS 7600 91 10795 114 12644 226 14158 259 15492 2211memplus MLrMSATS 5662 171 9427 247 12283 554 14176 1371 15661 2315

rMSATS 861 70 1554 111 2261 186 2807 483 3355 1898cs4

MLrMSATS 418 151 1103 216 1696 319 2430 598 3371 1706

rMSATS 10422 534 29685 708 52697 826 68424 1132 86580 1905bcsstk32 MLrMSATS 5193 418 18821 550 34596 836 51431 1465 78260 4407

rMSATS 711 194 3874 357 8028 522 14816 932 20676 2830brack2

MLrMSATS 668 334 2808 507 8582 911 13770 1626 18245 3933

rMSATS 3966 386 10486 588 15920 862 23375 1629 32624 4300fetooth

MLrMSATS 4436 725 7152 793 14081 1206 19201 2056 26016 4044

rMSATS 2058 358 9445 898 17735 1251 28694 1971 39102 4308ferotor

MLrMSATS 1974 654 8143 1148 14495 1687 23807 2650 33900 5776

rMSATS 406 598 2670 727 6583 1058 12232 2220 18482 8415feocean

MLrMSATS 317 1172 3035 1124 6023 1606 8699 2979 13954 10039

rMSATS 15496 1166 30899 1642 47786 2409 58013 4209 74920 7767wave

MLrMSATS 8868 1493 18246 1595 30583 2420 44625 4022 63809 10127

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