# This file contains results of numerical calculations described in # the paper: # # T. Ebenlendr, J. Sgall: # Semi-online preemptive scheduling: One algorithm for all variants # Theory Comput. Syst., 48(3):577-613, 2011. # # The calculation was performed for # # m = 210, # # and the lower bound obtained is # # R = 1.91282667208773227, # # improving upon the bound of 1.88 reported for m=100 in the # paper. However, the previous version of the calculations contained # an error, the actual bound for m=100 is only 1.84. # sol :=[ "pmax", [ m = 2, R = 1.19999999999999973, p = .399999999999999967, s = [ 1., 1. ], q =[ .399999999999999911, .399999999999999967 ], O =[ .399999999999999967, .599999999999999978 ] ], [ m = 3, R = 1.25150476916725362, p = .264474076964203997, s =[ 1., .866025403190300969, .866025403190300969 ], q =[ .458082538274641737, .264474076964203886, .264474076964203997 ], O =[ .264474076964203997, .361278307816905619, .458082538669607242 ] ], [ m = 4, R = 1.28748346147570025, p = .272077269207753325, s =[ 1., .577350269189645937, .577350269189645937, .577350269189646159 ], q =[ .314167813014243680, .157083840838196792, .272077269207753214, .272077269207753325 ], O =[ .272077269207753325, .272077269207753325, .371664461530086365, .471251653852419572 ] ], [ m = 5, R = 1.33333333333333370, p = .222222222222221905, s =[ 1., .500000000000002220, .500000000000002331, .500000000000002220, .500000000000002220 ], q =[ .444003325920138359, .441118524307294413e-3, .222222222222222154, .222222222222222127, .222222222222221905 ], O =[ .222222222222221905, .222222222222221905, .296296296296295503, .370370370370369129, .444444444444442699 ] ], [ m = 6, R = 1.36452259817265831, p = .194825649522870681, s =[ 1., .440610228901078371, .440610228901078260, .440610228901078316, .440610228901078371, .440610228901078205 ], q =[ .429082757919604596, .128112240763007752e-3, .156009129920809009, .194825649522870209, .194825649522870042, .194825649522870681 ], O =[ .194825649522870681, .194825649522870681, .243532061903587782, .304357081777865857, .365182101652143765, .426007121526422061 ] ], [ m = 7, R = 1.39546935878098033, p = .199352765540140087, s = [ 1., .378166958018986699, .378166958018986754, .378166958018986477, .378166958018986699, .378166958018986588, .378166958018986699 ], q =[ .450179894604057051 , .109255593019518503e-2, .996088444639899734e-2, .136824961639768761, .199352765540140003, .199352765540139976, .199352765540140087 ], O =[ .199352765540140087, .199352765540140087, .202075786867240176, .243931060183778581, .304913825229723157, .365896590275667843, .426879355321612530 ] ], [ m = 8, R = 1.42514457870010625, p = .178143072337512948, s =[ 1., .359713265087168332, .359713265087168721, .359713265087168721, .359713265087168999, .359713265087168943, .359713265087168943, .359713265087168887 ], q =[ .448405536781272651, .113155823632951741e-3, .685763157541944245e-2, .910752648360650119e-1, .166120700333663218, .178143072337513586, .178143072337513558, .178143072337512948 ], O =[ .178143072337512948, .178143072337512948, .180079784842522711, .205968201497623321, .253188507835111209, .303826209402133951, .354463910969156692, .405101612536179156 ] ], [ m = 9, R = 1.45020559684102834, p = .171233546334679215, s =[ 1., .313620744030300769, .313620744030300824, .313620744030300824, .313620744030300880, .313620744030300769, .313620744030300658, .313620744030300769, .313620744030298271 ], q =[ .423986153809613187, .112359887544126436e-2, .112359887543922346e-2, .759785005845096534e-1, .918260130226293547e-1, .171233546334678910, .171233546334678993, .171233546334679215, .171233546334679215 ], O =[ .171233546334679215, .171233546334679215, .171233546334679215, .191921326010392662, .218090292672479480, .266889154976986065, .315688017281492594, .364486879585999290, .413285741890505876 ] ], [ m = 10, R = 1.47169543677812253, p = .163521715197568585, s =[ 1., .296585357264405436, .296585357264405436, .296585357264405325, .296585357264406768, .296585357264406768, .296585357264406879, .296585357264406657, .296585357264406713, .296585357264406824 ], q =[ .361915373806091067, .265202270394105620e-1, .275015730769646721e-1, .598888396371063461e-1, .793043355932616656e-1, .989565116374452602e-1, .163521715197568501, .163521715197568585, .163521715197568640, .163521715197568585 ], O =[ .163521715197568585, .163521715197568585, .163521715197568585, .174243934002243112, .195857054368004130, .222826059038382596, .267391270846058848, .311956482653735045, .356521694461411298, .401086906269087495 ] ], [ m = 11, R = 1.49237738187971125, p = .149237738187971675, s =[ 1., .288055953892905336, .288055953892903949, .288055953892903449, .288055953892903727, .288055953892903727, .288055953892903782, .288055953892903949, .288055953892904115, .288055953892904115, .288055953892904171 ], q =[ .405913908616258867, .371033927518430590e-2, .375646098801944934e-2, .518950796180596002e-1, .775459647495870957e-1, .775459647495875537e-1, .125820972943157167, .149237738187971314, .149237738187971342, .149237738187971342, .149237738187971675 ], O =[ .149237738187971675, .149237738187971675, .149237738187971675, .158356938095544603, .178340129687184740, .198323321278824988, .230746731274222322, .269204519819926213, .307662308365629855, .346120096911333719, .384577885457037638 ] ], [ m = 12, R = 1.51118289586205923, p = .139159974796830482, s =[ 1., .278918118544871863, .278918118544871751, .278918118544871696, .278918118544871640, .278918118544871751, .278918118544871918, .278918118544871974, .278918118544871807, .278918118544871918, .278918118544871807, .278918118544871863 ], q =[ .336086688925368526, .388142383470837307e-1, .388142383470837515e-1, .444042699334187274e-1, .667878653214935281e-1, .749867572677784117e-1, .763289889388499426e-1, .139159974796830316, .139159974796830482, .139159974796830427, .139159974796830399, .139159974796830482 ], O =[ .139159974796830482, .139159974796830482, .139159974796830482, .146820263154206987, .163237725052427868, .181670597916215870, .200433411514182619, .234641026520094387, .268848641526006238, .303056256531917978 , .337263871537829829, .371471486543741569 ] ], [ m = 13, R = 1.52832848496242235 , p = .135487448212208039, s =[ 1., .261924420729445828, .261924420729445773, .261924420729445551, .261924420729445773, .261924420729445662, .261924420729445495, .261924420729445551, .261924420729445606, .261924420729445606, .261924420729445606, .261924420729445606, .261924420729445773 ], q =[ .421757042839370322, .819597232302038642e-3, .819597232302042436e-3, .192201900182828629e-1, .562507996730560664e-1, .657713528255839813e-1, .712759052361485040e-1, .794893106321306331e-1, .135487448212207429, .135487448212207512, .135487448212207540, .135487448212207567, .135487448212208039 ], O =[ .135487448212208039, .135487448212208039, .135487448212208039, .139534369305935685, .153111375424553220, .168986315246396568, .186189864478179923, .205375846954713837, .238077851620621922, .272123939560308226, .303481860952438232, .336183865618346400, .368885870284254624 ] ], [ m = 14, R = 1.54423783861738806, p = .131546292994272784, s =[ 1., .251907662865669291, .251907662865669457, .251907662865669457, .251907662865668958, .251907662865669180, .251907662865669291, .251907662865668958, .251907662865669346, .251907662865669180, .251907662865669180, .251907662865669124, .251907662865669069, .251907662865669124 ], q =[ .336961046994754820, .329256281758873101e-1, .329281070719624966e-1, .329305122748979259e-1, .441934925871651785e-1, .599923483880834760e-1, .679696359783254073e-1, .715633011155011045e-1, .754960080651751603e-1, .131546292994272340, .131546292994272396, .131546292994272340, .131546292994272507, .131546292994272784 ], O = [ .131546292994272784, .131546292994272784, .131546292994272784, .132706006901949725, .143044150568095024, .157078106252459965, .172978181592596009, .189718919761151267, .207379632502037420, .238152137595212920, .269819644250192392, .299697147781563811, .330469652874739339, .361242157967914868 ] ], [ m = 15, R = 1.55825653277412624, p = .129044826079793867, s =[ 1., .235714163867526805, .235714163867526888, .235714163867526277, .235714163867525917, .235714163867525944 , .235714163867525917, .235714163867525917, .235714163867525750, .235714163867525445, .235714163867525389, .235714163867525306, .235714163867525195, .235714163867525195, .235714163867525223 ], q =[ .385616440853512654, 0., .139216451969989483e-1, .263096198863181675e-1, .387495505493454309e-1, .495171947531829748e-1, .630675816112616777e-1, .642623477546739041e-1, .712715978450327442e-1, .712715978450325499e-1, .129044826079794617, .129044826079794839, .129044826079794867, .129044826079794894, .129044826079793867 ], O = [ .129044826079793867, .129044826079793867, .129044826079793867, .129044826079793867, .138056353038372520, .149571984293065813, .164238869556266237, .179183607520864013, .195758404292586452, .212333201064409394, .242343637638167131, .272628282910752529, .302364510784078888, .332374947359440898, .362385383933198413 ] ], [ m = 16, R = 1.57096597364807700, p = .123460380051731988, s =[ 1., .226455242495585879, .226455242495584991, .226455242495585241, .226455242495585241 , .226455242495585185, .226455242495585213, .226455242495585074, .226455242495584852, .226455242495584769, .226455242495584658, .226455242495584658, .226455242495584796, .226455242495584741, .226455242495584824, .226455242495584685 ], q =[ .342678496198052351, .255650861167095178e-1, .255650861167093651e-1, .255650861167093617e-1, .381248867771074307e-1, .417894808060179715e-1, .554764580145896344e-1, .620034051658899660e-1, .651712136727004288e-1, .681939198984487932e-1, .800705744547510062e-1, .123460380051731766, .123460380051731822, .123460380051731738, .123460380051731738, .123460380051731988 ], O = [ .123460380051731988, .123460380051731988, .123460380051731988, .123460380051731988, .132131376790726840, .141635836539335203, .154253216607840360, .168355063706907337, .183177386577952378, .198687183643468768, .216898167299516914, .244977583222305700, .273799822351645517, .301136415067883356, .329215830990672198, .357295246913461095 ] ], [ m = 17, R = 1.58292100741879338, p = .118434452326443840, s =[ 1., .219688279326330144, .219688279326330227, .219688279326330477 , .219688279326331087, .219688279326330838, .219688279326330865, .219688279326330949, .219688279326330921, .219688279326330893, .219688279326331448, .219688279326331393, .219688279326331726, .219688279326331809, .219688279326331559, .219688279326331837, .219688279326331670 ], q =[ .416230968007243185, .876013004141625932e-11, .210280151071699732e-4, .465808922983173651e-4, .345688109145924349e-1, .375722823198334291e-1, .512588361253235522e-1, .539698506283156076e-1, .600791367810052448e-1, .643484955006697473e-1, .657414587808424072e-1, .884768454861371706e-1, .118434452326444339, .118434452326444548, .118434452326444284, .118434452326444062, .118434452326443840 ], O = [ .118434452326443840, .118434452326443840, .118434452326443840, .118434452326443840, .126090867593729505, .134412501835275089, .145765479319253183, .157718901592493910, .171025428901588478, .185277547975813750, .199838185212562691, .219434331253255621, .245665588059964884, .273474472841956473, .299248819668544719, .324359358039272738, .350590614735805439 ] ], [ m = 18, R = 1.59390070136268935, p = .112651946845562997, s =[ 1., .216922666603067582, .216922666603067721 , .216922666603067388, .216922666603067471, .216922666603067305, .216922666603067138, .216922666603067249, .216922666603067221, .216922666603067360, .216922666603067332, .216922666603066860, .216922666603067027, .216922666603066999, .216922666603067027, .216922666603067138, .216922666603067388, .216922666603067249 ], q =[ .396974338949979910, .106495640266332276e-2, .218269730773111049e-2 , .152029393717324785e-1, .330048049298544421e-1, .353332885137964472e-1, .408590601821226043e-1, .532880398750482653e-1, .548639831974415057e-1, .587346282291706379e-1, .638164034142200270e-1, .672123986243376020e-1, .954514812912114763e-1, .112651946845563178, .112651946845563358, .112651946845563303, .112651946845563553, .112651946845562997 ], O =[ .112651946845562997, .112651946845562997, .112651946845562997, .112651946845562997, .119692693523410720, .127230163726603202, .135946418612782643, .147314084336505530, .159017938010291127, .171547496644497255, .185161124456743820, .199499202604152770, .219861380209057322, .245654549197217714, .270762982720605228, .294189650226701460 , .315987240936486391, .340018706118343561 ] ], [ m = 19, R = 1.60416704560722345 , p = .108253930962452199, s =[ 1., .209451449312143434, .209451449312143573, .209451449312143489, .209451449312142324, .209451449312142629, .209451449312142685, .209451449312142740, .209451449312142574, .209451449312142490, .209451449312142629, .209451449312142574, .209451449312142629, .209451449312142740, .209451449312142768, .209451449312142796, .209451449312142823, .209451449312142962, .209451449312142851 ], q =[ .358175417362426640, .175981286743873769e-1, .176793254983282008e-1, .178292998426580994e-1, .314459486327352961e-1, .340560092315795801e-1, .365942057770754087e-1, .466707577290173606e-1, .519010283228271210e-1, .554003116948835819e-1, .595293004676695423e-1, .613287899432025801e-1, .656840435980658999e-1, .100750893057651447, .108253930962452588, .108253930962452616, .108253930962452713, .108253930962453143, .108253930962452199 ], O =[ .108253930962452199, .108253930962452199, .108253930962452199, .108914542885710300, .115506810690610931, .122646246547447602, .130317785015170495, .140101752330028334, .150982183448512608, .162596197559936650, .175075804885652109, .187932653701950447, .201702529464468483, .222823751672648063, .247795030749414613, .271215696147749652, .292806710789512925, .313600329879584583, .336294474431318602 ] ], [ m = 20, R = 1.61358173057907961, p = .104641795116949710, s =[ 1., .206371926133571110, .206371926133571165, .206371926133570499, .206371926133570749, .206371926133570777, .206371926133570666, .206164331505589854, .206164331505589521, .206164331505589521, .206164331505589576, .206164331505589493, .206164331505589576, .206164331505589521, .206164331505589465, .206164331505589576, .206164331505589549, .206164331505589521, .206164331505589687, .206164331505589660 ], q =[ .409972200212438020, 0., 0., .283929237455470647e-2, .295141035114380307e-1, .322044685845989040e-1, .346679238844831081e-1, .392668100796977476e-1, .502895562603439816e-1, .502895562603439539e-1, .548737126334203074e-1, .590712337897163695e-1, .592686107137342447e-1, .633142638699690924e-1, .100159227702643863, .104641795116949238, .104641795116949626, .104641795116949501, .104641795116949515, .104641795116949710 ], O =[ .104641795116949710, .104641795116949710, .104641795116949710, .105208333691684128, .111209125888058882, .117756921713738041, .124805585991475537, .132789293421771093, .143014139880321661, .153238986338872202, .164395881090194262, .176406213662829714, .188456676809139245, .201329700053869742, .221694022207853503, .243929470694984385, .266164919182115434, .286524993718977161, .306796883937546117, .328072599369969242 ] ], [ m = 21, R = 1.62236791757757048, p = .101833007580474255, s =[ 1., .202072576414090849, .202072576414090682, .202072576414090460, .202072576414090876, .202072576414090599, .202072576414090932, .202072576414091293, .199115235186467204, .199115235186466843, .199115235186466927, .199115235186467010, .199115235186466899, .199115235186466871, .199115235186466899, .199115235186466871, .199115235186466816, .199115235186466899, .199115235186466871, .199115235186466955, .199115235186466899 ], q =[ .406275840094023399, .454103216857671440e-3, .454103216857720013e-3, .454103216857695998e-3, .269188678546290819e-1, .302937619747216773e-1, .321183215315470685e-1, .346848264090923175e-1, .443044939595488574e-1, .486872233493184231e-1, .506441513640894930e-1, .536943922172006607e-1, .577231607658560825e-1, .614147576718257412e-1, .614147576718258245e-1, .101833007580473894, .101833007580473978, .101833007580474047, .101833007580474130, .101833007580474144, .101833007580474255 ], O =[ .101833007580474255, .101833007580474255, .101833007580474255, .101833007580474255, .107213546272191304, .113268658222009433, .119688462823247924, .126621259979388834, .135476834636294952 , .145208428492234920, .155331172784238247, .166063598695035369, .177601294172628710, .189876865406884310, .202152436641139938, .222506800737654969, .244517820565669841, .265718353128199747, .285655588650886527, .303924257123715125, .324278621220230212 ] ], [ m = 22, R = 1.63053577927475013, p = .100126599433468993, s =[ 1., .192944847544156473, .192944847544156167, .192944847544155723, .192944847544155695, .192944847544155251, .192944847544155307, .192944847544155307, .190640668936808394, .190640668936808227, .190640668936808283, .190640668936808422, .190640668936808477, .190640668936808505, .190640668936808505, .190640668936808533, .190640668936808422, .190640668936808505, .190640668936808505, .190640668936808588, .190640668936808588, .190640668936808561 ], q =[ .345253178484292877, .190661470974184295e-1, .190718967729353560e-1, .190759844060967160e-1, 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.509968680757427462e-1, .509968680757425588e-1, .509968680757428849e-1 ], O =[ .509968680757428849e-1, .509968680757428849e-1, .509968680757428849e-1, .509968680757428849e-1, .509968680757428849e-1, .509968680757428849e-1, .509968680757428849e-1, .509968680757428849e-1, .509968680757428849e-1, .520776677305111249e-1, .533223971440730179e-1, .546012798476407865e-1, .558922660795814347e-1, .572219277428582043e-1, .586229482051017978e-1, .601062780838744204e-1, .616732522024667010e-1, .633929204594564921e-1, .651422825320327747e-1, .669296776419426587e-1, .687339889141917459e-1, .705923538354979313e-1, .725292897723151947e-1, .745411142667103260e-1, .766259818804033016e-1, .787770264363091555e-1, .811228848144310566e-1, .834770964218130435e-1, .860003809532330354e-1, .886478149350046069e-1, .915519767918771404e-1, .944277152865206637e-1, .972565855939152013e-1, .999498783888420755e-1, .102987639849358714, .106135693024374894, .109398042264609238, .112763943546100823, .116225955751989823, 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1.86516157245604020, p = .329766391146714966e-1, s =[ 1., .110236425397124249, .110236425397123153, .110236425397123444, .110236425397124374, .110236425397124041, .110236425397124818, .110236425397124263, .110236425397124485, .110236425397124679, .110236425397124430, .110236425397124110, .110236425397124110, .110236425397123791, .110236425397123888, .110236425397123847, .110236425397123888, .110236425397123708, .110236425397124416, .110236425397124471, .110236425397124319, .110236425397124346, .110236425397124305, .110236425397124360, .109436631743909024, .107384745873445320, .105371331907298527, .103395668515183781, .101572540605931336, .996066220856819950e-1, .978807887750844791e-1, .960131299584032205e-1, .940603783968945034e-1, .924774945583351632e-1, .908751840166503455e-1, .891411988212897494e-1, .873282112094019847e-1, .855520968292467765e-1, .841123935903909520e-1, .826550209011797654e-1, .810778842591378113e-1, .793751877241986176e-1, .777608249610977631e-1, 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