# This file contains results of numerical calculations described in # the paper: # # T. Ebenlendr, W. Jawor, J. Sgall: # Preemptive Online Scheduling: Optimal Algorithms for All Speeds # Algorithmica, 53(4):504-522, 2009. # # The calculation was performed for # # m = 210, # # and the lower bound obtained is # # R = 2.11630824775611792, # # improving upon the bound of 2.054 for m=100 reported in the paper # sol :=[ "online", [ m = 2, R = 1.33333333333333348, s =[ 1., 1. ], q =[ .666666666666666630, .666666666666666741 ], O =[ .333333333333333370, .666666666666666741 ] ], [ m = 3, R = 1.46105945203824605, s =[ 1., .607625218509903697, .607625218509903697 ], q =[ .439697299417123377, .361816203494152000, .659545949126970621 ], O =[ .198486497088188024, .361816203494152000, .659545949126970621 ] ], [ m = 4, R = 1.54859608739786503, s =[ 1., .613723544145231670, .613723544145231670, .613723544145231670 ], q =[ .433551150277049602, .235475812311595672, .3345134813, .545055643514897215 ], O =[ .152595956514365499, .235475812311595700, .353213718467393523, .545055643514897215 ] ], [ m = 5, R = 1.61169611053484330, s =[ 1., .669948786045049927, .453294677651002564, .453294677651002564, .453294677651002564 ], q =[ .324675543253503118, .159951864122077597, .238752375485579232, .3563740698, .531942257808689090 ], O =[ .107159557194121638, .159951864122087395, .238752375485598967, .356374069866481513, .531942257808689090 ] ], [ m = 6, R = 1.65257173462523799, s =[ 1., .717691335025481991, .456132698244528567, .456132698244528567, .456132698244528567, .456132698244528567 ], q =[ .328830728918764970, .129347756553832072, .180227557783233100, .2128020144, .3348283568, .466535320176690027 ], O =[ .928317640836700403e-1, .129347756553832044, .180227557783233183, .240303410377644300, .334828356774163782, .466535320176689916 ] ], [ m = 7, R = 1.69092706399900727, s =[ 1., .750000000000009104, .562500000000004774, .421875000000004385, .421875000000004385, .421875000000004385, .421875000000004385 ], q =[ .300948688880683490, .100316229626894002, .133754972835859187, .1783399638, .2377866184, .3170488245, .422731765999748765 ], O =[ .752371722201665982e-1, .100316229626889158, .133754972835853164, .178339963781137451, .237786618374852404, .317048824499809923, .422731765999748765 ] ], [ m = 8, R = 1.71579922232137516, s =[ 1., .763150559967267883, .582398777178080307, .375308426198193934, .375308426198193934, .375308426198193934, .375308426198193934, .375308426198193934 ], q =[ .271155124812065662, .841550053729119285e-1, .110273135849563830, .144497221956153138, .1525201220, .2366787590, .3101337683, .406386085016039844 ], O =[ .642229394743329129e-1, .841550053729119285e-1, .110273135849564663, .144497221956151445, .180621527445189195, .236678758976249654, .310133768343367866, .406386085016039844 ] ], [ m = 9, R = 1.74063280076004867, s =[ 1., .758634226411387558, .597721140751147462, .460995393555296840, .355544983087156652, .355544983087156652, .355544983087156652, .355544983087156652, .355544983087156652 ], q =[ .259361142085596352, .708649906529416757e-1, .899426232374590240e-1, .105042188993999405, .1361964521, .1765906988, .2289653984, .2906053945, .383063911936954660 ], O =[ .564432797987559839e-1, .718652218182746771e-1, .914389197454319874e-1, .114298649681790015, .143938303452395611, .182368725775282403, .232197153979801757, .295439941472186995, .383063911936954660 ] ], [ m = 10, R = 1.76009018014762364, s =[ 1., .734445434373993900, .587556347499267662, .447837979387782747, .341344037185110805, .341344037185110805, .341344037185110805, .341344037185110805, .341344037185110805, .341344037185110805 ], q =[ .253871597989706321, .597635070401397878e-1, .784087762574616071e-1, .980109703218270817e-1, .980109703218271788e-1, .1285888434, .1687065292, .2213402987, .2766753733, .376713313691725837 ], O =[ .526933701474647728e-1, .650978321755223410e-1, .813722902194035785e-1, .101715362774253942, .122058435321861905, .148748224865774326, .183764806691981974, .229706008364967101, .287132510456208967, .376713313691725837 ] ], [ m = 11, R = 1.77743880134375032, s =[ 1., .744801023523448680, .616081094506844784, .480521121587556721, .374789212573635122, .305809572234647942, .305809572234647942, .305809572234647942, .305809572234647942, .305809572234647942, .305809572234647942 ], q =[ .228556179710156071, .523421412782994130e-1, .671084001073798814e-1 , .811295875374043463e-1, .858272617266478827e-1, .105186804993672819, .1348610894, .1729067961, .2216855896, .2680031177, .359831833198173134 ], O =[ .452492422143548137e-1, .556118682948313556e-1, .688978982544079382e-1, .849598238688701185e-1, .101951788642644134, .122776529513544633, .149476144935618421, .183707997716204496, .227597009833686914, .280655903278072882, .359831833198173134 ] ], [ m = 12, R = 1.79243208680893829, s =[ 1., .721025774942847808 , .622709184835330554, .486196147449326432, .379610096576746880, .296390307037605272, .296390307037605272, .296390307037605272, .296390307037605272, .296390307037605272, .296390307037605272, .296390307037605272 ], q =[ .225512020604420743, .473225044836117978e-1, .610678116222444708e-1, .707095178155055099e-1, .809223709051564433e-1, .809223709051564849e-1, .1036435683, .1327443714, .1700160310, .2177527416, .2521326858, .349686092464041698 ], O =[ .426760702062305916e-1, .516314177671475735e-1, .631879379435299482e-1, .765690621002616811e-1, .918828745203140174e-1, .107196686940366354, .126810276432672647, .151930924526088057, .184104890483759942, .225312588692659382, .273026374289927765, .349686092464041698 ] ], [ m = 13, R = 1.80589250923925393, s = [ 1., .730729709253377546, .608475687901886775, .499780974517628762, .392907096605144668, .308887281497015609, .283018098563709908, .283018098563709908, .283018098563709908, .283018098563709908, .283018098563709908, .283018098563709908 , .283018098563709908 ], q =[ .219107084663609175, .408778819534243026e-1, .527546196808451190e-1, .625479172595756749e-1, .752742674583667393e-1, .752742674583668225e-1, .821546889046807227e-1, .1045014225, .1329266465, .1690837593, .2058568893, .2472173463, .338315718062037196 ], O =[ .396796011261340356e-1, .470824564618409352e-1, .566361514950720416e-1, .679633817940864388e-1, .815953139262485805e-1, .952272460584107222e-1, .110105200787190979, .129030078391657227, .153102674314482601, .183723209177379249, .221003241760853369, .265969801367388237, .338315718062037252 ] ], [ m = 14, R = 1.81782539864799286, s =[ 1., .723609743835881725, .625117164881139331, .506257687539004242, .399833717847601966, .315781875244148857, .267932965708378490, .267932965708378490, .267932965708378490, .267932965708378490, .267932965708378490, .267932965708378490, .267932965708378490, .267932965708378490 ], q =[ .207492800384035864, .372132903634769252e-1, .472962275649610603e-1, .584004636624945936e-1, .584004636624948711e-1, .702678229963685369e-1, .702678229963685647e-1, .828166286162380777e-1, .1048599781, .1327706185, .1681102501, .2075792734, .2402851709, .332064587331502625 ], O =[ .363126495380631659e-1, .428252281365791992e-1, .511023892373992303e-1, .613228670848790444e-1, .715433449323589071e-1, .838406912766523627e-1, .961380376209458043e-1, .110631510191076643, .128982718656594580, .152218478790361489, .181638914507628868, .217966697409154586, .262258967688393851, .332064587331502625 ] ], [ m = 15, R = 1.82865450711165245, s =[ 1., .730858483932664393 , .627133229963692473, .513857837442092014, .407916854329519851, .323817499552766064, .309535748524950638, .257041254121627261, .257041254121627261, .257041254121627261, .257041254121627261, .257041254121627261, .257041254121627261, .257041254121627261, .257041254121627261 ], q =[ .200710129800303227, .322710421596986985e-1, .428471159429082218e-1, .522923817794943638e-1, .546867782804006941e-1, .546867782804006733e-1, .658552375465480816e-1, .793045860203155373e-1, .829636410997544732e-1, .1045103107, .1316529133, .1658447809, .2024037886, .2358805419, .322744480714564463 ], O =[ .336228865864929075e-1, .390289196135406580e-1, .462066526026033778e-1, .549666530253953012e-1, .641277618629611662e-1, .732888707005270451e-1, .843209156967465595e-1, .976059905666725597e-1, .111504028987926426, .129011557524767589, .151066004791193587, .178848261047639706, .212754868736077185, .256204933996246165, .322744480714564463 ] ], [ m = 16, R = 1.83844895702139954, s = [ 1., .739626462693297793, .598263274258385658, .518987986201937201, .412208161459007183, .327397883748510421, .290997398236499172, .248345881979937150, .248345881979937150, .248345881979937150, .248345881979937150, .248345881979937150 , .248345881979937150, .248345881979937150, .248345881979937150, .248345881979937150 ], q =[ .199873388433770199, .278887202783883112e-1, .393027882017447233e-1, .461550154705018326e-1, .522033187307342078e-1, .522033187307344576e-1, .625273549654550148e-1, .625273549654551952e-1, .732659525839415571e-1, .824306951614178635e-1, .1037838269, .1306683476, .1645171274, .1896470784, .2344586468, .316996022484141160 ], O =[ .326452129644808631e-1, .372002626383220389e-1, .436195658832306266e-1, .511580397201945522e-1, .596843796735603213e-1, .682107196269261251e-1, .784232788622908766e-1, .886358380976556698e-1, .100602326702721762, .114065687780658800, .131016644376511920, .152358635269511461, .179229129138176402, .210204084378374761, .251775283998892874, .316996022484141160 ] ], [ m = 17, R = 1.84786476324081872, s =[ 1. , .744554837235001155, .603989656887840343, .523915163913815762, .420062375253105691, .335253533649338908, .289176902141374703, .277566710867622801, .239187383593767899, .239187383593767899, .239187383593767899, .239187383593767899, .239187383593767899, .239187383593767899, .239187383593767899, .239187383593767899, .239187383593767899 ], q =[ .193743294430489071, .249811991566201430e-1, .347901234949805974e-1, .422524361803482754e-1, .492945088770729151e-1, .492945088770730330e-1, .492945088770731440e-1, .590626802660090752e-1, .685397099553985284e-1, .714066212643829634e-1, .827843507818701446e-1, .1037262475, .1299658007, .1620974831, .1868722456, .2303626110, .309396433260211712 ], O =[ .305241874384573758e-1, .344599665204548961e-1, .399411381588366740e-1, .465979945186427852e-1, .543643269384165573e-1, .621306593581903641e-1, .698969917779641708e-1, .792022961414261678e-1, .900007031769377713e-1, .101250791074054977, .114293436228145792, .130635469803051130, .151111535678344122, .176649936737684393, .206091592860631778, .246930583789590680, .309396433260211712 ] ], [ m = 18, R = 1.85617395330561719, s =[ 1., .742771956597332195, .609570377508190431, .529500750131986719, .423593670992330362, .338869393593932144, .287463933491123202, .275734032047519173, .229957114605763013, .229957114605763013, .229957114605763013, .229957114605763013, .229957114605763013, .229957114605763013, .229957114605763013, .229957114605763013, .229957114605763013, .229957114605763013 ], q =[ .188125794369530946, .223146593230827209e-1, .312387190556579486e-1, .399618995979960714e-1, .460048266556517607e-1, .468065570002741405e-1, .468065570002742168e-1, .468065570002741127e-1, .561242069421267337e-1, .672966953083932035e-1, .701595396138837424e-1, .827057514833927920e-1, .1033838805, .1292319645, .1615425981, .1859706195, .2266083884, .305084738919074616 ], O =[ .289109602763942194e-1, .323402519981035724e-1, .371409831723178777e-1, .432822829112447377e-1, .503522528769331443e-1, .575454318593521530e-1, .647386108417711825e-1, .719317898241901843e-1, .805568947593527096e-1, .908989751280440544e-1, .101681014186465371, .114391140959773485, .130279059315525164, .150139282126924345, .174964966731203125, .203544722156196123, .244063798758088008, .305084738919074616 ] ], [ m = 19, R = 1.86399242307114799, s =[ 1., .749332355480561874, .615833261098137852, .529510754608312872, .424178124361428044, .339798728582627774, .287853249989348026, .287516121747826925, .240315055703725189, .225643786244672684, .225643786244672684, .225643786244672684, .225643786244672684, .225643786244672684, .225643786244672684, .225643786244672684, .225643786244672684, .225643786244672684, .225643786244672684 ], q =[ .187142164499398855, .207935738332665557e-1, .264655126089941573e-1, .371376856039015504e-1, .387912766493660535e-1, .451543273141341434e-1, .451543273141342752e-1, .451543273141341434e-1, .480902437614468548e-1, .575358058183645590e-1, .688366016106602419e-1, .689173162586448201e-1, .813540109167137232e-1, .1015559767, .1267745288, .1582553945, .1840546861, .2239536903, .298870973164636733 ], O =[ .278039527703670859e-1, .308932808559634307e-1, .348252962015945522e-1, .403428900548761168e-1, .461061600627155968e-1, .528147967153840825e-1, .595234333680525890e-1, .662320700207210677e-1, .733768995668885038e-1, .819250684514634536e-1, .921522111435324476e-1, .102391345715036094, .114478216053733761, .129566518505744993, .148401573776788615, .171913781872530230, .200113320493456731, .239418232245446783, .298870973164636733 ] ], [ m = 20, R = 1.87132273399131699, s =[ 1., .754968741386732978, .613786042799193576, .528602591500784924, .423407282377594230, .339146515081194810, .302706357905937029, .272435722115343670, .259831961541257372, .219272206766632727, .219272206766632727 , .219272206766632727, .219272206766632727, .219272206766632727, .219272206766632727, .219272206766632727, .219272206766632727, .219272206766632727, .219272206766632727, .219272206766632727 ], q =[ .183563705584183584, .203959672871315660e-1, .230088360806328177e-1, .339149751648953474e-1, .372690691595489731e-1, .372690691595489731e-1, .433728921682023441e-1, .433728921682024621e-1, .433728921682027882e-1, .513957688298189996e-1, .612732783869714692e-1, .642454829063710542e-1, .713838698959673446e-1, .799771464190641435e-1, .9984742497e-1, .1246544634, .1556247971, .1807034810, .2222687877, .294407934410745531 ], O =[ .265769376565471935e-1, .295299307294968859e-1, .328612232642521082e-1, .377715413345489776e-1, .431674758109131043e-1, 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.1024660046, .1249739226, .1478377535, .1722140182, .222729289190314067 ], O = [ .120785395713428820e-1, .125818120534821627e-1, .131066663489926190e-1, .136527774468673067e-1, .143029097062419459e-1, .149840006446344404e-1, .156650915830269244e-1, .163771412004372306e-1, .172463335121306738e-1, .181750264510308172e-1, .191316067905587667e-1, .201091783051905067e-1, .211146372204500353e-1, .221776999867904084e-1, .232407627531307955e-1, .243038255194711755e-1, .254415864268577319e-1, .265793473342442639e-1, .277171082416307960e-1, .289511113869358565e-1, .301851145322409482e-1, .314191176775460365e-1, .326629670330952013e-1, .340221758850388911e-1, .355301394314896796e-1, .370381029779404819e-1, .385460665243912912e-1, .400540300708421074e-1, .417074181164403812e-1, .435611318567292946e-1, .454975086290009614e-1, .474485764400415164e-1, .493702621735442812e-1, .513066389458159550e-1, .535145401791746675e-1, .560320398342381565e-1, .587741216351718651e-1, .615728893320847959e-1, 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R = 1.99965671364596531, s =[ 1., .771464029935774676 , .664758590929551030, .564523049505368024, .463614054581536872, .380742631844375401, .312684549295204561, .264399284237759380, .264399284143412572, .254081407276158966, .254081407276160021, .218838931519760138, .198067137508815105, .198067137508815300, .198067137508815466, .189455522834501205, .184951972992253882, .162423992739207851, .157092195687133479, .157092195687133562, .157092195687133951, .151588874161225767, .135228404522390461, .135228404522390516, .135228404522390239, .135228404522390155, .135228404522390017, .133149384968626383 , .118737355608833320, .118737355608833320, .118737355608833320, .118737355608833320, .118737355608833320, .118737355608833320, .118737355608833320, .118737355608833320, .118737355608833320, .118737355608833320, .118737355608833320, .118737355608833320, .118737355608833320, .118737355608833320, .118737355608833320, .118737355608833320, .118737355608833320, .118737355608833320, 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R = 2.00500925045440992, s = [ 1., .769965885231437941, .664758193922394991, .567458458156211987, .466646477642722546, .383744275843377891, .315570086345538625, .259507400279172240, .259507400279172462, .254036374491963424, .254036374491963091, .221328556161234036 , .196118352926800021, .196118352926800160, .196118352926799577, .190351562417138215, .190351562417138520, .167399115333513898, .155493352106310767, .155493352106311267, .155493352106311156, .155493352106311072, .138782380606455674, .131923934752085553, .131923934752085553, .131923934752083249, .131923934752081112, .131923934752083583, .131923934752083583, .114621463379209060, .114621463379209060, .114621463379209060, .114621463379209060, .114621463379209060, .114621463379209060, .114621463379209060, .114621463379209060, .114621463379209060 , .114621463379209060, .114621463379209060, .114621463379209060, .114621463379209060, .114621463379209060, .114621463379209060, .114621463379209060, .114621463379209060, 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.109886956068858829, .120766369777478108, .135308009391053030, .153860377002748988, .178414033762817920, .216957712879128239 ] ], [ m = 61, R = 2.00672554465288622, s = [ 1., .770823228696447815, .666368870256887069, .567300525943137957, .466581900064952926, .383744875092954796, .315614748749584617, .259580455906106899, .259580455906107121, .249777917064349986, .249777917064350097, .223012224938845732 , .192318115665163603, .192318115665163381, .192318115665165407, .191940536790429189, .191940536790429273, .173574224443097780, .152712873019380441, .152712873019380468, .152712873019381384, .152712873019382106, .146137948682389884, .130559830000873706, .130559830000874511, .130559830000890303, .130559830000886612, .130559822127962077, .130559822127964464, .130559822127966102, .113232865656709689, .113232865656709689, .113232865656709689, .113232865656709689, .113232865656709689, .113232865656709689, .113232865656709689, .113232865656709689 , .113232865656709689, .113232865656709689, 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.8282426865e-1, .1006429887, .1222952082, .1431548421, .1656935739, .215050962875909218 ], O =[ .109089775582064483e-1, .113092245521536593e-1 , .117447628480772375e-1, .121967685565005819e-1, .126487742649239263e-1, .131676944559057513e-1, .137321131325048498e-1, .143042845130258844e-1, .148983505155760726e-1, .155010638466321592e-1, .162409663306826019e-1, .170143456797627358e-1, .178248984261338526e-1, .186354511725049729e-1, .194460039188760932e-1, .202941825676181235e-1, .211423612163601539e-1, .219905398651021981e-1, .228872863251859023e-1, .237840327852696029e-1, .246807792453533036e-1, .256397661531895596e-1, .265987530610258122e-1, .275577399688620751e-1, .285167268766983381e-1, .295561027337614725e-1, .305954785908246346e-1, .318067473504417900e-1, .330180161100589661e-1, .342292848696761492e-1, .355605974644665132e-1, .368919100592568772e-1, .382232226540472134e-1, .395545352076516893e-1, .408858477612561444e-1, .423757840699180918e-1, .440432438995868453e-1, 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.510978202348329885e-2, .515917424573518035e-2 , .530241165159570267e-2, .573878109824876425e-2, .641902563704879921e-2, .668648503859232968e-2, .693008456446977256e-2, .696368842117109886e-2, .862170947383084779e-2, .903226706782307188e-2, .903226706782222361e-2, .946739371412776316e-2, .946739371412775969e-2, .946739371412776490e-2, .990775634178929152e-2, .990775634178918396e-2, .990775634178911978e-2, .104755951462693914e-1, .104755951462702848e-1, .104755951462706526e-1, .112026340773644269e-1, .112026340773646559e-1, .112026340773644303e-1, .120500806868383964e-1, .121296139272301061e-1, .140508681381077416e-1, .140508681381081805e-1, .140508679805324138e-1, .142098485033221450e-1, .156186202108511470e-1, .156186204426379208e-1, .156186204729241111e-1, .156186204729241128e-1, .156186204729241197e-1, .174787101343088884e-1, .195603259896619287e-1, .205894180025292528e-1, .205894180025292459e-1, .205894180025292181e-1, .205894180025292181e-1, .233766983255584218e-1, 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.109704548304828606, .121867106070831066, .137176784276704072, .157641422478675824, .189538997751092231 ] ], [ m = 104, R = 2.05822182015808419, s =[ 1., .766972703053520055, .666295582062963021, .590504492490223409, .491128300264225381, .408476159602474298, .339733574452564635, .282559701213982883, .282559701213979220, .261961295817393913, .261961295817397410, .227984666526430152, .198414838379017522, .179378546935314631, .179378546935307137, .179378543381864541, .176964279107984596, .176964279107974326, .176964279107982236, .157238914570286437, .147220749131312556, .147220749131313916, .147220749131314471, .147220749131313777, .147220749131312639, .147220749131309392, .132559037430727500, .126177577184932055, .126177577184927808, .126177577184936524, .126177577184937911, .126177577184936635, .115493207472818646, .110613485416597310, .110613485416599239, .110613485416598115, .110613485416598767, .106892913553551419, .991892498471536321e-1, .986494988572104298e-1, 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