带服务器的三台平行机排序问题的复杂性和近似算法

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F26F3agkUUVol.26No.32003W7xACTAMATHEMATICAEAPPLICATAESINICAJuly,2003GAJMFCQLVTU(IkVVvt200237)SNXgBJZQBLifxBAUJgLU1EBGAIYPeyWAlAOHxMhHmeIjAfOpuaAejjJ={j1,j2,···,jn},JejNbAfjGFAwnPeQvlGAIYPOHJfjejunjNjfFjejpO!K#sAmxmeftoPAjjejj$%meftjs&mKDOjIjeOHyGAIYPOHAopJejAjs!’u!#jP$%mftOjjIA$smIAj$KiSrYxMOHhHmfyse%fbms,hH#jjJ={j1,j2,···,jn},buaejjiAjJs!#jPE#&(jPme%fsiA)$%jjiPfER#&(jjPmfpiA)$OjjiAj’dedb)K#iRtnPO(si,pi)&(*jji.eOH+)’e%fVPfejfV(jPejljAfVj)j*VejQej+)’#V+e%f(+fjOpeOHxr,njA)$JCp0,)GAIYPOH,-Kn,njA)$Jp0,QjAj)$Cp0,-.,nA.pJ//2001X6y28w0012002X5y22w00Mbd13a12*3gBJZQBLzU545npeOH)!,h+(#O,$AW’PHallC[1]O4e%fAOHFWbnpj)$(ejjAj)’)eQvHallC%NOpn!Ie%fl,njA)$JCp1mP2,S1/si=1/Cmaxb5zKNP-,TA6,njA)$JCps)P2,S1/si=s/CmaxkNP-,TA[2]WernerCh7P2,S1/si=1/CmaxAe2PD3)$4T8OpPIAm%NP,S1/si=1/CmaxkNP-,TAYY56y-6mP,S1/si=1/CmaxALS4TyLPT4TA.Op-OHmpf9%fPc-P)’xrnPp%fAf+)jejuQNGAjSHmp%f&uAMr:s;’PFfpC(7Q’VjGjq[3]8EA=blockingOHnF9MAj/NAjmp0juAf+Aj)iQ+1:CjAf?Q*2Aj-fj,-8EA4!e%fA3IYPOHQv(j)$KAQ+eYPσ;jAj)$EOpeiIA3.MOV34(P3,S2//Cmax,bP3(*3IS2(*!e%fQCmax(*Qv(j)$Op-mpf9%fPe,3f+)Nj):snf75=AmK&,5=(kK5=A8E’dedb)K6&b(5=-.,-A8EK,-AfA5=)$-Af,njj@.jAkK5=)$.yQ’7Df?,njj@)’3fAjJj@A)’.$A5=)NO-Auae4TAyuae’I,KiA(I)(*4TAO’Ii,AYPσ∗(*’IAlYPCmaxA(I)(*YPA(I)Aj)$C∗max(*lYPAj)$K%sY54TA8m.ρA&We4TAAw8LKh7e4TAA8m.AHb/O4TA8m.uhe4TA,x44TAA8m.ρA=maxICmax(A(I))C∗max.,-K%%8E-A5zKs6AmA994T8lY5e4TA8m.2P3,S2//Cmax01PKOBeAGAIYPP3//Cmax,K#NP-,TAQlnPD3)$99VLsQ2%fe.ATL:A2c(Opj)$AQvP3//Cmax’;eYJfjAjY=wgfjA3YPnA#)?FjE@HCPfjJ’aWQvQP3,S2//Cmax’smp%f9fRe,3f+)Nj):Hnf75=cQJfjA’+A3YPhC5=7A#)hCQvc-OpP3,S2//Cmax’546fjZTTX26?HxZ%jY=hgf?HFj@HZAPj]s9GAIYP5z’@K%h7xAE/42.1P3,S2//CmaxkNP-,TAWK?3tYqw5-ABH$%h73tYAe’I:hHe6A={a1,a2,···,a3n},G3ni=1ai=nK,lOuaA1≤i≤3n,nK4aiK2.Z\AAeYA1,A2,···,An,;OpuaA1≤i≤n,naj∈Aiaj=K?K?’I7SmP3,S2//CmaxAe’I:jJmxA4n+3ejji:si=ai,pi=0,i=1,···,3n.j3n+1:s3n+1=(n+1)K+n+2,p3n+1=0.j3n+2:s3n+2=K+1,p3n+2=0.ji:si=1,pi=K+1,i=3n+3,3n+4,···,4n+3.K%%N3tYA’InIlRP3,S2//Cmax’IneYPσ;Cmax(σ)≤(n+1)K+n+2.1.z3tYA’InI^A1,A2,···,An(AAe3tYn(c(Kx_m’IAYPσ,bJI(*fAjmj3n+3A2j3n+5···j4n+2j3n+2j3n+1U‘A1j3n+4A3···Anj4n+301(n+1)K+n+2_AAi(*Aj)$qAiAB+ASFjA[4YPσnfM3[0,1])N5=AQl3fAj)$JB+nCmax(σ)=(n+1)K+n+2.2.xr’I\eYPσ;Cmax(σ)≤(n+1)K+n+2.c(s3n+1=(n+1)K+n+2,,j3n+1:H?0)’Pf’W^(fM2.o\M2jjj3n+1.^T(3A75=)$c(4n+3i=1(si+pi)=nK+(n+1)K+n+2+(K+1)+(n+1)(K+2)=3(n+1)K+3n+5,QCmax(σ)≥134n+3i=1(si+pi)+T,3a12*3gBJZQBLzU547,133(n+1)K+3n+5+T≤(n+1)K+n+2,T≤1.c(f9%fPe,5Rnf[0,1])N5=AnT≥1.,T=1,3f7lne_{A5=)$’W^A0)’jAf(M1,M10)’Aj:(j)$p0Ajc-:Hj{j3n+3,j3n+4,···,j4n+3}Ae’W^(jj3n+3.,fM3[0,1])N5=A)’1’&5=QfM1,M28In5=,)’1uafj):snf6jjmjAm\nj{j3n+3,j3n+4,···,j4n+3}Ajbj)$*p_QFjA7j)$(4n+3i=3n+3pi=(n+1)(K+1).+)jj3n+1A)$((n+1)(K+1)+1.,1,(n+1)(K+1)+1)NfM28j,mLA8Ej{j3n+3,j3n+4,···,j4n+3}jAjjP:H1,(n+1)(K+1)+1)N‘RABQ={j3n+3,j3n+4,···,j4n+3}.,OuaAjji∈Q\{j3n+3},jiA)N:HqjeQjAe_{Aj)$9’W^Q+jAj(j4n+3,OuaAjjl∈Q\{j4n+3},jlAj)$nKe_{)$Ni&j1,···,j3nyj3n+2Ajc(s3n+2=K+1,,j3n+2Vjj4n+3Aj)NUj3n+3,···,j4n+2lnneK_{)$Ni&j1,···,j3nAjQj1,···,j3nA7)$(3ni=1si=nK.,OuaAjjl∈Q\{j4n+3},AjKe_{Aj)$iwOe7‘(KAj1,···,j3nAe3jQ,nOeAne3j,OeAiwmAAe3tYc(P3,S2//CmaxkNP-,TAc-cXP=NP,Z’\P3,S2//CmaxA2PD3)$Al4T?Q#’\qPD3)$A99VL,WeA994T(!WA3A5zK|+7AICJXnabAj$%K7D6_mjAj)$J(0,o\-)P3,S2/pi=0/CmaxyGAIYPOHP2//CmaxC}cQb5zK(NP-,TQP2//CmaxnPD3)$99VL[4],,P3,S2/pi=0/Cmax#BeDnPD3)$99VLb@K%6myY5P3,S2//CmaxA994T3RI:;OpGAIYPW!}7LS(ListScheduling)4T6OpP3//Cmax,Graham[5]%NLS4TA8m.(53,QlwA64T[6].QHallC[1]%NOpP3,S1//Cmax,LS4TA8m.(73,’#LS4TZ(wA64T548fjZTTX26,@K^[P3,S2//CmaxAeLS4Tx$^jj(’IjjAj%bYh3f~AfOpLS4TKnxAAE/43.1ρLS≤2.WuhP3,S2//CmaxA’I,^’IlnnejQOuaAk,jjkA)$yj)$Y(skypk.BLSO’Ii,AYP(σ,YPσAj)$(Cmax(σ).’IAlYPAj)$(C∗max.’W^YPσ)’Cmax(σ)jAf(M1,QjjiM1

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