Tra¥elling in the World of Local Searches in the SDace of
Transcription
Tra¥elling in the World of Local Searches in the SDace of
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GE $Q@ $ $ ! t L ! d I $L` D ' AD FE + C= = yI = 7=z $I @ 1+f FD Lgv'I B + g +E JI C "<,N8z)*$X*K6SY,Q"{(#"Wh"h_Bk FEL T f= 6Y,Q"M("hG#"WhGck 8ASS)z6#*N(#"Wh"h_Bk 6*<"$<S§*F8 a sL {"S,a8)+*f *6Y,Q"("h#"WhGck A ¬ -I bI A +E J@ + D _L Assigned variables Dead end variable Conflicting variables Chronological backtracking Conflict directed backjumping Dynamic backtracking Decision repair Unassigned variables ø ¤ìië SHK@QB Oÿ¢U R@ ÿ KU1þOHRD lMC@IHRD tBLN · ! ¸ +#I ! <U <U L °ë ì ¾ð ¿ú ît÷Kðø °îtõ"öOù ½öAô|ðø³÷ ³î úOô [öOù¨øWõöAð?ø³úÎù nN °ÿCÿCBX=N8HRNO> ý = O@ lÿV=?>H(ÿ °=?D2B °D]BLNOý ÿMIHKNOD= ý KU Dü]HKý JLJL=> HRNO>Ì= _HKJ OH_MQ=>ÌBXM RN [=N nÿ ÿCD => JLBLN @ RþJL= ÿ = Rþ =ý DxMQB i= KU @¨ÿVM O> ]HRÿ¾ÿCJLB ý MQJ >Aý B [=@C=NlM ÿVMQHR@VMQBXN ]Uý ³@ H BLNB HRJ #ÿQD = = ¢=£HRB =?>&H_M¢JXBEÿVMCBLN HRJXJ°M = OHR@QH =MC=@QÿM HKM °ÿM]þ°=ÿC=2MÇM i=2M¢ý HRN HRDxM OHKJ[HKJ i@CBXM ý ý HKNO>"HKMÇ= J R@QBLN HKN°>Ë= _HKJ OH_MQBXN BXNlMC=@C=?ÿMQBXN HKJ i@CBXM BXNOÿVMQHRNOD2=?ÿ nN KM =@ R@I>ÿ @ HKBLN Rþ =DxMQB i= ¢ý HiÿËN KMTM = ý BLþBXM-HKN%= TDBX=NlM BXNOÿVMQHRNOý D2= þ AM&M HiD BL@C= tN ý JL=> ý i=HRþ AM-HRJXJM = iÿQÿVBLþJL= OHK@IH =MC=@"ÿC=2MCMCBLN iÿ HKNO>#M ý =BX@@Q=ý JEH_MCB R=Ç= "D2BL=NOD BXM M =¢J iN MC=@ ; iþ =D2MCý B R= RU°HRD BX@QBLN £HRþ AM1J ADHRJ ÿV=?HKý @ID BLNM =ÿ °HRD2= KU OHK@CMCBEHKJ¤HRÿQÿVý B RN =NiMIÿ KU F)ý ÿM =ÿQH =#JL= R=J KU tN JL=> i= HRÿ Hiÿ]þ°==N6HRD OBX@Q=>ÌHKþ AM'>A= AM O@IÿVMMC@Q==(ÿV=?HK@ID U MC=@#H O@C=?ÿV=NiMIH_MQB iN KU)M ý = R=N=@QBEDHKJ i@CBXM ý )=ËÿMIHK@CMC=?>6U³@ BLN =?DxMQB iN )= @Q=ÿC=NlMBXMQÿÇ>ý = R@Q==?ÿ KU[U³@C==> ý BLN =DxMQB iN ÿ = iÿQÿVBLþJL='HKJ R@QBXM ý BLNOÿVMQHRNOD2=?ÿ BXN =D2MCB RN M =6@C=?ÿ OJMIÿ RU M =6= [=@QB =NlMIÿ ¢=6DHR@C@QBX=?> AMTBXN =D2MCB RN HRNO> >ABX@Q=D2MCB RNOÿ¢U i@]U AM O@C= R@ TBXN =?DxMQB iN ¹ º _»b5 1+3 ¾ ` zr¼ !½ b L#¿SI #~ ^ LÀ c(Wj6#*<"W*F8AS Á + A#I *98 I D I $cI {U D $ 0 [ ! I f= !I I ZD' U AÁ - $ /= fcI fL 6#*"$W H > 0 $ z#I r U D A L 0 + I y= Ã= @ + HA= 0 AI MN8zWSW + /D d ^ 7 = z#I A g JI I  Á A A@ ]= 6*<"WS*98 + fp + S@ + à d= + $ $E D f#I D = C {= +E I - = K= I VD' J= #=z HA= '= $ + $L>`  t AEPD { I l L R 7D 0 D d= #I + 0 \A 2 nN&M ý BLÿ OH [=@ )= iNJ -D RN°ÿVBE>A=@ÿQH_MQBLÿVUWHRD2MCB RN @ ý iþJL= ý ÿ ³N AMCB BLÿQH_MQB iNÌD@CBXMC= @CB RN ý BLN iJ tBLN NOHK@ &HRNO>ÌþBXN°HK@ -D iNOÿVMC@IHKBLNiMIÿ HRJM ËDHRN>=HKJ BM D RNOÿVMC@IHKBLNlMQÿ KUHKN &HR@CBXM èݨâ'ݨÞOàVÙ ÚÛVèØÞOàãß é =(ÿVMQHK@CMC=?>"U³@ H i=@ R=NO=@QBLD R=@QÿCB iN RU WÿC== B @C= >=@QB i=> U³@ M ý = °@QÿVM HKJ i@CBXM ý O@C=?ÿV=NiMQ=>-BXN ` C= 4 B + D D S= ^I $ Ä P +E E E ' BE = P. y#= I + $@ 6*<"WS*98 FEL Å - P Ey lI N + K 6*<"$W*98{. 1+3 = 2c4 +#I ¬ + L q(`\i» %qrtqGkaVqpnjri¥#qknknj¥?ri(mIr_ Æ jklm]rKgiG¡AmQpf:Éqpq¡ihmQk)jr £Æ ¹ ¼ Ki µ§x§?¶ ¹ ¼ Ä K ° |·Cª E ¹ ¼ E ¹ ]¼ K ° ©t§ E ¹ ¼ ¯t«³§VÁ K [ ø ¤ì R=NO=@QBLDG>A=DBLÿCB RNÌ@C= OHKBL@'HKJ i@CBXM ý ü]ý = ÿMIHK@CMCBLN HRÿQÿCB iN =NlM H þ[= = AM OHR@VMQBLHRJ R@&D JL=2MC= NODxMQB iN OÿC=ÿD iNOÿMQ@QHRBXNlM @ OH iH_MQB iN(M G=NU R@ID2=]HKN #J tDHKJAD iNOÿCBLÿVMC=NOD @ =@CM iN"M ý = O@ iþJX= @C=?ÿMQ@CBEDxMQ=>&þ a M¢ @Q=2M @CN°ÿ ý BU BLÿ¢J tDHKJLJ "D RNOý ÿCBEÿMQý =NlM HKNO> BXU¢N KM NOD2MCB RN D lÿV=?ÿH |HR@CBEHKþOJX= BED BLÿ N KMËHRÿQÿVB RN=?>ÐBXN M ý =D @Q@Q=NlMHRý ÿQÿCB iN =NlM ý HKNO>Ð= lMQ=NO>Oÿ Óþ Ðý D ý lÿVBLN ý H |HRJ O= U i@ aM@Q=2M @QNOÿ BXU]M =@C=&BLÿN ÿ O D _ HK@QBLHRþJX= ý aMBEÿ(M =-DHRÿC= =N ý Ãý BLÿ D iÿC=ÿ¨H _HK@QBLHRþJX= BLD BLÿ D JL=2MQ= ; Rý N i=@IÿV=J U NOD2MCB RN HRÿQÿVýB RN=?>(BLN#M =¢D ý @C@Q=NlMHRÿQÿVB RN =Niý M %HKNO>(@Q=ý °HKBL@Qÿ þ N°HRÿQÿVB RNý BLN aM@C=M @QNOÿ BUÎM =@Q='BLÿÇN #ÿ OD _HK@QBLHRþJX= aMÇBEÿM = DHiÿV= ý =N ½BEÿ= M i@ ý ý =NTBLNOD RNOÿCBLÿVMC=NOD = JEHKNOHKMCB RNOÿ ÿV=MQÿ RUÎHiÿCÿCB RN=?> _HR@CBEHKþJL=ÿ1M = HiÿCÿCB iN =NlMQÿ RU BLD B J 8BLNOD iNOÿVBEÿ MC=N°D HR@C= O@ A> OD=>6 HRNO>6@Q=D i@Q>=>HKNO>6M ý =8D @Q @C=Nl M BXN°D RN°ÿVBEÿMQ=NOD -= JLHRNOH_MQB iN6BLÿ = AM N°DxMCB RN°ÿ HKN°> OÿC='@Q=ÿ °=?DxMCB R=J BXNOD@C= =NlMQHRJ'HKNO>¿>Aý =D@C= =NlMQHRJ'HKJ R@QBXM ý ÿý M Ò=NAU R@ID2=J tDHKJ'D RNOÿCBLÿVMC=NOD ý BM ý M D MCBLN ý = i=@ lM BLN 6H lHKBLN U³@ ÿCD@QHKMQD ÿ> l=?ÿ M = @C=M @QN BXUN KM NODxMQB iN B U M = D Q @ Q @ = l N ' M ÿ þ @ i þ L J = L B ÿ J A D R H X J J D R O N C ÿ L B V ÿ C M = l N M K H O N > "!# B JL= =NiMIÿ"HKN ¿ÿM BLN ÒD2@QBXMC=@QB RN ü]ý = HRJ R@QBM ý =NO>ÿ BXM ý H @ KU KU D RN°ÿVBEÿMQ=NOD KU HKN°>"HKN&HiÿCÿ AD2BEH_MQ=ý >"ÿ RJ Aý MCB RN HKNOÿ ¢=@ BM ý H @ KU RU¨BXN°D RN ÿVBEÿMQ=NOD RU WHKN°ÿ ¢=@ R@ BXM N RM BLN ËBXN6DHRÿC= RUHiDxMQB _H_MQB iN RU¤M ý =#ÿVM BXN Æ Ç È >É yÈ Ê rËSÌAÍÎ ÏÐ$ÐfÑÒÔÓ ÊÕÖÕ!× Ñ Ø Õ Ñ ÖXÙWÚ ÈgÛ9É ËSÜ5Ë Í+Ý <ÞËÎ Òàá ÖXÙWÊâ ß ÍÝ Éãã Õ!äSÊåQÙÊÖ ÈTÛXÉ <ÞËÎ ß]æÊOç $Ë Wè fÎ ± Ëé <Ë-ÏÐ$Ð_ÑzÒêÓ ÊëÚ_ÙWå^ÙWÊÖ × Ñ Ø Õ Ñ ÖXÙWÚ ÈgÛ9ÉaÛ ß Ëé <Ë Òì ß ÍÝ Éãã ÕäSÊå^ÙWÊÖ ÈgÛXÉ ÙFíc×SÕ!Ú <ÞËÎ ß]æ&î $Ë Wè Ëé <Ë-ÏÐ$Ð_ÑzÒêï èÎ WÍé fÎ Ø ÙWëÚ_ÙWå^ÙWÊÖ × Ñ Õ Ñ ÖXÙWÚ ÈgÛ9ÉaÛ ß ðñ Ë Wè $Îóò ËÎô · ! õös÷9øX÷9ùBú ûP÷Xúø9ü_ý FEQ N= ! = L HA= I E 4 =I $ E I = BE þ == þ $E^ $EK S JI = . JD E dD I Ã. D ]Y*W ] + J@ + I = E ûP÷9úø9ü_ýB D ¬ I I + = B ] O= B r + M +E I $E _L yD 4 D E = +E $ +# I $HA= ûZùBú _ü rL zLG` $ ûP÷Xúø9ü_ý õ#ös÷XøX÷9ùBú +I PD $E $ ¥ a T sD yD ! t L 4 Z $ c = FE7 D ü Wýü {ü_örø9ùBú + ÃD + ûP÷Xúø9ü_ý +E BE B I Wýü {ü_örø9ùBú BEZI ¬ I EZ= =@ { {ü_örø V¥ 7 þ Q¥ g¥ dD #L #Lr` $= õ#ö ý ü ø f÷ cö ¥ = c T¥ #LS` AI = FEL ¬ I d. O= ý ü $H I $ BE ü_örø 7¥ ü ù#÷Xý = ! I $I f÷ Bö + = FE + ¥ +E !I B ø9ü_ö ö I cEy¥-LA` ¬ I I Lb` f= GE T= = ÿþ fL ù K¥ ûZùBú _ü + I t |r¸ @ == 2D @QBMQ=@QB iN WHKN°ÿ ¢=@%ý $ == B ý @Q= U R@]HD OHK@QBLÿ RN BXM ý ý M ý = AM ý AMIÿ RU¨ý D2JEHRÿQÿVBEDHRJ MC@Q== R@J tDHKJAÿC=HK@ID =?ÿ RMC=¢M =D JL=2MC=ÿ =MC@ KUM ='HKJ i@CBXM BXM @C= iHR@Q> M T= tMQ=NOÿCB iNÌHRNO>-@C= OHKBL@HKNO>-M TD RNOÿCBLÿVMC=NOD -HKNO>ÌBLNOD iNOÿVBEÿVMC=N°D &(' [ EI O ÎII Î R ) [ ' Î EI ÎIQ Î R + ·Cª ,]§ * T Kl + ·Cª]fp - 'O? Kl R E .' 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D > [B4 S= fL l \ $ I = P= þ L G,B R,B x2 x2 x3 x1 x4 R,B R,B G,B Pc +#I ¬ $ I ¬ C= x3 R,B Pi ø ¤ì D iNOÿCBLÿVMC=NiM i@QH ý D RJ @QBXN @ RþOJX= 0/ HKNO>ÌHKNBLNOD iNOÿCBLÿVMC=NiM iN= 21 nNÌþ KM ý DHRÿC=ÿ H_U MQ=@'=?HRD ý HRÿQÿVB RN =NlM RUH _HR@CBEHKþJL=3 M ý =HRJ R@QBM ý [=@CU R@ ÿ U R@ ¢HR@Q>¿ý D ý =D tBLN U³@ ý M ÐM ý = D @Q@C=NiM&> HKBLNOÿ KUGM ý = NOHiÿCÿCB iN=> _HK@QBLHRþJL=ÿ Rý@]=?HRD ý @Q= R=?> _HKJ = M =(ÿVBLN RJL=2M RN5476£BEÿ)@Q=D R@I>A=>&HRÿ]H@Q= _HKJ[= ý JEHKN°H_MCB RN =NÒM =&> HKBLN KU'H _HK@QBLHRþJL=98)BLÿ B [=> AM H _HK@QBEHKþJL=98 8)BLÿD iÿC=NÐM þ[= NOHRÿQÿCB iN=>ÌBLN-M ý =D @C@Q=NlM'BLNOD iNOý ÿCBLÿVMC=NOD -= JEHKNOHKMCB RN M ý H_M BEÿBLNM ý = NB RN KUM ý = |HRJ O=Ç@Q= _HKJR= JLHRNOH_MQB iNOÿ¾BLN#M =]> HKBLN K7U 98 U MC=@ ONOý HRÿQÿVB RN =NlM K:U ;8 8 H |HRJ O= @C= _HRJO= JEHKN°H_MCB RNTBEÿ]D2@Q=HKMC=>8U i@)BXMQÿ @Q= tB Oÿ |HRJ O= ³M = @C= tB ý OÿÇBLNOD ý RNOÿCBLÿVMC=NOD = JEHKNOHKMCý B RN BXN Oÿ 8 8 ü]ný @C@Q=JL= _HKNlM _HKJ =@Q= _HKJ= JLHRNOH_MQB iNOÿ M lÿV=]M H_M¢ý BXN RJ R= 98 8 HK@Q= M =N@Q= R=?> =(HRÿQÿ AD2BEH_MQ=> |HRJ O=ÿHK@Q=G@C=?ÿM R@Q=> AMU R@ ¢HR@Q>&D =D tBLN OÿVý MTþ°= [=@CU R@ =?> H iHKBLNÒU³@ M ý =6HRÿQÿVB RNýO=> _HK@QBEHKþJL=ÿM M ý =D @Q@C=NiMT> HRBXý N°ÿ KUM = ONOHRÿQÿVB RNO=> RN=?ÿ R@£HRÿQÿVB RN =NiM M ý = |HR@CBEHKþOJX= RU1J )=?ÿM'BLNO>A= ÌH ý iN ËM = |HR@CBEHKþOJX=?ÿ KU#ÿ HR/ JXJL=ÿVM-D @C@Q=NlM&> HK1 BLN¿BEÿ&D iÿC=N )SHKJ =ÿ"HR@C= MC@QBX=?>%BXN%M = R@I>A=@ 4<>=<?6ËU R@ HRNO> 4<>?6ËU i@ i@ NOHiÿCÿCB iN =NlM H _HK@QBEHKþJL=ËBLÿ@IHKNO> J D ý iÿC=NÌBXNÌM ý =#D @Q@Q=NlM¢BLNOD RNOÿCBLÿVMC=NOD &= JEHKNOHKMCB RN ý )=?DH OÿV= TBXN N KMHTMC@Q==ËÿC=HK@ID þ AM(H"J ADHKJÿC=HK@ID ý BLN M ý =8ÿ OHRD= KU OHR@VMQBLHRJ)HRÿQÿCB iN =NlMQÿ BXMQÿMC@IHRD2=&BLÿ RNJ ÐH ÿC= =N°D2= RU ÿMIH_MC=?ÿ =HiD ý ÿMIH_MC=-þ°=BXN D iÿC=> RU H OHR@VMQBLHRJ¢HiÿCÿCB iN =NlMHRNO> KU H ÿV=M RU |HRJ O=&@Q= _HKJÇ= JLHRNOH_MQB iNOÿ nN=?HRD ý ÿVMQHKMC= BLNBXMCBEHKJLJ ÒU i@CþOBL>>=N _HRJ =?ÿËHK@Q= RBLNlMC=> AMËBLN¿>HR@ i@C= D ý @Q@Q=NlM HRÿQÿVB RN =Niý MIÿþ H6ÿ HRJXý JÇþJLHiD ÿ OHK@Q= HRNO>Ðý D @Q@C=NlMCJ @C= R=> _HKJ =ÿ#þ M =&BXý N >ABLD=ÿ RU¨M = |HR@CBEHKþOJX=?ÿÇM H_M HR@C=GBLN RJ R=?>"BLN-M =BL@@Q= _HKJÎ= JEHKNOHKMCB RN ASHRJ O=ÿ¢M = @C= _HRJO= JEHKN°H_ý MCB RN ý KU ý BED ý BEÿ)= AM M ý lÿV= M ý HKM]HR@C= BXNOD RýNOÿCBEÿMQ=NlM ý HKMC= R=@)M ý = HRÿQÿVB RN =NiM RU¨M = KM =@ _HK@QBLHRþJL=ÿ¢BLÿ HR@C= RBLNiMQ=> AM'BLNJXB M R@Q= · ! t G 5¸ ` d <U ¬ y I {= ZI $L I + = & +E HA= d K rD d sLBv'I Z E <U A $I $H +E M= I E P= +I w HA= $ MI §I = FE = V 7 C +I ! D à fcI E rL & cI +I B # D I § a $ I + HA= { rL fL 5L b f +#I ! HA= N= + - c # Z Q. ¬ ZI <U +I $HA= ! Z E + BE L 7 /= ` þ -I & = L bI + / +I $ A 6*<"WS*F8AS C= > ! I L t $ I K ¬ þ Z I J $I ! v y $ sL ! L#` ?= ÃI I HA= A ! 4 += E þ d +# ^ $ -D + BI ^ / $HA= HA= HA= $I +I $I & + I Ôþ 7= A $ I ! D I = d $HA= + U& fE I cE A@ rL +I ?D f $E#L fL I R@£= H JL= RN ý / WÿCý == B @C= BLN ÿVMQH_MQ= @ M ý => ý HRBXN KU _HK@QBLHRþJL=A @ BLÿ B [=> AM8HRNO>ÒHKJLJM ý = RM =@ _HK@QBEHKþJL=ÿ#HRý @C=TBLN iJ i=> BXN M =-BXNOD RNOü]ÿCBEÿý MQ=NOD = ý OJLH NOH_MQB iN =HiÿCÿ C =M HKM _HK@QBEHKþJL=7BBLÿ£D iÿC=NÌý M -þ°= NOHRÿQÿCB iN=> ý BEÿ'BEÿ HKM BLÿ > RN=&BXN ÿVMQHKMC= 1ü]Sý HKJ =%= BEÿ#@Q= R=?> U³@ M =-> HRBXý N Rý UD B BXM 4 <E7FG6-Hiÿ HKNÒ= JEHKN°H_MCB RN = _HRJ =&@C= _HRJ= JEHKNOHKMCB RNOÿBXN BLD B ]HRÿ(BLN iJ i=>ÐHK@Q= U Rý @ KMCMC=N ýHKNO>HRÿQÿ AD2BEH_MQ=> _HKJ =ÿ@Q=ÿVM R@Q=> _HKJ =H=áU R@ý 7FÌHKNO>I @ AM8U R@ ¢HR@Q> D =D tBLN GM ='D @C@Q=NlMÇ> HKBLN RUJ B @C= R=ÿ _HKJ =K? BXM 47FL6 HiÿHKNË= JEHKN°H_MCB RN ¬ D += H = þ . &#I K I + rL L - ! +I J V R G B -I rp5 I g I + A HA= 7 $ I A $I A B + I 5L <U N A HA= \ 4 +#I ¬ $E sL & D &D S@ ® B + D ! LTv'I D ! D HA= R G B x1 x2 x3 x4 1 R G B x1 x2 2 x3 x4 1 2 R G B x1 x2 x3 2 x4 1 2 3 s1 s2 s3 s4 R G B x1 x2 1,3 3 x3 3 x4 1 R G B x1 3 x2 3 x3 x4 3 R G B x1 3 x2 3 x3 1 3 x4 R G B x1 3 x2 3 x3 x4 1 3 R G B x1 3 x2 3 x3 1 3 x4 s5 s6 s7 s8 s9 x1 x2 x3 x4 $HB= CD 5L ø ¤ì lÿCÿCBLþJX== t=?D AMQB iN KU iN M/ N 1 BLNÿVMQH_MQ= N WÿC== B @C= M ý =6> HRBXN KU _HK@QBEHKþJL=% @ BEÿ B [=> M ý BM 4 B 6HRÿ¢HKN-ý = JEHKNOHKMCB RN lSHK@QBLHRþJL=( B BEÿ ONOý HRÿQÿVB RNO=>"HRý NO>"BXMQÿ @Q= tB Oÿ _HKJ = BLÿ @C= i=> BM HKN= M Ì= JLHRNOH_MQB iN aM BEÿM Oÿ ÿ @Q=M HKM _HKJ =A U R@( B > t=ÿ N Ký M(MIH R= °HK@CM(M HKN ý ÿ RJ AMQB iNÐHRNO>ÐDHRN þ[=T@Q= R=?> U³@ BMIÿ#> HRBXý N B BLJLHR@CJ =N BXN6ÿVMQHKMC= M => HRBXN RU _HK@QBEHKþJL=37F(BEÿ'HKJEÿ B [=> M BM 4 B 6HRÿHRN = JEHKNOHKMCB RN _HK@Q"BLHRO þJL= B BEÿ NOý HiÿCÿCB RN=?>"HKý NO>-BXMQÿ @Q= tB Oÿ _HKJ = ? BEÿ¢@C= R=> BM ý HKN= AM -= JEHKNOHKMCB RN aM'BEÿM Oÿ'ÿ @C=M H_M _HRJ A= ?ÃU RK@ JB#> t=ý ÿN KMMQH R= OHR@VMM HKN &ÿ RJ AMCB RN6HKN°>ÌDHKNÌþ°=@C= i=>"U³@ BXMQÿ'> HKBLN ¢=DH OÿC=£M => HKBLN R0U JB(BLÿ N = M BLNOD iNOÿCBLÿVMC=NOD RU 1 BEÿ @ i=N · þ ! ¨r¸ t =z $H . D SU y= D = FE I = FE A R B EV x1 x2 x3 x4 þ = ! ! rLv R B x1 x2 x3 2 2 x4 2 s9 s10 _¹5¸ iÿQÿCBXþJL== A=D AMCB RN RU = H $I U P= M rL R B x1 x2 x3 2 x4 3 2 s8 0 A s5 t I A rL I s4 2 2 ! A s3 R B I I E I aD s2 x1 x2 x3 x4 ? I R B x1 x2 x3 2 x4 1 2 s7 ø ¤ì +I += ? R B x1 4 x2 x3 2 4 x4 1 R B · $ I A += $ I A R B x1 4 x2 4 x3 x4 1 x1 x2 x3 x4 s6 = C R B x1 x2 x3 x4 1 s1 R B x1 2 x2 x3 2 x4 2 2 I QD '= N yD I I { g rL` I + I HA= + rL` L § a ?I $HA= I ® D BE = FE HA= BE A rL MD þ + { 6#*<"W*F8AS7 lc4 +#I ¬ HA= I R B x1 x2 x3 x4 RN { 6*<"$W*98Q s11 01 L þ VD QÚÞÚéêÝ:ãAݾ޿ÜlÝ:ãtãàVâ èÇÜ P =#DHKNÌN JLBLÿVM HKJLJÎM ý = OHK@IH =2MQ=@Iÿ)M ý HKMMQH i= JLHiD2=BLNÿ OD ý HKN6HKJ i@CBXM ý ¢M ý = 5R tBEH6D RN°ÿMQ@QHRBXNlMD ý =?D lBLN i@ D iNO ÿMQ@Q HRBXNlM @ OH iHKMCB RNH_M¾=HiD ý ÿVMC= KUlM ý =)HKJ R@QBXM ý ³U NOD2MCB RNOÿ HRNO>S aU(H OHK@CMCBEHKJ'HiÿCÿCB iN =NlMTBLÿ D iNOÿVBE>A=@C=?>HiÿTD RN°ýÿVBEÿMQ=NlM ý =N½HRý JXJ]M ý = D JX=MC=J HiÿCÿCB RN=?>D RNOÿVMC@IHKBLNlMQÿËHK@Q= ÿCHKMCBEÿ °=> )= i=2M#M ="J tDHKJÇý ÿC=HR@QD D NlMC=@ °HK@CM RU R aU'BXMBLÿ D iNOÿVBE>A=@C=?>HRÿD RNOý ÿCBLÿVMC=NlM =N8N Gý > HKBLN RU[HRN ý ONOHRÿQÿVB RNO=> _HR@CBEHKþJL=¢BLÿ B °=?> AM¤þ U R@ ¢HR@Q>D =?D tBXN )= R=2M:M =J ADHKJlÿV=?ý HK@ID D NlMQ=@ OHK@CM KU TR U aUÇBXMBEÿGD RN°ÿVBE>A=@Q=> HRÿGD RN°ÿVBEÿMQ=NlM =N N Ì> HKBLN KU)HRý N ONOHRÿQÿVB RNO=ý> _HK@QBLHRþJX=8BEÿ B [=> Mþ ý 6=NAU i@QDBXN )= R=MM =ËJ tDHKJÿC=HR@QD D NlMC=@ OHR@VM KU V%W M =@]U R@ ÿ RU¤J ADHKJ¾D RNOÿCBEÿMQ=NOD H &þ°= Rþ tB OÿCJ D iNOÿVBE>A=@C=?> ¢M ý X= ý R H_MGM ý =8þ[= RBLNNBLN KUM ý =8ÿC=HR@QD ý HRNO> HKM =HiD ÿVMC= RU°M ý ='ÿC=HK@ID ý H_U MC=@ _HK@QBLHRþJX=HiÿCÿCB iN =NlM R@ N°HRÿQÿVB RN =NiM ZY =ÿVMCB RN°ÿ HK@QBLÿC= OHK@CMCBED OJLý HR@CJ ºHKþ AM _HR@CBEHKþJL= NOHiÿCÿCB iN =NlMQÿ ³U NOD2MCB R[ N HRý NO>&M = ]H KUH RBE>ABLN O@ OH lH_MCBLN ËD iNOÿMQ@QHRBXNlMIý ÿ)H iHKBLN"U³@ ÿCD@QHKMQD ý H_U MQ=@¨=?HRD NOHiÿCÿCB RN =NlM ý aUAN 'BLNAU R@ H_MQB iN(BLÿ¨@C=?D R@I>A=?> =N ý @ OH iHKMCBLN D RN ÿMQ@QHRBXNlMIÿ D RN°ÿMQ@QHRBXNlM R@IH BLNAU i@ H_MQý B iNTDHKNTþ[= °ÿV=?>8M #JLB BXMÇM = R@ #M > #BLN DHiÿV= KU NOHiÿCÿCB RN =NlM aU¢M = _HR@CBEHKþJL=ËHRÿQÿVB RN =NiM i@Q>A=@(BLÿ@Q=D R@I>A=> ý BM DHKNHKJEÿ 8þ[= OÿV=?>-M ËJXB BMý M ý BEÿ i@ nN HRÿQÿ ADBLHKMC= BM HKN _HKJ = RU¤ý HKN _HK@QBEHKþJL=M =GN þ°=@ KU¤D @C@Q=NlM]ý D RN OBLD2MCBLN Hý iÿCÿCB RN =ýNlMIÿ)HRNO> HK@Q= OÿV=?> BXM TR M tN H_M#=HiD ÿVMC= RUÇM ="HKJ i@CBXM BXUH _HKJ = RUGH |HR@CBEHKþOJX=Ìþ°=J iN iÿ R@ËN RMM BXMQÿËD @C@Q=NlMT> HRBXN ³N JLJ i@ËN KMËN JXJ D ý NlMC=@ BXNOHRJXJ BU _HRJ = @C= _HRJ OÿVMCB °DHKMCB RNOÿ R@= OJLHRNOH_MQB iNOÿHK@Q=@Q=D i@Q>=> =N @ OH lH_MQBXN "D RNOÿVMC@IHKBLNlMQÿ R@Q= _HKJ =#@Q= _HKJEÿ DHKN6þ[=ÿQH R=>ÌBLN DHiÿV= KU ý NOHiÿCÿCB iN =NlM ý =N M ý = HR@C= O@ ¢M \= R X] L] >^ > OD=> HRNO>Ð@C=?D i@Q>A=?> ; HR N i@C="M ý HRN RN=&@C= _HRJ = JEHKNOHKMCB RNÒþ[="@QE=_ D i@Q>=> °=@ _HRJ = U N°DxMCB RN°ÿ HKNO> OÿVM BX@Q@Q=JL= _HKNlM(@C= |HRJ= JEHKNOHKMCB RNOÿ WBXN°D RN°ÿVBEÿMQ=NlM E_ BXM ý ý M ý ="D @Q@C=NlMHRÿQÿVB RN =NiM þ°= HRBXNlMQHRBXNO=> U N°DxMCB R`N iý ý =N8BL@Q@C=JX= |HRNlM@Q= _HKJA= ý JEHKNOHKMCB RNOÿHR@C= HRBXNlMQHRBXNO=> ½ÿ JE>M ý = JL=HR@CNOBXN = i@ 8ÿVB = þ°='JLB BXMC=?> _ ¢M a= ] a] cb U ONOD ý MCB RNOÿ ý K H ° N > \ ½ BM >A= M O@IÿM ý MC@Q==#ÿC=HK@ID ý iNý J -M ý ý = _HK@QBLHRþJX=?ÿ¢M ý HKM£HK@Q=(N RM HRÿQÿVB RN=?> R=2M HRNO>ÌM ý = _HKJ =ÿ)BXN&M =BX@> HKBLü]NOÿý M H_M H i='N KM]þ[==ý N-@C= Rý => i=2ý M]HK@Q=£H Îý =D2MC=?>Tþ "D RN ÿMQ@QHRBXNlM @ OH iH_MQB iN BLÿ¢BEÿ °ÿMQB O=?>&þ ËM =GUWHRDxM¢M H_M¢M =(ÿC=HK@ID l=?ÿ)HRJ ]H Aÿ U R@ ¢HR@Q> ý R@Q= _HR@CBEHKþJL=ÿHK@Q=-HiÿCÿCB iNü]=>ý R@Q= _HRJ =?ÿËHK@Q=&@Q= R=?>ÐBXN M ý =6> HKBLNOÿ RU:M = NOHRÿQÿCB iN=> _HK@QBLHRþJL=ÿ ='þ°HRD ¢HR@Q> R=?ÿÇý HK@Q=N RMÇý U³@Q== HRNO> OÿC= H ÿVMQHiD £M @Q=D R=@ @C= tB Oÿ¨ÿVMQHKMC=ÿ ½BM ý M =¢ÿC=HR@QD l=?ÿ:U³@Q==J U R@ ¢ý HR@Q>&HKNO>&þOHRD ]HK@I> iHRN _HK@QBEHKþJL=£Dý HKN HKM]HRN TÿVMC= &U³@ M ý = ONOHRÿQÿVB RNO=> M 8M =#HRÿQÿVB RN=?>&ÿVMQHKMC=(HKNO>-BLý N i=@IÿV=J lM =#ÿCH ý = ]H HKN _HKJ = KUHKN _HK@QBEHKþJL= DHRN ÌH_M(HKN ÌÿVMC= U³@ M = @Q=ÿC=NlM£M -M =8@C= R=>6ÿVMQHKMC=8HKNO> BXN R=@QÿC=J nN D L SU P= w)+_"S)'"<WWX*$"$Yy8zW8A*$Y s= = õö ýGü {ü_örø9ùcú f=Z F D y $I $ I cE ! 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S M I + #= ! 1 2A 22G3 Ls` ZI BE^ S= J -= _L$` ^ I I G + I ZD I $ ûP÷9úø9ü_ý 4 O = à A ! >Y)+_"<)>"<<X*"YQ*$fS"<*6 = [ ND $ sq f=Q R cEZI BE§S"K"<WWX*$"$Y 7 + $I I = ûP÷Xúø9ü_ýc P 7(#"Wh >6":B*<"h_BkSLg` 7 #I D / õös÷9øX÷9ùBú +E = = p <U . !I ûP÷9úø9ü_ý 4 L` yD ü Wýü ü_örø9ùBú I T:#":&M*_"<*<6 ûP÷Xúø9ü_ýc 2 Z= # I P ]I +E BEy B ELz` ÿ °D ý D RN°>ABMQB iNOÿ BXM H &þ[=BLNlMC=@Q=ÿVMCBLN Tþ KM ý U R@ M ý =8ÿCH R= KU= TDBXý =NOD HKN°> KU BXNU R@ HKMCB RN OHKJLBXM M °=@VU i@ D RN°ý ÿMQ@QHRBXNlM @ OH ý iH_MQB iN iNÒHKJLJM = |HR@CBEHKþOJX=?ÿ N°HRÿQÿVB RN=?>-HRNO>HRÿQÿVB RNO=> HKNO>HRJXJÎM = _HKJ =ÿ RU¤M =(BXNOBMQBLHRJ¾> HKBLNOÿ @C=?ÿV=NlM R@¢@C= ý R=> OD ý Hÿ AÿMQ= ýH_MQBLD£D AMCBLN BEÿ Rþ tB OÿVJ i@C=GD lÿMQJ þ AMDHRN ý = H OR@C=#BEÿMQM BLD(=8D D ý RBED2=ÿ MCBLÿVN =&H=(_þ°MG=J =HiD ÿMQ= 6=HiÿVBL=@GHKNO> O@ tBE>A=#BLNAU R@ H_MCB RNU i@ þ[=2MCMC=@ ¢M ý = (M ý HKM£HK@Q= OÿC=>þ -U NODxMQB i5N ] BLN DHRÿC= KUJ ADHRJ1D RNOÿCBLÿVMC=NOD HKN°> ] JLJM ý ='ÿM O>ABL=ÿý M ý H_M ý H R=]þ[==NTDHK@Q@CBL=> AMÇHRþ ý AMM ý H_MÇBLN8M ý = D RNlMC= tý M RUÎ>= AM ý O@IÿMMQ@C==ÿC=HR@QD ý HK@Q= )@Q= °ÿCHRþJX=GBLN-M BEÿJLHR@ i= @] J tDHKJ¾ÿC=HR@QD D RNlMQ= tM ¢M ý = 8M HKMHR@C= OÿV=?> þ U NOD2MCB RaN ] -BLN"DHiÿV= KU:ý BXN°D RN°ÿVBEÿMQ=NOD )ý =?DH OÿV='M ý BEÿÇD ý iBLDý ='BEÿM ý = HKBLN N R=Jý M KU BM @C= iHR@Q>"M ">A= AM O@IÿVMMC@Q==#ÿC=HK@ID D JX=MC=J Ný = = @QBEÿMQBLDÿ OÿM¢þ°=>A=?ÿVB RN=?>"HKN°>"= [=@QB =NiMQ=>Ëý U i@ÇM ý H_M tSHK@QB OÿÇD@CBXMC=@CBEH ÿ JE> þ°= MIH R=NÐBXNlM 6HiDD NlM(M O> R=ËM =TBXNlMC=@C=?ÿM#BLN NOHiÿCÿCB iNBLN H _HK@QBEHKþJL= ý KU)D @Q@Cý =NiM |HRJ O= d BLNBXMCBEHKJý > HRBXN d HRNO> D @C@Q=NlM£ý> HKBLN 8 e ³B M =8UWHiDxM(M H_ M BEÿBXN iJ i=> BXN M ="D @Q@C=NiMBLNOD iNOÿVBEÿVMC=N°D H_MC= R=@ M ý = ]H #M ý BLÿ¢BLNOD iNOÿVBEÿVMC=N°D 8BLÿ¢D ý AMC=?> WD RNOÿVMC@IHKBLNlM R@IH ý BXNAU i@ ý HKMCBý RN |HRJ O= @C= |HRJ= JEHKNOHKMCB RNOÿ ý WBXB M =TN þ[ý =@ RU'D Rý N°ÿMQ@QHRBXNlMQÿBLN BED BLÿ#BXý N iJ i=> WBMIÿ'>A= R@Q==GBXN-M =#D RNOÿVMC@IHKBLNlM i@QH WBXBLB M =N þ[=@ RU _HKJ =?ÿ]BXNÌM = > HRBXNOÿ RUÇM ý ý = RM ý =@ _ý HR@CBEHKþJL=ÿ£M ý H_M#HK@Q=BLNOD Rý NOÿCBLÿVMC=NlM BXM ý d ³BLN ý M ý =TD RN ÿVBEÿVMC=N°D R@IH ³B M ý = °HKJLBM KU e BXM @C= iHK@I>Ìý M HKN 6ÿVMQH_MQBLD = @CBEÿVMCBED R@I>A=@QBLN KU d M =£ÿCB = KU d HKN°> 8 d tB M ='@C= |HRJ= JEHKN°H_MCB RN°ÿ HKJL@C=?HR> ý @ A> °D2=>HRNO>&@Q=D R@I>A=>&U R@'M ý = _HKJ =?ÿý BXN d Mf 8 e tBLB M ý =#@IHKN KgU BXN M =TD @Q@C=NlM(HiÿCÿCB RN =NlM R@I>A=@ tBLBXB M = _HRJ =Ë@Q= _HKJ= JEHKN°H_MCB RN°ÿ M ý HKM OJL>Tþ[=>A=ÿVMC@ R=?>THKNO>ËU i@ KMCMC=N&BXN&ý M ý => HRBXNOÿ KU:M ý = KM ý ý =@ |HR@CBEHKþOJX=?ÿ BXNDHiÿV= RU NOHiÿCý ÿCB RN =NlM K0U ý ý RMC=GM HKM )=(DHRN-þ BXJE>&U³@ M =?ÿV=(D@CBXMC=@CBEH NOHiÿCÿCB iN =NlM = @QBLÿVMCBEDÿ BED HRB HKMGþ OBXJE>ABLN ÌH-D iNOÿVBEÿVMC=N°D @ RU WHÌÿ iJ MCB RN ý þ ý @Q= tBXN #þOHR>TD ý RBED2ý =ÿ ý U i@Ç= H OJX= M NOHiÿCÿCB iNTH _HK@QBLHRþý JL=]M ý = |HRJ O= KU ý BLD ý BLÿGBLNOD iNOÿVBEÿVMC=NlM BM M ý = i@C=?H_MQ=ÿVM ý N ý þ[=@ KU |HRJ O=ÿ£BXN M =T> HRBXN°ÿ KU'M = KM =@ |HR@CBEHKþOJX=?ÿ HKNO> RM =@ RN=?ÿ BED HRB HKM8þ OBXJE>ABLN HRN BLNOD iNOÿVBEÿ MC=ý NOD O@ KU U R@= H JL= M NOHiý ÿCÿCB ý RN-ý H _HK@QBLHRþJL= M ý =(> HKBLN-ÿCB = KU ý BLD ý BLÿ M =#ÿ HKJLJX=?ÿM R@'H ý _HK@QBLHRþJL=£U i@ BEýD M =(ý N þ[=@ RU>=ÿVMC@ R=> _HKJý =@C= _HRJ = JEHKNOHKMCB RNOÿ8BLN M =6> HRBXNOÿ RU'M = KM =@ _HK@QBLHRþJX=?ÿ OJL>þ°=ÌM ý =6ÿ HKJLJL=ÿVM BXN DHRÿC= KU ONOHRÿQÿVB RN =NlM BLN R@I>A=@M &>=ÿVMC@ ÌHiÿJX=?ÿCÿ£HRÿ lÿCÿCBXþOJX=(M = O@ KUBLN @ R@Q=ÿQÿ ¢M ýý = O@C=?ÿV=NOD2= Rý @#HRþOý ÿC=NOD= RU O@CB R@QBM U i@HRÿQÿCB iN =NlM W@C=?ÿ NOHiÿCÿCB iN =NlM ý M M = _HK@QBLHRþJL=6M HKM Hiÿ"þ[==N NOHiÿCÿCB RN=?> ³@Q=ÿ )HiÿCÿCB iN=> OÿVMÌþ[=2U i@C= =N HKN¿HRÿQÿVB RN =NiM ³@Q=ÿ NOHiÿCÿCB RN =NlM B =?>ABEH_MCý=J ÐU iJXJ 'ÿËHKN NOHRÿQý ÿCB iN ý =NlM ³@Q=ÿ HRÿQÿVB RN =NlM == U i@Ì= H JL= OD @CB R@QBXMCBL=ÿ-JXB BMÌM =ÒD iBLD= KU¢M ý = |HR@CBEHKþOJX=8M HiÿCÿCB RN i@(M N°HRÿQÿVB RNý ÐBLN M ý ý =ÿC="ÿCBM OH_MQB iNOÿ þ AM(UWH @M ý = @ t> ODxMQB iN KU:BXN°D RN°ÿVBEÿMQ=NOD O@ KUWÿ =NTþ KM @CB R@QBXMCBL=ÿHR@C= O@C=?ÿV=NiM ¢= ÿCH M ý HKMM ý =#ý HiÿCÿ AD2BEH_MQ=>&HRJ R@QBM ý [ý =@IÿVý = R=@C=?ÿ ONO HRJXJ M ! = ý BLD BEÿ OÿV=?; >Tþ 8U NODxMQB iN "!# ý =N&N @Q=ÿ JXM HRÿ-þ°==N HKJL@C=?HR> @ A> OD2=?> F MQB = N þ°=@ RUHRÿQÿCB iN =NlM h i@ = tMC=NOÿCB iNOÿ R@@Q= OHRBX@Iÿ JI ! + &cI .!I GE FE L 0 I $I BE O I 4 X. . 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M ý HKM U R@ B`{ HKJLJ RUM ý = HR@C=BXNOD RNOÿCBEÿMQ=NlM HKN°>M ý HKM U i@ B w RNOJ RNO= R=NO=@IH_MC=?>"BLNOÿVMQHKN°D2= M RU BLÿ]BLNOD iNOÿCBLÿVMC=NiM :ì °ú°ô_ø ð?ñ Ðõ ü]ý = HKJ i@CBXM ý ÿ )= D OHK@Q=>%HR@C= ü ; ; HKN°> U @ _HK@QJB U ü e| HKNlMQÿ KU |} W@QHRNO> |} iÿVMQ> þAM |x} BLNO>A=ÿVMC@ _HK@ HRNO> |} BXNO>=ÿVMC@ H |HR@ ; ; ý ý ý ü HKJLD2J = KAUM M ý = HRD JXJ KUtM AMC=?=8ÿV=)HKHKNOJ >6R@Q@Q=BXMD R@I> ÿ _[HK=J @CU =R@ @Q= U R@ _]HKHKJ¤@I= >£D JEHK=?NOD tHKMCBXN B RNOÿ HKDN°= > AM HKBLNiMIHRHKNOBLN> RNJ M ý iÿC= M ý H_MÌ@C= HKBLN½@C=JX= |ýHRNlM R@ ý ¢HR@Q>%D ý =?D tBXN BLÿ RNJ °=@VU i@ => iN½M ý = D @Q@C=NlM¢> HRBXN°ÿ D2= AMÇU i@¢M =£U @CM _HK@QBLHRNiM K2U |x} |} BXNO>=ÿVMC@ H |HR@ BXM BLÿ RNJ [=@CU R@ => iNM ý = O; NOHRÿQÿVý B RNO=> _HK@QBLHRþJL=ÿ ý D2= AM ; HKJLJ RUlM ý =ÿC=Çý HRJ R@QBM ý ÿ °=@QÿC= i=@Q= D2= M-U i@ M =ÐHRÿQÿVB RN =NiM = O@CBEÿMQBLDÿ-D RNOÿCBEÿMIÿ-BLN0D lÿVBLN HRN NOHRÿQÿCB iN=> ý _HK@QBLHRþJX= KU(ÿ HRJXJL=ýÿVMT@QHKMCB Ðþ°=M )==N¿; BMIÿ"D @Q@Qý =NlM"> HKBLN%ÿVB =6HKN°>BXMQÿ >A= i@C=="BXNÐM =-D RNOÿVMC@Iý HKBLNlM R@IH ý D= AM#U i@ HRü]NO>ý M =-ÿC=D iNO> _HK@QBLHRNlM KKU ý |x} e|x} iÿVMQ> þAM M = _HKJ = = @QBLÿVMCBED(BEÿ@IHKNO> =#U @ _HK@QBEHKNlMQÿ R~U |} H i= BXNËD iN#M ý =]D ý RBED2= KUOý M ý = _HK@QBLHRþJX=)M NOHiÿCÿCB ý RNBLNOÿCBL>=)M ý =D @Q@Q=Nlý M1BLNOD ý RNOÿCBLÿVMC=NOD = JEHKNOHKMCB RN : )= R=@ M = ->AB [=@ HKBLNJ "BXNÌM = ¢H KU H lBLN 8M BLÿ'D RBED2= |} ³@IHKNO> °ÿV=?X ÿ qr -HRÿHRN NOHRÿQÿCB iN =NlM ý = @QBLÿVMCBED WÿCý == =?DxMQB iN |} iÿVMQ> þAM OÿC=ÿAqr ÎHRÿ¨HKN NOHiÿCÿCB RN =NlM = @QBLÿVMCBED WÿC== =DxMQB iN Hý KN°> r bÃHRÿHGÿMIH_MCBEý D _HKJ = ý = @QBEÿMQý BLD ü]ý BLÿ _HRJ = ý ý = @QBLÿVMCBED¢@C=?ÿ JXMQÿ¤U³@ M = @C= aD Aý MQBXN -U i@#=HiD |HRý J O= Ký U]=HRD _HK@QBEHKþJL= KU¢M ="N þ°=@ KU _HKJ =ý ÿ BM'@Q= i=ÿ)BXN-M =#> HKBLNOÿ KU¤M = KM =@ _HR@CBEHKþý JL=ÿ tSHKJ =ÿHR@C= R@I>A=@C=?>TBXN=?HRD > HRBXNHRDD R@I>ABLN M "HKNÌBLNOD2@Q=HiÿVBLN |HRJ O= KU¨M BEÿN þ[=@ |} BXN°>A=ÿVMC@ _HK@ OÿC=Xÿ qr &HRÿHRN NOHRÿQÿCB iN =NlM ý = @QBEÿMQBLD ÿV== =D2MCB RN |} BXN°>A=ÿVMC@ H _HK@ >AB [=@QÿU³@ |x} BLNO>A=?ÿMQ@ _HR@ RNJ BLNTM ý H_M)U R@ ¢HR@Q> D ý =D tBLN ËBLÿ [=@CU R@ => RNHKJLJ:M ý = |HR@CBEHKþOJX=?ÿ :ì ¾ïîlô_ø ÐîAù[ðö ¢ô_îtõ ðõ ý Hiÿ )=?DH OÿV=HKJLJ[M ý =(D RNOÿCBL>=@Q=ý >"HRJ R@QBM ý ÿÇBLN ý RJ R=£@Qý HRNO> D ý RBED2=?ÿ =HiD ý KU¨M ý = Ó ; þ°==N&@ N MQB =ÿ RN-=HiD BXNOÿVMQHRNOD2= HRD @ N HRÿ)þ°==N iB i=N"H H AB F MCB ý = ý KU ÿC=D RNO>ý ÿ ý ; F MCB = KU ÿC=D RNO>ÿËBEÿ&Hiý ÿCÿ AD2BEH_MQ=> ; BM ý HKN @ N BLD >ABE>ÌN KM °NBLÿ þ "M =#>A=Hi>AJXBLN= B @C= @Q= R@CMQÿ¢M = =>ABEHKN F MQB =#Hiÿ HU NOD2MCB RN KU B ý B @Q= @Q= 3R @CMQÿM ý ='N ý þ°=@ KU:@ NO ÿ ýü]BLý D ý >ABE>TN RM ONBEÿ ý þ M ý = >A=Hi>AJXBLNý = H RN 8M = U R@=?HRD |HRJ O= RU B =?ÿV=@Q=ÿ JXMQÿHKJLJ Oÿ¢M H R=GM =; U RJLJ BLN RþOÿC=@ _H_MCB RN°ÿ aU ý H þ[= = "D2BL=NlM RN-D RN°ÿVBEÿMQ=NlMÇBLNOÿVMQHKN°D2=ÿ BXM)þ[=D =ÿ BLD tJ BLN= TDBX=NlM =N"H @ iHiD ý BXý N 'M ý = D iý NOÿVBEÿVMC=N°D |BLNOD iNOÿCBLÿVMC=NOD U³@ RNlMCBL=@ aMÇBEÿ HRÿ KM ý =@)D2JEHRÿ ÿVBEDü HRJ:; J ADHKJ¾ÿC=HK@ID HRüJ R@QBM ÿ ý N°HKþJL=M Tÿ RJ R=BXN°ýD RN°ÿVBEÿMQ=NlMBXN°ý ÿMIHKNOD=ÿ HKNO> | @C=?ÿV=NlMM =8ÿCH = °ÿ OHRJ¨þ[= H tB @ BM H °=?H KUD JL= ABM HKM M ý =8D RNOÿCBEý ÿMQ=NOD :_BXN°D RN°ÿVBEÿMQ=ý NOD "U³ý @ RNlMCBL=@ }ü =ÿ JXMQÿ KU ; -HKNO\> | ü HK@Q=(ÿVB BXJEHK@'HRNO>&þ KM D2JL=HK@QJ Tþ°=MVMC=@M HKNÌM lÿV= RU R[ ! g ZI ¨ | ¡M~! 4 v ¿ d $ VD = v f= b E EN= = ! $ « L I + f= P H $= I Q HA= rL aD 4 -. -. $@ $ 0 [B4 ©Nª = I U ` b D t fL +D GE Q v P H . $ 0 +I L [A4 + L 0 d. fI + JI BI I O I ] BI Z E _L {I + $I y. ]v $ A B E ! D I $ ! I +I ] I >xC@ D BE $= > SH +#I K + _2S BI >D SL I >xC@ cE I D I $L E I E $ E = $E 4 E I $L S_c4 > +# vd¿ FE fI fL O. $= 2S + = 2S# == U G $ ^ d #L ¬ I ! ?xd@ BE SL ¬ #L « $ y y +# d !I - _»b~ ? _2S D y. T d L Z $ ZI + M ~ I c GEK Z,76*SY 4 ! ¢ 2 u !#I C $I +I +# A L Q I 44 $ ZD P E G <U v ' 4 f= g E G I $I +I ! E I + $= b L -. ! E I E= ! Q {I H O. I P,yGX6Sjz( -. $= ' K . A + I =I +@ 4 $I ]I fE FD A H zL « HA= H $I P,Q* K= « P6 4 A#I [B4 I f fL « L <U P S= ' I !#I V E I <U ? O 4 O. ! D - D ¬ ! { 4J4 4 A#I I !I $ O. +E{ "<fe'"fQ6S*<"$X*<6(#"WhXiWjA,a8 ,Q£"<Sfe'"$. ! { fL ! I $ ¨ H 4 .v = $ f $L « O. =I A 5 L 4 O. g I . 44 E G P 4 6SY,Q"&("hG"hGck£. ]v O. H RR ! _L ("h#"Wh ] P6*<"WS§*F8ASw. « g¢ ck£. $ _ ZI $E ?cI _L` <U E JI _L J@ fL G I aD $ T P Tv I L y= ] vd¿ SU Nv @ 1. BT 2. CBJ 3. DBT 4. MC 5. DR(rand) 6. DR(mostdoubt) 7. DR(mindestroy,uvar) 8. DR(mindestroy,avar) 120 Median CPU-time (in seconds) 100 80 4 1 60 40 3 2 8 7 20 5 6 0 30 32 34 36 38 40 p2 ø ¨ìy 6=>ABEHKN ; F MQB = RNÌ@IHKNO> J i=N=@QHKMC=?> @ RþJL= BXNOÿVMQHRNOD2=?ÿ · ! r¸ |}-.³@IHKNO> >xC@ A Z +EV V= $L HRNOa> |} iÿVMQ> þAM @ A> °D2= OHRÿCBBL>=NlMCBEDHRJ@C=?ÿ JXMQÿ(HRNO> @Q=ÿC=NlM H °þ = ý H tB @ ý BLD ý BLÿËÿCB BLJLHR@8M M ý HKM ý KU ; JXM ý ý M ý = HK@Q=&M ý = iÿVM = "D2BL=NlM RND iNOÿCBLÿVMC=NiM-BXNOÿVMQHRNOD2=?ÿ-HKM"M = D iNOÿCBLÿVMC=NOD |BLNOD RNOÿCBLÿVMC=NOD U³@ iNlMCBL=@ M ý = -HR@C= HRÿ ; HKNO> RM ý =@'D2JEHRÿQÿVBEDHRJ[J ADHRJ¾ÿV=?HK@ID ý HKJ i@CBXM ý ÿ NOHRþJL=M Tÿ iJ i= BXN°D Rý N°ÿVBEÿMQý =NlMý BXN°ÿMIHKNOD=ÿ JXM M = HK@Q= þOHiÿVBEý DHRJXJ %J ADHKJÿV=?HK@ID ý HKJ R@QBXM ý ÿ-BXN M ý =Ðÿ °HRD2= KU °HK@ MCBEHKJ HiÿCÿCB RN =NlMIÿ HRNO> M Oÿ ý 8BXN°D ý JL=2MQ= |x} BLNO>A=?ÿMQ@ |HR@ ý HRNO> |} BXN°>A=ÿVMC@ H _HK@ @Q=ÿC=NlMM =£ÿQH ='þ[= H tB @ÇHiÿÇ> 8D OJX=MC= HRJ R@QBM ÿ ÿ °D ý HRÿ ü ; HRý NO> | ü i@C= R=@:M ý = #HK@Q=M ý = iÿVM¤= "D2BL=NlM iN#ý BLNOD iNOÿVBEÿ MC=NiM]BLNOÿMIHKNOD=ÿ]H_M)M =D iNOÿCBLÿVMC=NOD |BLNOD RNOÿCBLÿVMCý=NOD U³@ RNlMCBL=@]HKNO>-HKJLJ ¿M = R@Q=H_M =ÿVM(N þ[=@ KU¢BXN°ÿMIHKNOD=ÿ£M þ[=Ëÿ RJ R=?> þ 6M =T>A=Hi>AJXBLN= KMQ=TH-ÿ HKJLJHR> _HKN MQH R=GU RK@ |x; } BLNO>A=?ÿMQ@ _HR@ ý =NÌD OHK@Q=> ý BXM ý |} BXN°>A=ÿVMC@ H _HK@ BLN MC=@ ÿ KU F MCB = iN-D iNOÿCBLÿVMC=ý NiM]BLNOÿMIHKNOD=ÿ¢H_M¢Mý =(D RNOÿCBLÿVMC=NOD _BXNOD RNOÿCBEÿMQ=NOD U³@ ý iNlMCBL=@ [=@CU R@ BXN &U i@ ]HK@I> D =?D lBLN RN HKJLJM = _HK@QBLHRþJL=ÿGBLÿ£M 6D ý iÿVMCJ N M =6D RNlMC@IHKý @ N KMQ=ÌH ÿ HRJXJHi> _HKNlMQH R="U i@ |} BXNO>=ÿVMC@ H |HR@ =N%D OHK@Q=> BM |x} BLNO>A=ÿVMC@ _HK@ BLN6MQ=@ ÿ KU)N þ[=@ KUÇÿ RJ R=>BLNOÿVMQHRNOD2=?ÿ£HKM M ý BEÿGU³@ Rý NlMCBL=@ [ý =@CU R@ BXN "U R@ ]HK@I>6D ý =D tý BLN iN HKJLJ1M ý = _HK@QBLHRþJL=ÿ @ tBE>A=ÿ M ý = HKJ i@CBXM BM H8þ[=2MCMC=@ NOHRÿQÿCB iN =NlM = @QBEÿMQBLD K':ã 'Þ Ý ÐØ:Þ )= iNO>TM ý =ÿC= °@QÿVM¢@Qý =ÿ JXMQÿ HRN O=ÿVMCB RNOÿ¢@Q= ýHKBLN N°HKNOÿ )=@C=?>"HKN°>"N==>&U @VM ý =@ = °=@CB =NlMQHRJ¾HKNO>-M = i@C=MCBEDHKJ:ÿVM O>BX=?ÿ RN 8M = @Q= M ý =@Q= ONOHRÿQÿVB RN =NlM ý = @CBEÿVMCBEDÿÇM ý HKM]DHKN"þ[=2MCMC=@ÿ RJ R= D RNOÿCBEÿMQ=NlM¢BLNOÿVMQHRNOD2=?ÿ HKNO> RM ý =@ RNO=ÿM ý H_MGDHKN6þ[=2MCMC=@£ÿ RJ R=(BLNOD iNOÿVBEÿVMC=NlM iN=ÿ _ aU ¢= tN äN KM ý BXN 4 O. C E -. I 4 E G JI P gv vd¿ + cI = ]v LG{ E $ ! ' ?xd@ _p= ! E $ fE N E I J + _pz= D a $ t aI { C $ ¾ MD ! D <U + N KI 4 $E $ EL D N= D !I p $ L fI @ 4 Q $I $L t ] K BEV#I cI A c E G J@ @ E G E O. P ^ ! 4 g @ 4 +# +D $ I = = -. A B I #L $ <U aI BE D E I ! E w -= E I A J= O. fE 4 = $ ! D O. ÃD E I G I f E Z O. = fE {8WW HA= #I fE v JI t L fL #I = ycI y P t = AI fE 4 A#I G +#I 7D C $ ` D OU D @ 1. BT 2. CBJ 3. DBT 4. MC 5. DR(rand) 6. DR(mostdoubt) 7. DR(mindestroy,uvar) 8. DR(mindestroy,avar) Number of unsolved instances (answer ?) within 120 seconds 200 4 150 6 5 100 1 50 3 2 7 8 0 30 32 ! 36 38 40 p2 ø ¨ìL · 34 ¾ 5¸ þ[=@ KU ONOÿ iJ i=> @ RþJL= BLNOÿVMQHRNOD2=?ÿ BM ý BXN I a bI J + M= ÿV=?D iNO>ÿ G2S D fL KH þ AM#D RNOÿCBLÿVMC=NOD i@£BLNOD RNOÿCBLÿVMC=NOD JE> BXMþ[= @ MIHKþJL=M -@ N M HKJ @CBXM ý ý ÿD iNOD @Qý @Q=Nlý MCJ iN= BM ý M ý = Rþ =?DxMCB R= RUþ BLJL>ABLN H6ÿ RJ AMQ_ B iNÐHRNO> M ý = KM ý =@ iN= BM M ý = Rþ =DxMQB i= KUþ ýBLJL>ABLN "HRN-BLNOD iNOÿCBLÿVMC=NOD O@ KU H_M OÿVMþ°=]M = N°HRÿQÿVB RN =NiM = @QBLÿVMCBEDÿM #HKJLJ BXN°D RN°ÿVBEÿMQ=NlMBLNOÿMIHKNOD=ÿ1M þ°=)ÿ iJ iý => _ ; HKN ¢=>A= ONO=Çÿ ý TDBX=NlM¤D iNO>ABXMCB RNOÿ iNM ý =?ÿV= ý = @QBEÿMQBLDý ÿÎM OHK@IHKNlý MQ== HKJ i@CBXM MC=@ _ ; BLNOH_MQB iN BM M8HKN ÐÿM OBXN D2@QBMQ=@QB iN HRNO> M _ Oÿ8HKJ i@CBXM D ý OJX=MC=NOý =ÿQÿ HRN )= ÿMQý BXJLJ¾þ[=2MVMQ=@ >A= ON=(N=?D2=ÿQÿQHK@ "D Rý N°>ABMQB iNOÿ ý H_MBEÿ¤M =]BLN =NOD2= KU°M =¢JX= R=J RU°J ADHKJtD iNOÿCBLÿVMC=NOD D =D R=?> RN=HiD OHR@VMQBLHRJ HRÿQÿVB RN =NlM iNM ý == "D2BL=N°D KUM ý BLÿ ý tBXNO> ý KUJ ADHKJ¤ÿC=HR@QD ý ³U R@ ¢HR@Q>D ý =?ý D lBLN HK@IDËD RN°ÿVBEÿMQ=NOD HKN°> þ[= iNO> M HKM M = @Q=DBLÿC=ËBXN =N°D2= KUHKJLJM = OH @QH =2MC=@Qÿ¢JLBLÿVMC=?>ÌBXN6ÿC=DxMQB iN 9_ &÷¨ù¨ú ³î °î ÐîAù[ðõ 6HKN 6M ý HKN Aÿ£M HK@Q=NO>A@IH OÿQÿCBX=N HKN°> JLB tBL=@ ý = U R@M ý = -HRJ ýR@QBM ý HKNO> OHR@VMQBLD JLHR@CJ M HK@Q=NO>A@IH&U R@GU³@ OBMCU JÇ>ABEÿ ý D OÿQÿVB RN°ÿHKþ AM]M BLÿ'HRJ R@QBM ݨçQݨÞݨâ ÙÎÝ¤Ü Ä?KÆ glknknjmIr°d|b£ÆjdKY°if?((m?d £Æ Y°fKsIqhO\Rmxq2pVsV`1f?rikanpVqjr_»:pf?tq¥|q2frËqrt#`1f?Gr tsCn^ ¡lqknmx ¢mIgRpjkaXsCkIÆZpnjÑtsQqh r_mIhjhjj¥?mIrlsQ3m G;Ìe¹ ?¼ KÆ'ekqrl¥Rd Æ olfglrllqjfrlkf¤`1frlkanpVqr_¢\iq2jka q?sVfr°ÆZ¢sIqimI(s]»:pmIknkÇYOVÆ[¹a#Ä |¼ RD Æ ¢mxsV_mQpxdKc'Æjdi»Îmxqph 9d iÆ b¢mQfpÔK^W¡lqknmxA ¢mIgRpjkaXsCkLfp)`1frlkanpVqjr_¢\iq2kaEq?sCjfrT»¾pf¡i^ hjmI(kIƨZpnÑAsQqh r_mIhjhjj¥?mIrlsQ(m Z ¹aTÄ ?¼ iD Æ ¢qpVqhsÔAdlc'Æjd ¾hjhjfx:d £Æ ¨ rtsVpmxqknjrl¥e1pmIm£\Rmxq2pVsV #sCmQrtsC Efp]`1frlkanpVqr_]\iq2kaEq?sC^ jfrT»¾pf¡lhjmI(kIƨZpnjÑtsQqh r_mIhjhjj¥?mIrlsQm L6¹aTÄ ¼ I $ E/ d PD I + &D ! I I c E NU C#I I E à @ B + FD? + $I + <U + Z = . ! 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