CloseGraph: Mining Closed Frequent Graph Patterns - CiteSeerX

Report 0 Downloads 359 Views
CloseGraph: Mining Closed Frequent Graph Patterns Xifeng Yan

Department of Computer Science University of Illinois at Urbana-Champaign Urbana, Illinois 61801

[email protected]

[email protected]

ABSTRACT

         !" #$ &%&   '( &) )*$+$%', -/.0/21436579853:8;05?@582 A)*0$% B .$C  . 0  $ *0D.0%A3:E5F58 G*HI3:3:1J@F58FKAL&EIM$N/8FOQP R %&0 F&DS$FT B .0 .$ KUL&EBIM$N;&;)* DV&)*0D 2 D+C  &0 W)*$%X$F#YZ[ \YZ,90$D+ 0 ]+\^$$'(& )R  K _`^9a$$D& F &bK/c OedfYg  K )*00%D+ %&S%& F&$90C   0 9 0&DD0%&+$%h.0* \ 0R$  0i&']&"aj$/ +&D  .$)9^j *'k'( -/.$/R .0^0% F&$0 OQlm0 B 'c)*00%`&DDf $

.$^0% F&0$ KgYg\ j& T h)*0h@Hn85oipE 5=>05?03kL&EIMN`MI3Jq 365EF?08 OXPr% F&$2s\ i@Hn&85o2hX0F^ *'V 0 #a$ B c0  j W .0j % F&0t'usX ] ] 0v &)*v .0$j& k ]sjOkP D+& 9% F&09  9)*00%f&D%&& [ 0)TK wyx z{B|}u~(/€//K  U$ D[C &j#^/!9a$$D& 0%c   F&D0/   B $%v .0$+$%W)* $ $ Oy‚].

j '4& )R0] B .!# 0YZ S wyx z{B|}u~(/€/k$&Z$D[!i F&)RC DD! .0 *.$0$   !" .0^0% F&$0 # `^jƒ%$ F ^0. D ; .0^0 BF/ ,DD!0 &  * $T„*$!&'k)*$+$%$KV jC ,DD!ƒƒ 0W  $k&'eD+ %c%& F0T0  $ O

Categories and Subject Descriptors

dvO … O †T‡ ˆX‰0Љ0‹Œ‰0Žt‰‘’‰$“Ž$”2Ž‘•Š–˜—y™WF&^0& cP00D +&0 SC ™WF*šƒ0

%$General Terms

PD%& [ $)* K›Œ '(& )R0Kœyaj )*/F +&

Keywords

', -/.0/e% F&$bK % F&$   /F •KD+& 90  •K0&$C D’D+&^jD

1.

Jiawei Han

Department of Computer Science University of Illinois at Urbana-Champaign Urbana, Illinois 61801

INTRODUCTION

 -/.0/X%& F&$Q0  ž)*0$%" F Q% \/   BT+ $F#)*0$%#)*) .0$6!* / D[!/OgšT&/!T / [Ÿvƒ&)#C   0kYg ¡XYS ] .$0j&  ƒ\ f^/!ƒ¢vO £¤O¥] 0&Dy£ 0 $.000 +&#¥k£\ll£ C6¦…C6¦§ ¨§§ K ¢]$+jO&'¤l6DD+$ K&0#&#lm©Sš 0&.$D6!XPYS F•O

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. SIGKDD ’03 Washington, DC, USA Copyright 2003 ACM 1-58113-737-0/03/0008 ... 5.00.

ª

)* +Db0$D+ 0 S -/.$ f 0W   !i&'’ B .0 . F&D¤C   $ k+`D, %R$Fƒ  KbYZ0Fh%T^j!/0`«¬­ «KŒ«¬®¯j¬°¤±¬«K &0A­B²&¬¬&«\ YS F `HI&3:3:1:@58 G9L&EIFM$N 8 Kk$@3:> E 58 OS³V F&0D[!/K  Vk%&0 FDj0FW B .0 . K % F&$*& )*b 0u$)R ’&'0)* $DD0%)*$D+ k D+ $ y&)*&0% 0FOX_h* #YZ[ $  h   F&DgD%& [ $)* 9 Dj2'4

 0 ZF&DD$%0%* ^0D)´‡[¨¦K’¨&¨K•¨µ K’¨¶/Kj·–˜O $ -/.$/*%& F0A0  )*00%2   X¸)*)*& ^C D)rYZ$X&D va+ B V+R'( - .$/g[ )* g&0R - .$0f)*$C 0%O¹©g & 0XºS€~4» z/~4»y$ $0D`‡[¨–JK\'( -/.$/*°jC6$% D+&^jD¼%& F0)R!¹/F&5?$3k1436579853:8ƒI&?jo 85=>5?@F58ć[¨·–˜K] T^j¹ j ¹   &)*\ 0 T„9C .$D6!h‡[¨¿K¤¿$KŒ¨†KŒ¨È–JO]PQ'( -/.$/]0  \ÉR #@Hn&85oT['y 0  a B k0X$ j c .0j C˜  ¸&'gÉXYZ ¸ 0 &)*# .$0j&  ` 0#0F O   0*&.0/    &D[    *h%& F0h)*$C 0%Kb7 14?014?/L*@Hn&85 opE5 =>05?$3UL&EIMN 8 K)R!*Di #9 )* 0% $[  +&& cYgDD:O20& a$&)*$D+&Ke'4&  0R$F& #)*/ $ &^j &KU&)*$%T 0 t¨R)*DD+&"', -/.0/ %& F00 Ky&0D[!"^j.$ … K ¦&¦¦c ZD 9'( -/.0 y% F&$0 Oyl6'0'4.$  $ u&0&D[! + Ê: .0F* D+&  [Ÿ0 X& SD+.$ B  0% Ëu gj '4 )*#* $f g&'bD  %& F0$ V0 B &#&'•# $SYZ0D u&'¤'( -/.$/u% F&$0 K [uYZDD &F0W 0W )*k&.$ F&!XYZ[ ƒD  Z .0$&$!i&0X^j 

„*+0!/O`d]Yg KV.$/ +Du / D[!/Ke 0 # .$+&DZD      V$&g^j* .0F0•O   $+ u K$^0& *&i&.$ g&D[!$  K  D[! ^j.0 k'e 0W&)*0Da[m!RT% F&0$ O   0*%& DV&'S $ v0&j v k \$ D;h„*+ v)* $  '4 S)*00%kD+& *%& F0R  0 OU›e  .0 u B .+ VRD  [ )* V)*+$0%*‡[¨¿K$¿Kj¨†–•&* .$^0 -/.00Z)*00%R‡[¨È–¤  $)*0 B F ¸ 0v .0F`)*$+$%ƒ)R!¸D2 ƒ)*& #„#/ )* $ $  0&")*00%¸D+DZ0  $ 9^/!"$ D$+$%2 &)*X C 0$ B +  $0+-/.0 * h .00X 0\  A  F¹ &O d]YV  K &)*]D%&/S$ &j   g'Œ[ )*  V&R -/.00 $¸0*0&D+%& F&$0 O0 *a$&)*$D+&Ku&.$ # / D[!$ /C  Ä j 6!&^j.ƒ- .$D+0\'c$ ÌB ¹0F^ 2

- .$/ +&D’0  ƒ)*+$0%T‡[¨È–e\ FD[!ƒ^jc00DTƒ $ % F&$T)*00%v['ŒYgc90Z.0 k .$%k)*.$ g&'ea  Fv B & C %Rt)*$.$F &bO    .0 K•[k -/.0[  Wa$D+ 0%T[ͤ / 0  &F0 u v&)*)* 0 S 0Z j[ŸZ j   u+R% F&0 0  $ O   $ * #mYgX%$ F&DV&$$  $ k`„#/c%& F&$`0C   ¸)*$+$%$O   $vŸ$ BK $  / \^ !2‡[¨¦ KU¨&¨Ke¨¶–JK•a    $gºS€~4» z/~4» C˜^ c&0$+0 g%$ F &$C6&0CJ  BU&$$ &Fƒ‡[¨–  2%& F0A0  )*00%O   0\F&DAD%& [ $)* R$ B $C %&.0 ƒ $)* D  Sƒ.$ 0%*ͤ /Z^0.0D+$$%#^0D/F¡ —y   ¹‡[¨¦–JKy$%& ć[¨&¨–JKu&2$%&C6$ 4ÌB&+/  0 c¹‡¨¶–JO   $

00$ &FbKu $    "^/!¹‡[¨µKS·–JKS*20  C % YS Î0$+D& 0/!χ †–v^/!ž%& YZ0%A  0 ƒ', )Ð $%D % F&$"$[  D[!/OTl˜ $&$ c C˜„*+ 9$$ $CJŸ$ Bc  FbO £ .0F*W)* $ 9 + U6YgW& B D[!#j F $ —ZÊB¨ËÌB$+$%WmYV Ñ C˜$%&k'( -/.0 % F&0$ S *%$ F RÊ ÑcÒ ¨Ë6C˜$%&c%& F&$T$C +0  Kj&0`ʘ…ËSF0F¡ +$%9 0f'( -/.00!X&'e $ k&0$+0 

 F D[!/O   0 2mYV"j F +&0 \.$ .&DD[!ž 2 0tj '(& C )R0]^j& D0¡ Z&'Œ $kºS€~4» z/~4» C˜D+¡k&D% [ 0)* O l6ć[¨µ–˜KyYVX)*$ B F t  Óԕ€/Õ/KyT0YÖ% F&0`)*+C $%t&D%  $)×^0& 2h 0*0  C˜%& YS ;&$$ &FbKe&.$C j '4& )* 9Ø/Ôj}V‡[¨¨–˜Kb 0c j&  ¸^j Bk&D%  $)Ù¸ $9 C %&& !i&'’ 0]ºS€&~:» z ~4» C6^0& ¤K&0$+0 W%$ F &$C6&0CJ  BZ$C   •Oed]Yg  K[e Œ B D+D FD+D$%0% ] D&  „*/ D+& t%& F&$\)*00%RD+%&& [ 0)Ú^ \\Óԕ€/Õ9 0 Óԕ€/Õ ^$.0D+$ k*  !\ B k& F kt%& F0t  0 Okl6\ 0 ]0&j K YV9  /vwyx z{|}u~,/€/Tʘ³VD  ¸Ûf F&$ 0  t)*0$%/ËK $ Ÿ$ Bi&D% [ 0)Ã'4 X)*$+$%2D+& ', -/.0/*% F&0A  0 K R 0YÄ 0wex z{|}V~,/€/k g0%&0D[!R„*/Oyl˜g. j '4 )* Óԕ€/Õ*^/!¸i'4&  c&'S¿i ¸¨¦XYZ0t 0v'( -/.$/k%& F00 c  D+ %\Ê4'4 ca$&)*$D+&Kb% F&$0 ]YZ[ `)*   0&2· …i$% FËO   $

.$  &'Z 0*)* 0 ` v^& hh 0R D&0)*/v&'S $ $ Dy$ v'v5=> 14ÜIH+5?03Wn@ @>EFE 5?@F5ƒ&0Ä5I&EH Ý\365E7 14?jIq 3:1:n&?; c0D"wex z{|}V~,/€/R$ .$09 $#  Fh 0&# .$^0 BF$C  +D+D[!YZ[ A )R&DDZ&0$[ 0&D BO_hƒ&D hDD+.$ B F \ &)* &  WYZ$   D[!\  )* +&t)R!X':+Dy\)*  ] &)* 0C   0 O¸©u!"  $%t&hD+)* 0%T 0 X  KyYgi%.0 C / * 0*&)*0D $  9h &.00  c' $*D ;% F&0 0  $ $   X^ !ƒwex z{|}V~,/€//O   $ )R00%R&'U 0vj k W % &$Þ¸& ]'(DDYZ O9£ C  &`…#/  $.$ Z 0c$W&'UD& T'( -/.0 f%& F0\0C   )*0$%2h 0X0F $ # 2^ji.0 ; $ &.0%&0.9 $ 0&j O2PÖ  F"', F&)*YV& ¡2+ D+D.$ B F ;£ &"·Otlm £  ž¿K $t)* 0  i'(& ƒ  B +$%;-/.0&&D/ƒ/.$  $K  D[!*  )* +&bK uYgD+D• u':D+. k$  i f$    •O £  #¶Z'(& )9.$D+  Œ $g&D%&& [ 0)0ߘL&EBIM$N 1(8n7*n&E˜M$N 148 7Ï148gI&?R14?û5@3:14Ü&5•p> ?j@3:1Jn?#üT— àRÊ4s$ËeýÃà#Ê4s ã ËGb8 >$@FN 3(NI&39þmÿ j ¯ à*Ê4s$ËGUâmÊ:¯¤ Ë  â ã ʘü’Ê:¯¤ËËGI&?o; þ  ŒÊ: ¯   Ë á*Ê4s$ËG

ʘü’Ê:¯¤Ë Fü’Ê Ë˃áRÊ4s ã ËSI&?joZâmÊ:¯  Ëhâ ã ʘü’Ê:¯¤Ë Fü’Ê ËËGŒN05E 5yâyI&?jo â ã I&E5c3(N05vHI ßF5Hp> ?@3:1Jn&?2nBpgshI?joks ã E 58JM$5@3:14Ü&5H Ý l6'us\ c¸8 >$ߘL&EIM$Nh&'us ã K• 0¸s ã  c¸8 >M$5EJL&EBIM$Nh&'gsjKb$C 0 ^/!; s  s ã Ê4M0EnM$5E\8 >M$5EJL&EBIM$N K['W s Æs ã,ËO¼Û] A D+&^jD%& F&$¹0F& K  "!$# %!&" (')' '( %! +½ * Kf«¯ ,,.-²­Ê4s$Ë Ê:& ƒü0²&¬®&¯j¬°¤±)/¤Ê4s$ËË90  * 0Tj /F&%&;Ê:& i .0)9^j Ë &' %& F0$ SÊ:+0  R˒vYZ$+F sW+ yf .0^0% F&$bO   $g y2' 1436Ž 57’Ž‘•Š “.3+‰ 8:9;8Œ‰$ŠŠMjO   0

RA ' @BDCFŽ EG1436Ž 57bŽ$‘¤Š`+“ 3F‰ 829H8Œ‰$ŠŠVKg RŸ$ & k'(DDYZ JK I>KLs M N s O=?>QP ° RTSVs ã =?>¹«¯(± U\V­ U+P/­ZW s  s ã P X° R«¯ ,,.-²­Ê4s$Y Ë  «¯ ,,.-²­Ê4s ã Ë * OÄ£0Z  I>[\=?>VO   0]$ ^$D)Â& ' @B]Cj6Ž E\1436Ž 57’Ž‘•Š “ 3+‰ 8:92N . ” ^4:‘ ^4‘’“* • Ÿ0] 0U&)*0D U Œ_' I>Xc 0y%& F0 0F&    YZ[ \9%&+`791(? 8F>MjO £$t)* BX&'v    B 0%"%& F0¹  0 X ¸&00  %& F0$ KYgkŸ0 Bf B . !ƒ)*$+$%#D+&^jD\&0$ ƒ.$   %& F0$ vYZ[ 0&.$9)9.0D[ 0D*% O¸œea  0 &0 v&'. 9)* $  '4 V)*$+$%W& $ U¡ +0$ y&'¤% F&$# B .0 .  U .0F*& y.0$D+&^jD %& F0$ Kb% F&$0 ]YZ[ t D['(C˜D/$ \)9.$D[ +$D % Kb   %& F0$ K$ $0 #%& F00 K# c•K YZDDj^ja0)*0#  0W$ .0  &\  •O `ba¤ò•÷ZF ó c&å ¨& O du1+L&> E 5iÿX1489Iƒ8I7]MjH+5#HI ßF5H+5oiL&EIM$Nho I3˜I&853:G ƒe G ŒN05E5X3(N E 5 5ƒHI ßF5H+5oTL&EBIM$N 8XI&E5 ME 585?0365fo hú7*n&?/L¸3(N0585 L&EIFM$N 8 G’5 I@FNvÜ&5E36V5 gcI&?joW5 oL/5ZIE 5gI&8 8 1+L&?¤5okI]HIß5hH JiŒ53¤7 14? 8 >M ßF5y+… jbN05SIH M$N$I ßF53:1J@Zn&EBo/5Eg148U3˜lI k 5?RI8u3(N05Zo/54pI>$H 3¤H+V5 g&1:@Fn L&EBIM$Nq 1J@ IHbn&Eo 5E  z a x c d b a b

z a x b

z

z a x e a b

b c

x b x b

y

(g 1 )

(“ Ž

mn^ _7 3 po.q?r

a

z b c y

x a x c d b a x b x b

(g 2 )

(g 3 )

•‰”N82B(ŽNtu3‰F829¹ˆX‰$ЉŽ ŠA s

PÎ%& F0Tsi¸^jca  0$X^ !ƒ$$0%R*$Y$% ¬ Ovb  0 0YÏ% F&$`0 ¸^/!\sw<x]¬ O9œu%*¬#)R!\ c)R!T0& /  $.0Sf$Y"   ak sjO’l˜'j¬S/  $.0 yf$Y"   a¤KYg $0& y 0U0Yh%& F0c^/!]<s w xly ¬ K& $ YZ K&<s w x z ¬ OePD+%&& [ 0) ¨\DD.0 B F  ƒ¸& X'( -/.0 R% F&$Ä)*00%2&D% [ 0)TOžl6 Ÿ0$ yD+D  0u'( -/.0 Œ%& F&$0 KD 9 U0C˜D ¤O$& y $   ¼% F&$žsjKf[\j '(& )* X $2a 0 ž . +D[! .0/ D DD  0e'( -/.$/’% F&0$ bYZ[ ks)9^j$$] u$   ¤O vb$k¿* 0YZ  $]  )* T& &b—U_¹0i 0k .$0j&  &'u#% F&0ƒ+ fD   0&h7 14? 8 >MjK0[] .00$   !ƒ *a  0 [f&/!i)*& O { » ||}u~, €/R v )*0DKŒ^$.$c$&c„*+ O   0*¡!¸+  .$*  0i0„#0!h&'a  0%\s2 \? s w<xc¬ —   0i &)*R%& F0 Ä^jTa  0$"¹$[ͤ /#Yg!$ OQ0 i&°¤C˜%\% F&0•K [i)R!"0 ƒ°Q$[ͤ /*Yg! # h^jX'4& )*'( &) Ê:[ ° }¨Ë6C %t%& F00 R['kYg¸;0&i&0 +$ ƒ )* 0$+ )TO¼_hƒ&DD h%& F0¹ i+ ƒ$   ¹&% Qžo&>MjH 1:@FI365TL&EIMN ~ O vb0 ¨X+PfD%&& [ 0) ¨X% 9 +'k$.$0D X%& F00 O   $ƒ .0)#C ^j f&'V$.$0D c%& F0$ ])R!ƒ^jc .0%&Ol6Z F&  ] )*c    $ &^0D)* O`Œ[ BKu $X%&0 F &; .$0j&  &)*0.$F  &'S$.0$D+ *%& F0$ cYg& B # )*Oi£ &•K’[  c0&/ + +&De   DDyYZ0 $ vƒ%& F0h vƒ.0$D+ OXÛ]$ F&DD[!/KŒYg*0   

x a y

rB(. “ C+3"^, Š 9e€ ” o { » ||}u~, €//Ê4sjFK ƒKb7914? 8 >Mj_K >yË l60$.$—yP% F&$XsjK09%& F0T$F eƒK0&0¸7 14? 8F>MjO ‚]. 0.—   0W', -/.0/Z%& F0T e  >VO

&¨ —^D1vsRa$ B ZZ>;Š 9’Ž‘[3Ž Š 7 3‘‚ …/—UŽFB(Ži$  Zs* u>b‚ · —U &Z  Â&0K$Ÿ0i !i$%&c¬c .$X  sR&ƒ^jka  R   s w x ¬cX[ S'( -/.0  ‚ ¿ƒ— 14C.3RŽ .‰ @„92', -/.0/S s w<xS$ ¬ EC ¶/— ³g&DD {  » ||}u~(/€/ Ê4ns w x ¬ +K ƒKb7914? 8 >Mj.K >UË ‚ µ ƒ— 3Ž Š 73&ƒ‘ ‚ )*0. *[ 0&0&DSD+^jDghF0F¡¸YZ$ 0 9[vYS& 9$ BC  \^j'4 O   0[ F•K¤ $.0D+TYgva  0Xsƒ['UYgcŸ0Xsƒ ] .0$D+ l …l˜'u $ va+ B ]kD Bk$ % F&$t 0]&¸%& Y &0D[!`', )  0 v$.$0D R%& F0•KeYgR B D+DV0` \a 2[O P vYVR&; &Ke 0 #  R+/  D `$ &^0D)* vͤ  $ „*0!2'V $#&D%&& [ 0)TO   0!t .$%%& Bk Ws\ 0&.0D+t^j a $Ä& X$    D[!¹ Xj&  +^$D`¹& F X h $.0  $ %&0 F ¸&'V$.$0D  %& F&$0 O   X   B'(!\ 0  -/.0[ C )* K$Yg $DjTÓԕ€/Ճ‡[¨µ–eYZ0  &t„#/]0&0&D D+^jD+$%T B! B )´¸iDa% F&$0*& F 0%ƒ¸%& F00 c  ^$.0D[OvÓ Ô•€/Õ#0& ] $ '(DDYZ$%T &D/c$ &j   —#ÊB¨Ëf[W C .0 R $\%$ F &¼'v$.$0D \% F&0$( ‚#ʘ…&ËR[X$/ i0 $R #  Fƒ  .0 +  i', -/.0/Z% F&0$ ST& F

 #$ $.0$D+ ( ‚0&02ÊJ· ËV[0  Sa  0$ Z !X.00D  % F&$`^0.k B DDu%&. F/  k 0 )*$D+ 0  ORwyx z&{|}u~, €/R ^$.0D[]&\Ó Ô¤€ Õ &0X'4 )9.$D,  Z 0c D[!X  )* &T0$[C  &0 f R)R¡ kÓ Ô¤€ N Õ †6  . + ‡R ] D!\& ]j&  ^0D9\D  % F&$)*0$%$O"lm; $X'4&DD+YZ0%2mYg¸  &0 KgYVX'4/.0 * 6Yg")RÌB& X F00+-/.0 i.$ ÄQwyx z&{|}u~, €//—AÊB¨ËR %& C˜)*& B a 0 2&0¸™ky£hÊJ$ C˜Ÿ$ B]  FjËfDa% F&$0*& F

'(& U'( -/.$/e%& F0#%&0 F  ‚/&iʘ…ˌ-/.0&&D/e/.$  $ ƒ D[!X  )*+0 i'4 ]$$C˜D& X% F&0ƒ$ .0$0%$O 3.

ORDERING   $LEXICOGRAPHIC

X  +&Ä/  $.0 R   FDf F0$,-/.$ R$Dj 

$  /V&0#a  9% F&$0 U„*/ D[!/Oel6u0D.0$ U)R&$00% %& F0c ]Z™ky£k $fÊJf -/.00ËK^$.0D+$0%fDa&%& F&$0  F$ $%\&)*&0%X $ *  Ke2)*$+$%ƒ™ky£t $ v^0&  &ƒ 0 ZDa% F&0$v F$ O

3.1 DFS Subscripting

_Ä0j '4 )*+$%hh$ CJŸ0 B*  ‡ ¶–]A`%& F0bKS &   j&$$%X™ky£X  t^j &0 B .$ •O]Œ%. *…ÊJË R'( -/.$/k .0^$%& F&$\'4& c $ )*0D*0F&   Ù+2Œ%. ƒ¨O Œ%&.$  …ÊJË6CÊJ0Ëg k 0k )*W%& F0•O   $c0 ¡0i$%& + Œ%&.$ *… Ê:^jË6CFÊJËg&0 B .$]  v$[ͤ /f™ky£X  '4& ] 0 % F&$bOe_¹$X^$.0D+$0%  ™Wy£# K$ $]$ CJŸ0 BS   ! ' 0u    b'4& )* yD+$ y F$ O’_hV.$ u $V)R&%&0[ .V'

.$^0   b SDD+.$ B F y 0 ’ F$ ’&& F+$%S Z $[ Œ   !  )**‡ ¶–JbO ˆb‰pŠ#)*0n "‹u ]   ƒ^j'4& ?  )Œ OU_hc0  !ž .0^$  $ 9YZ[ Rk™ky£v n  ^ A ! !eŽU2O  V)*#$  d 8 >$ß8@E1 M3:14? Lƒƒ' ! O Û] ‘  !eŽuK0YVk&DD’ $WŸ0 B0 W F  ƒ‘  !eŽU.K "’&K0 $ EBnn&3:K¤X $WD+& Bf0 $W F  •FK ½ K$ $#E1LN 3Jq˜7#n&8 3gÜ&5EF36V5 g&O   $\ B F&%/R0 ', )“ "’ƒ W  *)*; 0`EF1+LN 3JqJ7*n&8 3 MI3(N OÄl6Œ%&.$ t… Ê:^jË6CFÊJËKU $ ƒ½ $[ͤ /9 .0^0  + 0% R  %&0 F ¤O   $X %/C˜)* B9  \Ê ”’”  6# V "•Ë Œ+%&.$ T… Ê:^Ëg&0`Ê:ËK$&0`Ê ’  # V & V • ËV\Œ%.$ v… ÊJËO

a

b Z

b Y

v2

X

a

base graph (a)

Y

X

v3

v2

b

v1 b a

Y

(b)

(“ Ž

Y

a

v1 b

Z

v0

X

a

b

X

a

v0

X

X

Z

v3

(c)



b X

a X

v0 v1 v2

b

a Z

(d )

" 7’‹e @”3„^D8’Š ^4‘’“

mn^ _7 3 N–q —m˜s

Û]   !eŽuK/ $Upn&%E VIEoR5oL/5 ÊB3:E5F5c5oL/5f‡ ¶–4Ëy g/F&0 g&DD  0S$% U# $g™ky£v &K/$0& 9^/!9á Ž y K &0  0cß I @%k„uI&EBo 5oL/5*Ê ßFI%@ kX5oL/5W‡ ¶–(Ëg /F&$ Z&DD• $W% SYZ0FT k0& ; 0i™ky£2 Ku$0& "^/!há Ž z Oh0 #a$)*0DKy 0i0 ¡/C $h$%& 9"Œ%. T… Ê:^jË6CFÊJËk R'(& Yg F"$%& YZ$+DR 0 .000 ¡ 0#0 S ^¡/YS Fi$% OU$ )r0YÄ&bK¤Ê "‹ V )ŒË Ê: )*0D[!cYS [ R& ZÊ ˆV 4Š/Ëˌ+ U Yg9& u&# F$  &[ U ] C

 /]&T$%&OSl6'SÊ "‹V V (Œ&nË tá*™Ê !kËS&0š  ˆb‰pŠ$Kj[f f9'4 YS F %”‚y 0 YZ KUƒ^0&F¡/YS F2$%&O   0vpn&E%uI&Eo25oL/5XnBp ‹ )*0 Œ 0 ga B u'4& Yg F9$%kÊ ˆV ™Š/Ëe$  ˆƒ‰WŠ$O   0cß I %@ k&q uI&Eov5oL/5nB: p ‹ )*&0 b 0 Ua B y^0&F¡ Yg Fc$%&]Ê ˆV ™Š/ˌ ˆ˜›œŠ$O9l6`Œ%&.$ R… Ê:^jËKuÊB” ¨ ·Ë]+ f 0 '(& Yg F`%#' MjH+5GZÊ ˆV ™Š” F⠋ â § ‹¨ Œ)© ⠌ Ëb I?j$ o )ŒXE 58JM$5@3:14Ü&5H ݃I&?jo â § ‹¨ Œ© 1(8]3(N05 HIß5H’nBpW3(N05#5oL/59ßF53 V5 5? 3(N$5u 7 d’nEvV5 g I&7]MH+5GuÊ ’ V # Ë]14 ? du1+L&> E e 5 þ6ß 1(8]E 56M0E 585?0365oƒßÝ ÊJ 7R5Ag59N$I&Ü&5iI‘/qm5oL/5#L&EBIM$NWeN/1J@FN2NI&8 IÏd\@Fno 5cÊÊJ$ß8@E1 M3:14? L\nB p · * ÃëfI&85o\n&? dQH+V5 g&1J@ n L&EIFM$N 1J@"n&EBo/5E$ G ÀšˆJ°y™Ê ®k™Ê !kË˸148¸@ IH4H+5[ o ìљí:љî‘ïî ËuÌnÍêðÓfÚ_ÏtnBT p ·ƒž(pW)± -„R ¬ ™Ê !$ ¡ ’  Ë GÀšˆJ°y™Ê ®k™Ê !kËË G V5X@ IH(XH  ’ 3(N059ß I&85k8F>$ß8@EF1 M3:14?/LTnBp!A ³V $ «6’u+   &^$D+f¨S y $g)*0)9.$)Q™Wy£v g&'j $V%& F0 *Œ%. ]… ÊJ ËOe_`S.0 n ÀšˆJ°yÊ ¹y˒ c$$& g $S)*+$)9.0)Q™ky£  X'f $X% F&0;   / h^/!h $š  ¹uO;šƒ0) .0) ™ky£  k&T^jk0 + T &0&0D’D+&^jD:O £\'4 KVYVTŸ$h™ky£h $&KV)*0) .0) ™ky£h $&Kg ^ \ .0^$  $ 0%O$& R  !% F&$bKSYg\&0D[!0$.$* 0

%/C˜)* Bta  $ Î&0ß8@EF1 M3:14?/L`nBà p ! OT³g&` $+ ca  $ h)* $  %.0 F  # 0#&)*0D $  k&'S $#)*00%R  .$D …   $R&C

BYg ]u

†Ý 5)8 ‡Ou_`]Ÿ0 B0] 0]'(DDYZ+$%*  .0D[O ñfô•åê•ñjå$÷ ë ì µfê•÷ZF ó c&åéjåè¤å$ööø˜ ù ò5E4pn&E7 14? L\E1LN 3Jq˜7#n&8 3 V5 g&365?08 1Jn?*14? { » ||}u~,/€/fL&>0IEI&?$365F58S3(N$5Z@ n&7fMjH+5365?¤58 8Znmpu7914?0q 14?/L*E58F>H 34 _¹$9j '(& )*0%f 0g %/C˜)* Bya  $ # { » ||}u~,/€/ K [i+ ij  ^$D+t   ¹ ó 7 d\@ no/5814? {  » ||}V~,/€/vL&>$I&EI?0365 58W3(N05k@ n&7#q MH+5365?¤58 8 nBpW3(N05c7 14?014?/L*E58 >$H 43  _`R&F0 2 0 *6Yg\)RÌB& c  .$D[ ;Ó Ô¤€ ÕO   0RC FD+" /&']&0h+)*$D)*/F h X&&D+&^$Dƒ¹‡[¨µ–JO`PfD[C %&& [ 0)¾…R. D+$ k 09', F&)*YV& ¡jO   0#$[ͤ $#^j6Yg Óԕ€/ÕR&0 {  » ||}V~,/€/* W 0v +%&/C6)*& Bka  $ +&`\  C )*0 0%Wa 0 #&#0&$C˜)*0)9.$)Q™Wy£v  ZÊJPfD%  $) …ƒD0 X¨Cm…&ËOT_h# $D+&R 0*a B $kÌB.%)* v"PfD%&&C

[ $)Ù? ¨ vb0#¨Cm…vYZ[ ƒ 0W$-/. &tA « œ ô À—ˆ˜°yʘ«ËOUPf .&DD[!/K « ê Q ô ÀšˆJ°yʘ«Ëc #)* i„*/9 ¸&D.$D+ [ O vb0ƒ¶\ - .$[  a$0&.$ B +] .0)* F R&'e«]š  ƒO   $+ Sa$0&.$ B +] .0)* C  TYZDD’^jW. +DÞX^ !Twyx z{|}u~,/€//O Œ%&.$ f·c $YZ u 0Z  R 0&&'•Ó Ô¤€ ÕK/YZ0 ZRD0¡

$  / cRj  ^0D# %/C˜)* B]a  0 &bO   09 %& C˜)*& B a 0 `F¡  k$D,#YZ02Yg*a Ê Ñ }¹¨Ë6C˜%#% F&$0  * $ Ñ C˜$%&c0 OZl6'yYgkŸ0XmYVR™ky£X  k«v&t«㒠$C

 /i $T &)*\% F&$Ä&0¹O « ‰Ù« ã KZ^/Q ! vb)*)R;¨KSYV\& )*0D D!T B t  F0$%ƒ !\$ 0/]'S«ãJOWÓ Ô¤€ Õ9& %&0 F W% F&0$ S B  D[!Xi™ky£*D+a$&%& F00W F$ —y% F&$0 YZ[ T )RDD+ f)*$+) .0)r™ky£i  SYZD+Db^jc$   XŸ0 BO

0-edge 1-edge 2-edge

...

s

s'

...

n-edge

(“ Ž

Pruned

•Ž ‰+3„@„9Ks8Œ‰+@Ž

mn^ .7 3 WõXq$s

(“ ,Š e” ƒÓ Ô¤€ Õ/ʘ«KFƒK’7 14? 8 >MjK_>yË l60$.$—yP™Wy£i v« K$9% F&$\0F& ƒKjt7914? 8 >MO ‚]. 0.—   0W', -/.0/Z%& F0T e>VO rB .C+3"^ 9 ö–

¨&— ^D1#Y « œ ô ÀšˆJ°yʘ«ËK0Š 9bŽ$‘ /… — 3Ž Š 7 3‘‚ · —U+$  ]«W+/ u>b‚ ¿—U ˜  IÎ A  ÷$‚ ¶/—U &Z  Â&0K$Ÿ0i !i$%&c¬c .$X  «c&T^j9EF1+LN 3JqJ7*n8F3Za $R 9', -/.0/f«2wyË ‚ § ƒ— 3Ž Š 73&ƒ‘ ‚ PD[ 0.$%kÓԕ€/Õu&c&F0U)*j [  yj '4 )R&$y)#C 0 RYZ[ T& $ &D% [ 0)* K$Z&0$&Z$Dƒ)9.$*YZ$X $ % F&$\ +Þ  D, %O   $va$j&0/ +&Db%& YS \T $c.$)9^j

']', -/.0/# .$^0% F&0$ 9)R¡   $ƒ)*0$%¸)*j&  +^$DO³V C F0D[!/Ky[9 9$„*/v TŸ¸ 0R)*$D #'( -/.$/9% F&0

#Ÿ$ BKg; 0;Ÿ0D  *[# 2&^$F+" 0XD "$ O"_h 0# vŸ0R&R„*+ g)* 0 # v)*+$S 0]D+& *'( -/.0  %& F0$ f[  D[!/O 4. EQUIVALENT OCCURRENCE

lmƒwyx z{|}u~,/€//KYVfYg&/g cŸ* F&X[ +&i 0S['b[  V  + BŸ0•K/ $#'4 S )*f«Z+iŒ%. ]· K&DDj&'•[ g 00 

.0j %& F&$0 gYZDDb$&S^jfD ¤KR0i$&g  ^j]F0F¡ ¤O 0 .$2& &KŒYg*h&)*0D D[!¸$ .$09 $#  Fh^ F&0F &'u«O   0 Z 9 !/K$TPD+%&& [ 0)ƅ D0#¨&K0^j , Z 0W +%C DŒ0$[ \'g— «  ô ÀšˆJ°yʘ«ËK0Ygv$ &^^0D[!Tt$T&$& 0

&$[ t WD W $v .$   '(.0$ \  .$ ¸T

†m D[F! ‡ & Xj  ^0DO l6A 0 i  •KfYV`+ .0  X"j&  ^0D2[C  ¸ ]Yg#`. +DÞ#;wyx z{B|}u~(/€//0 O v’  kYg9YZDDu $Y  * 0X„*/R)*0D)*/F +&"&'W $+ 90$[ AD+ %D[!

D #&;Ó Ô•€/Õ ø 90  C˜%& YS ;)* $DV&0h va.0 B    .0)* F X)* 0 ¤O vbZ  ùVÊ4_s Bs ã Ë# $  /ƒ 0t .0) ^j R&'vj&  +^$D` .0^$%& F0  )* 00 )* Œ'$sW+ks ã K:O OK 0V .$)9^j b&'$[ͤ /ŒÌB   '4.$0 &0 Za B +$%#T™WŸ00[ ¸¨O ävåæ/ç(è¤ç,éjç,êb[ è ú ì Æ?Å.Åî¤ñjñjåè Å0åøY ù ·g14Ü&5?Rs2I&?j? o Gû„!$# ! & ('(')'( %! * G ( 3 0 N h 5  n @  @ >  E  E  5 j ? F @ ; 5 B n i p ¼ s 4 1 ? \  4 1 T 8 ( 3 0 N 2 5 8 > 7 nBp¸3(N$5 ?0> 7#ß5Evnmp]½ 8F* >$ߘL&EIFM$N\148n&7#n&E˜M$N 148 798WnBpVst14?¸5Ü&5EFÝ L&EIMNtnBpnƒG ™1 4

5 ü ½‹Dý:# ùVÊ4_s ! ‹ ËGuo/5?n&365oTß Ý þZÊ4_s VR Ë  `ba¤ò•÷ZF ó c&åζ/ O d’n&E\3(N05iL&EIFM$Nhsž14 ? du1+L&> E T 5 þ6)I ;I&?o\6s #t14? du1+L&> E 5Sÿ þB%ÿ G+ùVÊ4_ s Bs # JË ž+… uúW8y3˜nus & 14e ? du1+L&> E 5Sÿ ™þ (G+ùVÊ4_s Bs & JË  ¨ bd’n&Ek3(N05v8I&7fMjH+5 oI&3˜I&853g14š < ? du1+L&> E 5 ÿFG þÊ4_s VRƒË ¹+·  £.$0j& Ws Xã ¹ns w x ¬ K¤üT f# .0^0% F&$T )*& $0 )Â&'esi ! K Rü ã  gk .0^$%& F0* )* 00 )Ï&'¤s ã   ! Oyl˜' â E " 5 !bþmÿ Gg3(N05#n@ @> Eq E 5?@F5WnBpys # 1(?i3(N$5f8I7]MjH+5o I&3˜I&853y148 þZÊ4s # VRË ž… Ò ¨ Ò $ ¦ ¹.·  d’n&E23(N05tL&EIMNA s &14K ? du1+L&> E # 5 !b þ  Gƒ1(3:8;V5 g&365?o/5oQn@ @> EE5?j@F5 b+( E +43 •s # 1( 8 fÊ4s # ms & VR˜ Ë օ Ò ¨ Ò  ¦ Ï·nG ŒN 1J@FN¸148#5=>$IHU3˜n

ZÊ4s6# RË ÃjbN$I3e7R5I&?08%$'& $`IH uI&Ý8I @ @Fn7]MI&?$1˜58us6#kßF53V5 5? 3(N$5XÜ&5E3:1J@F58XHI ßF5H+5o;y143(N'()$+* ÇjbN/>8 Gv5Ü&5?Qy143(N$n&> 3c@ n&7fM> 3Jq 1(? L 3(N05]8 >M Mn&EF3gnBpZ3(N05ZL&EIMNi14u ? du1+L&> E,5 !b.þ -(G2g5W@ I&?\@Fn?j@H >$o/5 3(NI&3g143:8f8F>M MnE3g7 > 8F3VßF595=>$IH¤3˜n*3(N$5c8 >M Mn&EF3ZnB p du1+L&> E /5 !b0þ !”" jbN/>8v143S148c?n&3W@Hn85f o 9úžpF>EF3(N05E#@Fn?j@H > 8 1Jn&?;148c3(N$I&n3 V59?¤5 5o ?n&3UL&EB"n tpEBn&G 7 du1+L&> E 1 5 !bþmÿ GSß> 3jpEBn&G 7 du1+L&> E 1 5 !b þ  " þ

z a x

z a x b y

z a x

b

b x

(1)

a x

z a x b y b

b x (3)

(2)

a x (4)

(“ Ž32q˜57:^‰.B(Ž‘¤Š4 Y@@7 3l3Ž‘:@Ž

mn^ .7 3

4.1 Failure of Early Termination

¢f$'(&  .00 D[!/K œU D[!    )*+0 X$/ g0g0&D+*'(& Z !

.$j %& F0#'jsjO   $  S   F&D0&  yYZ0 ZœU D[!    )*[C 0 ƒ&$0&Z^jW&0$D+•Ou‚]0]&'’ $)  ZD+D.$ B F i^jDYkO _`Z$D9 F0$+- .$ e k$F¡c $ Z&  u*& F y k)R&¡  œU D[!    )* ƒYV& ¡i&   D!/O µò•öå ¨&e O 0>M Mn85*Iio I&3˜I&853f@ n&?08 148 3:8 nBpc3 Vn9L&EIMN 8c8N"n y? 1(œ ? du1L&>E5 ¦ þmÿ "I&?o ¦ þ  "65T‘ 5 uI&?$3#3˜T n ÛU?oA@Hn&85ohL&EBIM$N 8 ŒN$n85`7 14?0147 > 7 8 >M Mn&EF3R148X+…  i’53vsÎßF 5 $ & /ÏI&?jo2s ã ßF5 $ & / z $Jú]e8 V59@ I&?t85F5 G / z $AIH uI&Ý8cn@ @> E?8 y143(7N $ & /  UI—? V5365EF7914?I&365kV5 g&365?jo14? LfsX8F1(?j@F 5 þZÊ4_s RJË  fÊ4_s Bs ã RË14? 3(N/148#@ I&885 95\5#@ I&?$?jn&43 ;:g3(N05%E y1485G g$ 5 y1:H(H’79148 8c3(N05]MI&3:365EF? 8BN$„n U?;z1(‘ ? du1+L&> E 5 ¦ .þ -("‘jbN 148WL&Ez IM$N`@ I&?$?jn&3]ßF5RV5 g&365?jo/5ovpEn&7 $'& / $JÞ(?p g5#Io ot5oL/e5 / $14?03˜un du1L&>E5 ¦ .þ -(GZ3(N05 ?¤5  L&EBIM$š N y1:H4H?jn3gßF5ypE 5=>05?03gI&?0Ý#7#n&E 5 ÃjbN$I&3V7*5I&?0 8 g5k@ I&?$?jn&3 n?H Ý V5 g&365?joZs ãb14?*3(N/148Z@ z I&8 5  E 5ZnB%p =ZI&EH Ý jj5E7 14?jI&3:1:n&?t14?*s ã  G / $;148]3(N$5VpI&1:H > E5SMn&1(?043  x a y b x c

d z (1)

x a y b x c

x a y c

z d x (2)

z d x (3)

(“ Ž?>q?m’‰+^ÜBÜ7 3Ž‘C.1"f‰F3"B0 ¯ Ž05GU3(N05?t143V1(8]> ?0?j5 @F58 8I&EF݃3˜nXV5 g&365?jovshV5 g @F56M3Œs ¡ã  De3lCXC.1AEJÊJ F'(Ë]l6 ' þZ Ê U RË  ] Ê U %U?w xly ¬ VRË&n þZ Ê U %RnË  f Ê U U2w x z ¬ VRËK  $9YVS&*&0D.0$g U0S'j 0g'(DDYSC $%i) .0 B^jk .0—]ÊB¨Ë !óNƒKj[' U;! K 0‘  Uw xly 0 ¬ !$‚ # £0à  Ut/F+$ fsjK0^0.$f0fs ãJK¤¬9  0c$%&vYZ$\t^j &0`/ ƒs¸+[  U; ƒ$ B .0cs ã p  U•O   0 '4 ƒK U0w xly ¬ T  Uew x z ¬WYZ+DDb/F&ƒs ã O mn^ _7 3

x a y b x c z (g 1 )

x a y b x x a y b x d + c c d x z z (g 2 ) (g 3 )

(“ Ž?FqcˆiŽ ŠŽ6@ŠYm’‰+^ÜBÜ7 3Ž‘C.1"f‰F3"B0

mn^ _7 3

x a y b x c z (g 4 )

breakable

Ž &” 4‘’‰$Š ^DCj‘

¯ VO

¨—y )* ]+'( -/.$/Z    &0X% (‚ … —b> ’1Q Q ’  $c&'Œ', -/.0/Z% F&0$ SYZ ƒ +$%Dc   aX‚ ·—b> > ‚ ¿$ƒ— 1™C.3RŽ ‰.@„9` $v«e‘> ’ E C ¶ — wyx z{B|}u~(/€/ ʘ«SK R#T˜ÉÉSK_ƒK•7914? 8 >MjK_>yË‚ PfD%&& [ 0) ·v+DD.0 B F  Z 0]', F&)*YV& ¡RYZ0X0D. S 0 0   !R $ /  0%9 B bOyl6u )*  u+'( -/.$/g    &0% O   $A[i&DD Twyx z{B|}u~(/€/\ .  D[!A^/!0% $$ $CJŸ$ BZ  Ft&0i %/C˜)* Ba  $ +&bO   0c  \ C $ e&'0D v%& F&$0 e e&0  B /ŒYZ[   $V™ky£WDa% F&0$ & F O rB(. “ C.3„^( Š 9ŒU ” 22wyx z{B|}u~(/€/ ʘ«”K ,b+K ƒKb7914? 8 >Mj.K >UË lm$0.—yPQ™ky£R $v«K$[ 0 /J ,’K 9%& F0\$F& ˜  ƒK0&02791(? 8F>MjO ‚].$ $.$—   $kD i'( -/.0 Z% F&$T ˜  >VO ¨— ^D19Y « K ô À—ˆJ°Uʘ«ËK

Š 9’Ž‘ … — 3ŽŠ(7 3‘‚ ·—^D10â$¬ã Bs ã.¹sWVbwfx¬ãb&0Xs ã‰"sYX]&0YþZÊ4sKV6 RËJ ]Ê4sWV6 Bs 㙠VRË is V + Z$& '4&D.$ c& c'e D[!i  )* +&T Š 9’Ž‘ ¿$— 3Ž( Š 7 3‘ ‚ ¶ —U ˜  I A  ÷$‚ µ—U Z  Â$KŸi  !i%c¬k .0FX 0 «k&T^jka  0$* 9', -/.0/fJ« wfxSf¬ ‚ 0  ]J« w x ¬k/ u  I$‚ È —u  !ij&  +^$Dc'4&D.$ c&'y D[!X  )*+0 Xt«”‚ †— ^D10S0:« w x ? ¬ ZI K«¯ ,,.-²­ʘ«2Ë ¼«¯ ,”,.-&²­ʘ « w x ¬ËV Š 9’Ž‘ §— 0  ]«k+/ Y>‚ ¨¦ —y )* cJ« w x ¬k', ) IYZ0Fƒ00^j E1+LN/3Jq˜7#n&8 3Za  R', )Æ«”‚ ¨¨&—U & e  I+ƒ™ky£iDa% F&$0c& F$

‚ ¨…/ƒ— 14C.3iŽ .‰ @„9;:« w  ¬kZ  I£E C ¨· — ³g&DDUwex z{|}V~,/€/ ʘ2« wfU¬ K«.K ƒK•7914? 8 >M.K >UË ‚ ¨¿ƒ— 3Ž Š 73&ƒ‘ ‚ PfD%&& [ 0) ¿ . D+$ S 0]$ .9 W&'Uwyx z{B|}u~(/€//O   0 '( F)*Yg ¡;&'kwyx z&{|}u~, €/\ # )*D+ # ¸Ó Ô¤€ ÕO;d]Yg  KU[ j '(& )* uW)RÌm& u+)*  )*/e.$ +$%W 0S  * 0&Z .0$C 0%9 $0+-/.0 S D&jƒ^jO   f K$^j'4 k0$.$ 0%  0W %& C˜)*& BZa  0 \&\*$   ƒ%& F0•K•wyx z&{|}u~, €/ Ÿ0 B F0F¡ vYZ$ 0  0 Ra B #œU D[!    )* &;+"PD[C % [ 0)Ù¿iD+$*·C˜¿K•YZ$¸ ci& +&$9'V $9&$[ tYg

P &)*$ $0  Uj '4 )R&$g B . !WYS e0$.$ c+v.

" a$j +)*  f2^j& t &DU&0¸ B!/ 0 + 0F&  O   0 &D $F] UYVg  B v+ U#Pfl6™c£c&/ [ FD0  9F0)*D$&)#C j&.00$F&  • OA$& * 0XD+  KgYVƒ.$ \2 B!/ 0 ƒ0F %&0 F & f$  +$i^/ ! Zk. F&)*/F0•&0  Zc !$$ k‡¨&¨–JO PDD0 0Zaj )*/ U f$&0R#¨O ÈÛ] d [ƒlm/ Dj›Œ  .$)#C ¿T›V³QYZ[ ¨ÛW©Î)R&`)*)*& !/Kj .0$00%i$d]vÈ/O · Oi©V&  Óԕ€/Õi&0;wyx z&{|}u~, €/i *)*0D)*/ \"³ ÒkÒ YZ[ "£   v D^$ F !; .0$j& 9&0h)*$+Dh^/!`% ÒkÒ YZ ;Cm‚W·T )*+ÞC  &bOSwyx z{B|}u~(/€/v    $Wa$&f )*W . +$ f&i .   $ X&'v 0\ %/C˜)* BXa  0 •K .0^0% F&$¹+ &)*& $0 ) ƒ)*$+) .0)r™ky£X v&D.0D+ +&\YZ \Óԕ€/Õ O   .$ K0 $ j '4& )R0k.$  f)R&0D[!R ] \ g 0Wͤ  $  S&'yœU D[!    )* &#iwyx z&{|}u~, €//O   0S)*00%  .0D[U&'’wex z{|}V~,/€/  * &  BC˜$¡"YZ[ Ó Ô¤€ Õ Ol6aj )*/KyYgƒ&D 

$YÄ 0j '4 )R&$f'ŒRºZ€&~4» z/~:» C˜D+¡ f&D%&& [ 0)TK¤Ø/Ô}‡[¨¨–˜O _` +/   B *+i+  !#'b', -/.0/u B .0 .  OyP] C [ +&D’)*00%9j F +&0 f&T^jk0 B .$ ƒ&ƒ 0 c', C -/.$/ B .$ .$  —#0 va$&)*0DK’Ÿ0%T&/ F& B B .0 .  YZ$i S', -/.0/u+*&0ZD+&  V^0.$U$', -/.0/uR&0 0 K &

.$ 0%] $u'( - .$/y B .0 .  y& e'( .  e ]D+&^jD.0$D+&  [Ÿ

B .$ .$  O   $Pflm™k£ &/  [ F&D  *)*j&.00#0F& U'( &)r™W D[C &0)*/FD   $  j.$  9›y &%& F&) ;¥k³VlBÅ¥flmdÖ +D+^0D $.0^$D+D[!/OŒ_`Z DV $Z)* Bu.0$CJ Cm$ S D K$šT FX…&¦¦… D O   0v0F& f& F0 ¿ ·K §&¦ ¶*$)*&Db)*j&.0 O   $ƒ  .$D *'W 0X  $0%2  B *&^jT %& ÞA     9D,   H — ^Ãrt—j$Ÿ$ )*t&  " ‚_^vr—¤Ÿ0 )*T)*  C  F D[!A&  ” ‚]&0`  ^a—V&$Ÿ$ )*0&  O¼P)*$%2 0  ¿·K §¦¶i&)*j.$$ K0¿/…&…R'U $) ^jD$%R   ^$r\K’¨¦† ¨#  ' ^vrKR 0W )R+$0%# kTD+&  ^aO _`9YS/k \$   k $9'( - .$/c B .0 .  k2 $#D+&  ^ÃrÙ&03  ^  )*j&.0 OS_hk )* cD+DŒ $c !$ %0 +  $ \&)*j.00$ O   $T)* Bij$.0D+ i )* RA 0 ƒmYV $F  k Y  I cK b9dK R2 K >gK¤ O   $ # #…/¨9¡  ]&'V &)* žD+& e

^$r )*j&.00$ *YZ0 & t…&¶"¹D+& ?

^vrO     ¡  ’'$^j& Œ uj$.0D+ ’+k $ u)*j.$ —¤ +$%DC˜^j0•K .$^0DC˜^j0•KZA )R +C6^j&¤OQ‚]Ä  F%KZD+&  ^Ãr &)*j.000& R¿ ¦h   i&0¿/…`$% O   $\)Ra[C ) .0)Æ0*0& *¨†&†ƒ    "¨§µT$% OƒœU&F`D, 7

^v )*j.$" R· …¸   i&0·¿h$%& *A  F&%&O   $ )Ra+) .0)r0k0& …&… ¨c    f\…·&¿#$% O Œ%&.$ f†$ÊJ Ëy 0YZ u $S .0/ )*gYZ T7 14? 8 >M & !0%W'( &) ¨¦ ÇÎ c¶ÇÎ&# 0SD+&  g³gPÄ)*j&.0090F& O   $Z.$)9^j

'Z'( -/.0  %& F0;0  $ 9hD ;', -/.0/v%& F0;0C   0 k 9 0YZ¸2Œ%&.$ #†Ê:^jËOcP fYV92 &Kewex z{|}V~,/€/ &.$ j '(& )* WÓԕ€/Õ9^/!t#'4&  c&'¨¦*YZ0;791(? 8 >MT WD+&   ¶&ÇiO ©u& ž&'v 0)  `^j  i .,.P °tD   0&T… &$ O NH O

N

N

HO

O

ÊJ ËS…¦ Ç

OH

O

OH

O

N+

S

N

N

HO O

N

N

O S

O

N

O

Ê:^Ëf¨¦Ç

OH

N

Ê:ËS¶Ç

N

(“ ŽhXqcˆš^4 @"CjŽ