Algorithmics and Applications of Tree and Graph Searching Dennis Shasha
Jason T. L. Wang
Rosalba Giugno
Courant Institute New York University
Computer Science Dept. New Jersey Inst. Tech.
Math & Computer Science University of Catania
[email protected]
[email protected]
[email protected]
ABSTRACT
! #"$ %&')( *,+ - . /' 0 1234%5 62- 0 34%,78 129 -:$ 9; <- =+ 0 >3-:? - :$ 0 @ /A 0 + 0 + BC- BDE?1F ') 9; G 0 " HI3-?=JK 0 - ? BL G 0 + G MJC1F- 7ON:$!3 P QR 0 SG:$& 00 129 0 0 D 3-T U"$ % V 0 K"$ % 0 & GW"$ %9W - B$(; + 0 X W9 :$Y1F ,%Z993-- 0 -? O- [ / 0 '\ ! 0 -? ] 0 (G 5 % ' 0 12 7X8 - 99; L +:$!% L(; 0 F3 0 12 G2993- 0 -? B -:- 2 ?12^129G 0 P?+CI &";7
University
University TA
Lecturer
Prof
TA
Lecturer
Prof
DB
OS
AI
IR
DM
DB
(b)
(a)
University
1. _K / 0 ')INTRODUCTION ? 0 -? . 0 ( ^ % 0
12 U3-- VI 0 `^#abB,c> (dB
0 &"e4 0 - W f 0 + 0 +e,+12 0 ^J 0 O123 0 2 0 0 V e9 728 F 0 .123- .!QR 0 - 3-+G^ad 3Lg hijBGN 0 +Gk^a5g hlijB; G.mK ;k^aYg4nHo,BpnqHijBJrI 124' 0 + 0 +M 0 B?`KkD+ %2g4nsHijB$`^#at'uk^aeg hvijB,`^wS 0 .g oxHi G `^Na>g y$oijBJr&`z#a{ 0 B Gg v,sHiJ| 0 + 0 +2,+12 0 7 8 2G:$M(; f :$ 3b9?9; O99? zJrM*,+ %- 0 Vg lB;qBGv$}Bv$sB;shB;olHiS =JrD*+ %- P9 Vg xBhBpnyB xqBUv?yBUv$oBCo}BCo,n ij7~L =993-- 0 - FH:$ F`z#a 0 B 0 >3-? 0 12 #G:$O993- 0 -? 0 < - 0 4GO 0 (G I z 0 PH^ G 0 +334%F9 0 .(,% 0 z + I9,%' 3-? ,%U G=9 W +# I12?3-+3HK 0 (G !7
\ #N 0 -? xV&^9 0 12 0 -: 0 - W*,+ % /1293- &? 0 G +:$ %.3- 0 12 IJ|D9, - 0 V*+ - 7IN 0 -?
hO -(; F3-? 0 12 FJr= H! >- A9 7N 0 -?
Lecturer
Prof
DM
DB (c)
C;pHYGFu;ubW.[H?FP¡ tp¢5H; =£pH¢Yg-nsHij7&+Wn$j$ G(;X 0 &M`^#a 0 U!' -(- #+ :? 0 z1F- 0 - {- >=`z#aA 0 (G 7=¤&? ' 0 I*+ %=g lij¥b¦L§|¨G©Vªr«¬I¨§|®¬!¯°§rª§)¬!°Iªr«±ªd«±®¬D±M²¬³ ª¯¬!¯ ª\¬±$³«§|¨,´2±P©$±ª)±PµM§|¨§r¨´F¶|·K¸=¹W³º¯° ¬z±¨;©Mªr«±ªp«±®¬z±C»¯º¼¬!°½ °!º¯2ª\¬±$³«§|¨,´f±©$±ª)±$¾±° ¬e¶|·D¿b¹³º¯° ¬!7.8 - V*,+ %{+3O(; /9 f(,%{ 0 9G 00 dBp z I O- >-?+n$!728 0 9 00 V- S 0 - V- 0 0 &- M-?+Kn$(;d GV 0 L+ :? 0 %V- P-+Dn?(;t&?+3W(;L 0 + V X ! 0 0 z*,+ %,7 =£ÀÁ£pH¢Ag y$x,BGlyBGl$oHij7LÂCkDm^ÂU K (Ãu 0 ')- 0 0 123&:$ 39;Y 0 ~LI 5mD :? 0 %eJ| +99; 0 - (+3-" 0 %9; X + 0 B? 0 B,(? B$ 0 ?7b¤& B?J|L /1' 93-?B 0 LJ12-34% 0 - P+Ixj$&g l?yHij7bÄL!M b9 0 #9; E(Ãu 0 7eÄbYF 0 G WJr 0 23 0 -? -9ÆÅ -3WJÇ^ GWK9G 0 V 0 0 0 G dJ| 0 L3 0 9fÅ G 0 JÇ7F_DÆ 0 2*,+ %{ +99; 0 f(,% 0 Åu 3 0 Çf9; 0 2- 5ÂCkDm^ÂÈg l?yHij¥#¦L§r¨;©O±²|²L¨Gº©,¬!°{¶»¬!¯°!º¨°)¹ É «ºE±¯¬e±¨;³¬!°ª)º¯°Oºu¼#ÊK²¬Ë5±¨;©E±?² °!ºE©,¬!°!³!¬!¨G©$±¨ª°>º¼.¸f±¯!Ì7 8 - z*,+ %+3(;P /9 (% 0 P9G 00 dBt ^ I
- e+x(;!7z8 P eÅ Ç.- 0 0 M9 00 {- zF:?H4' (3-3- 0 A? tÍ 0 fÎ^adÏz¤U=g q?hBDn}yijB I5 ?+3E(; - 0 0 0 0 {1F 0 .I 0 ;K29 0 JL DJL= 0 0 K 0 z 0 7X
u 2+L /1293-?B 0 I L- 0 IJ|12-34% 0 1F 0 F(,% 0 DÎDadÏV¤ÐÅ Ç. ?B~&-3-3d GFÂK1=S +3.(; 0 + . C 0 0 ^*+ %,7 8 z9- 2*,+! C z 12^! 0 - 0 - 7
2. SEARCHING IN TREES 2.1 + 0 bApproximate "$ % M H!- Containment ^1F 0 ! LQueries $- 0 *,+ B
"? % 0 M - =1F 0 0 W9G 00 D$- 0 + G!3-%- 0 0 7M8 WJ|?3-3-I- 0 &.!/1293- ^ ?12VJr?1 0 P3- 0 ' ! 0 +7 c>"e +99; 0 >- Y9 0 (%fmM7 N;7p_^N 0 W
N,'uqq?ll?hv$s G
N'\q?ql?ly?h?y7
Permission to make digital or hard copies of part or all of this work or 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. ACM PODS 2002 June 3-6, Madison, Wisconsin, USA © 2002 ACM 1-58113-507-6/02/06...$5.00.
39
I L , 0 I 0 F^9G4LJR- 0 ?! & (3-- 0 I 0 !' 12- G 0 PJR 0 '\ 0 3 0 - -9 &12? K 7 Äb V- 0 0 V C- G /# 0 0 D:3-+V G 0 V,+12 0&0 PI-# 0 (; 3 7 + 0 B3-3t9GH 0 '\-3 ? CD 0 = . /R7bwS, - FM*,+ %F - 0 IJ 0 2Jr?3-3-HI- O 0 9 ¥nHW129;? 0 =*,+!%O- 0 9GH 0 ' -3F? 0 '\ G 0 9 0 R)xXJrU!.*,+ % ??Bp+ 0 P / 0 G 0 9; G- # W 0 0 0 Vjh$WJr=O*,+ %Y9G 0 <:- O! z3- 0 { jt n " "Gx!BI3-, 0 e 0 O #9G4 ejRn?BIx? 9;? - 0 0 K 0 '\ 0 J 0 C*,+ %P9G 0 F GF 0 12- I 0 PtnF- M 5 0 PJDx.(,%O+ - 0 F94PJI- 0 !' ?! I , 0 .I 0 Rn^ G=G#x G{v,L1P( 0 K +3 0 0 { 0 12- I 0 0 !=- M#1F 0 0 0 F*,+ %O9 0 t7 ÂD 0 -? 3 0 ! *,+ U #(;DJr?+ G- Og o,BpnhHij7
John Mary
Mary
Jack
Rene
Bill
Joe
Lisa
*
Jeff
Adam
Kirk
Helen
Alex
Alex
Jose
IrGpH eu;F)fr¢@H;YuXF tpH¢@H2 F (a)
(b)
2.3 c Extension / 0 G- 29G 0 to')?Trees
34% H!-
0 0 W - BR? G 0 D ?1P(- b9G 0 V1F 0 ! - 0 0 L1F 0 7tc>& !(; ?+W3-? 0 1#B3-3-%$'& (*) +-,BtJ|W9, - ÂC¤[*,+! z?
0 C K #-3-3+ 0 0 -? t7
8 &*,+ %z ?+3z(;&!/9 W S 0 L9G 00 ! dB 0 12 Å*,+ % 0 Ç7f8 . 0 (G . Y(;29 0 Y P - 3 0 Oj F- <ÂKkDmDÂ^V= Fe 0 J 0 j 2
`KkD+ %!7 Äb 0 M+3{(;.º¯©,¬!¯¬©M I 0 W z12? -(3-- W- V -? - 0 j V- 0 P`^#aA 0 12 3rC +3(;P¨;º¯©,¬!¯¬©W C- 0 H% 0 7 8 b*,+! XJ 0 V DI 0 0 VÅu9 0 ')-3ÇB Å 0 '\ G 0 ÇBpeÅu9 0 Ç=3 0 -? -9Y12? 0 D CJ 0 0 7 8 P*,+ - K {(;W /9 {(,%{³º¨ª)±§|¨µ2¬!¨ªX1F9' 9- 7S8 0 B L " dI 0 0 L*,+ % 0 L99; B 299/-1F 0 34%Y99; BL- Ee 0 0 ? 7 D ?B 0 Å99H/-1F 0 - Ç2- K12 +#(% 0 W +1P(; UJb9G 0 - 0 M*+ % 0 0 0 . 0 99;^- 0 M 0 0 g lvi)BXW(%{ 122 0 W- 0 J|+ 0 - =g xxBbxhBbxHvB l$s,B;qyBpn}vBpn}?oHij7 8 .*,+ % 0 F1F%O ? 0 - ©$º¨ ªV³±¯¬!°VPI-3H g o?xi)7L8 ^HK/3- 0 . dÍ 0 H ^jSatÏV¤& !BXÅ ÇB 0 G 0 1F%K1F 0 VI - ?3-& L Gz:(3-L3- 0 W dÍ 0 H MÎDadÏV¤& !BbÅ Çg lvi)7
.$'&/(0) +#, 0 0 0 f 0 9 ?B 0 0 (G (+3 9G B 0 3- 0 1 !, 0 ' 0 '\3-HJ 9 0 JL:$!% 0 0 M- 0 =2 +6/#% 0 ( Pg yyij7b
u 0 C G29 ?B 0 K ')3- D H!F9G - I- 0 V*,+ % 0 2 1 - I?-:$ dB 0 V3- 0 1 ?129 1ÐI 0 {f 0 0 4 3È- 0 M 0 (G 4 5 1 3-3-HI- #3-3-= 4J ' J|! 6 367#898PBRj7 ?7W 0 12? 0 367#898Ð9 0 D
3 5 0 e? : 3 0 f(;e1F 0 !t7 0 e(;#( 0 -% c 129GH 6 1[I 0 3;B $'&/(0) +#, 0 "$ U:? %F, 0 ' 0 ')3-J 9G 0 Y-<
1È OG z, 0 J 0 G 0 9G 0 Y-<
3Á(,%> - - 0 V +6P/%# 0 (G ?7WjÂK KF + 0 Qf?9 0 -12T 0 -? tB 0 3- 0 1Á 0 ?9 P H! ! 3 4JI12 0 =
367#898 9G 0 WJ 19G¡ 0 2#-12@ - 1 -7A e
\JzJre> 1 37 N+99;? 0 ! ?Y, 0 ' 0 ')3-J
AB
3 - 0 ., 0 Jz3C3 ?59G 0 B 0 0 K +( 0 D 36E;, 0 . 0 A1F 0 !F 1ZI 0 .- 0 ^}B 9H:# F (3- ? KG:$ 0 W 12V3(;3S- 0 0 M 0 W*,+ % 0 ?7=
)J 0 H -(3-- ? z:- 0 P 12M3(;3B 0 >9;? 0 ')9, - { O:$ 4Jr% 0 21F 0 !t7#8 0 ! *,+ I-3-3U :$!M12- M1F 0 d7
)J AA- 0 , 0 CJ ?GnF9G 0 B
36EU1F 0 H 1 I 0 E- 0 {n G= 3 99/-1F 0 34% 0 < 0 - I 1I 0 .- 0 Vn?7X
)J 0 C -(3- P - 0 K*,+ % 3B 0
0 9 1[1M+ 0 (;K9 !:$F M9+ 0 0 -:$K1F 0 =I 0 J 0 U L12? 0 9 0 b-K 11M+ 0 (;U"$M?- 0b0 U12? 0 K9 0 L-L 3È+ - 0 I9;? 0 U +1M(; bJ 0 D3H:? KJ 0 D9G 0 IJ 3BJrC /1293!7
2.3.1 8 A Suffix Y3-?Array 1 Based " Algorithm &A9G 7È
\
cOF G3-3&!J| 0 0 - M 3 JK*,+! P #±!»$»¯ºË§|µ±ª\¬#³º¨G½ ª)±§|¨µ2¬!¨ªLjÂK¤U *,+ - 7
\ O 3BX#*,+ % 0 21F%{ ? 0 - O+ 0 Bd ' &Jr12CH:123$-B$ N-J12I-:?-T- 0 VP:? P?*,B?++3 G Wz% 00 33- H?QRB?(; +0 0 I g l - B$qH!0 i z0 :$ (0 3 9; *, V+z 3- %,?.7dÂC- 0 120 12 ' 9 &J- 0 0 %z? 0 - 0 7X8 -S3-? 0 12 SL+ Jr+3 JrV*,+ %9 0 -12-T 0 - 0 V -TPJ&2*,+ % 0 WHQR 0 0 z 62- %=J 0 z9 00 .1F 0 - 7
1
M$'& (*) +-,
2.3.2
\J 0 *,+Techniques % 0 for 0 Queries - 2? dwith Í 0 Don’t B Cares " 2-
0 z 0 9 ¥
2.2 # ,%ÂCPath-Only ¤@*,+! I^Searches ! FI 0
. 9G 0 U? 34%{g vBdnlBGohHi)B 7 7X¨;©{ªr«¬#©,¬!°!³¬!¨;©$±¨ª°º¼P¸f±¯Ì É «ºe§|°=±f³«§²-©eº¼º«¨7 N- F9G 0 W29 0 Y M 0 - BX /- 0 {3-? 0 12 G 0 ,3- D + KÂK9.J|K 0 - 2 H!- FW993--(3- 0 z9, - 0 I*,+ - I Vg4n}BGn?nB;nHxB$vn iJ| D:- K!7 `K
NN{g yvip- IP`^#ae- /- P G=*,+ %- M % 0 1 0 K +99; 0 +3X9 0 W /9 -? 7X
u WP`^#a 0 ?B$!
40
9G 0 0 -? .1È- 0 f ? 0 5 +( 0 MG: f O? tÍ 0 1F 0 2FJ 0 ? D dÍ 0 HKJD +( 0 bI 0 . 0 0 I- 5K J| 0 U1F 0 !P +( 0 + 0 + 0 G 0 (;3-? 0 0 U 12 0 0 ?Bp 0 !12 WI 0 ! 0 % ?1P(- 0 .1F 0 1Z(G 2? 0 C1F 0 - z 1F 0 - bJ 0 K? tÍ 0 H 7
\ #? 3jBJ|^*,+ % 0 21[I 0 #? tÍ 0 BG
2 0 0 3 - 0 ^, 0 Jb +( 0 0 G 0 1F 0 ! 1 4JL3-3 J 0 DJr?3-3-I F?3R¥
(I B 0 {*+ % 0 {- 93%,<:Y$: 0 { È9' 93- 0 BS G 0 21F 0 - `z#a 0 F- 93%,f:#?H: 0 993- 0 7U8 z1F 0 =9; 0 -? K- 0 z1F 0 - P`z#a 0 VHz-?3- 0 # .1F"?=I 0 P(+3-3- 0 7 -?+>vA HI { 993- 0 -? *J !'"$##%"$# $ 0 A - 9,%3-? 0 - 0 C1F- 0 - .-
^H:?HtÍ C8d~&Â^NÄZg l}ijB -(3-PJ?1 00 9t¥ " "HUUz7 (GH7 G:R7 + " 0 ( ?7 8 WG+W I 0 W e ?Í z*,+ %- F- 0 J#-
0 =3- J 0 I- K!BUe*,+ % 0 O- 0 F 0 B 0 9EI- GK f= 0 0 .- 0 M-? 0 Bd(; 00 ?1 I- GK!7M
u 0 WG' +B 0 *+ % 0 1F 0 ! 0 0 0 I 0 > 0 F}B Å Çe1F 0 eÅ.%9;Çf ÆÅ Ç{1F 0 P9G 0 YJ 0 0 0 ?7Ð8 - #*,+ %A G =33 0 {9,%3? 0 - 0 -
8d~ Â^NÄ 0 G 0 ? 0 0 V*,+ % 0 ?7
n7I8 M9GH 0 0 - fJF1 ? 0 - - 0 W, 0 J 1È3-3 0 G 0I0 D, 0 9 0 0 -? #J 1W&1F 0 3 0 7 x,7C¤&? 0 X9G 0 zJ?1 0 S, 0
J +( 0 L- 21 0 7bN+99; 0 G 0
1F 0 3 0 9;? -(34%M1F ,%
7S8 &9G 0 zJr?1 0 3- 0 ? & +V -: 3B, % B, 0 U99; 0 % 0 G 0L0 I G- z9G 0 Jr1 0 1F 0 ! V|I 0 f99?9 0 M +( 0 0 + 0 -? J|Å Ç2 GAÅ Ç, 0 z9 0 .J?1 U0 7 8d:$? 0 0 0 f, 0 {J2 +( 0 e+ H34%,B 0 1F 0 !- W+ U+- 0 - I3-"? 0 KJ|?3-3-I- ¥L4J 1[- 0 P1F 0 ! 0 F 0 0 L 3¡ 0 B 0 0 2? 34%e3-: 0 1F 0 VJU +( 0 WJ 1Æ, 0 { 0 W 0 0 M G 0 J 7 c@ =V- 0 M 367#898- U3-3- =- =1F 0 !- VW*+ % 0 11CB I$' &/0 (0E) +#e,{ G0 20 3-?3CBL +Jr( 20 <Jz? t Í 00 ') H0 'jJr 0.G +0 ( 0 #J I1 0 E J - 0 2 367#898[J 1 E 7b8 z?3-+ 9, K- :$3:? I 0 0 J I 0 ! 0 ^?3-+ 0 V CMI3z- C- G =I 0 - - 0 367#898[J 0 ^ 0 4V*,+!% 0 2 17
2.4 Related Approaches
-
g ln ijBI GE¤&?3-5¬!ªM±?²/.g xliK9 0 53-? 0 12 J| G - 0 U, + bJRKI-3'jJK *,+ % 0 112- # K (3- ? b.1F 000 0 7 VM~&3 0 7C4
\1 G H3Æ U 0 ?BM0 K G 0! [ ,+ IJ ] 1 - 3 Jr 0 0 ? z +( 0 UJ 3 0 G 0
(;D( 0 Jr1 1 (,%F 00 !- W +( 0 0 0 K3-:$ J 17V8 - ^9 00 ')1F 0 - 29?(3-1 - z3- " HI e 0
2.4.1 DQR1F zApproximate G,+MÍ Ï^? 3-Embedding 3g v?qijB? G^3 0 Queries (K12 z G-(K1F"'
¬ Ë$±$³ ªIº¯©,¬!¯¬©=ª¯¬¬¬!µ2¾¬©$©§r¨´^9(3-1 g l?hHi)7 c3- 0 XJrb`z#a. M 0 + 0 +M,+12 0 SU RB - 0 0 - *,+ - W2J 0 >( e? >+ 0 B(;!' + - >- 0 # 0 O12- 0 0 1F 00 0 0 #+ 7 8 G 0 - RI%D`KkD+ %,B!J|p /1293B +99; 0 t+ z*+ - 7 N3-- C ._^+1F {g l?hid / 0 0 ^!/ 0 1M(; 9(3-1Æ GP 0 +- 0 V±!»$»G¯ºË§|µ±ª\¬z¬!µ2¾¬©$©§|¨,´VjÂKÄ&p9?(' 3-1 Jrz+ 0 7M¤&? BRJ|V!/1293-?B 0 P*,+ %R¥ ¦L§|¨G©P±?²|²¾ºº 0° É «º° ¬z¬©§|ª)º¯C§|° ºH«¨#±¨;©Vªr«±ªb³º¨ª)±§|¨±M³«±!»;½ ª\¬!¯ É §|ªr«fªr«¬ª§|ªj²2¬ 1K4¸ 3.d-?+=s. I 0 2*,+ % 0 2 G { 0 0 F YI 0 =*,+!% 0 F Y(;=99/-1F 0 34% 1M(;t7 K ?B &{3-3- O1F 0 ! > 0 0 0 >G:$
2(; 0 Af9 0 ')!-359G4F 0 #*+ % 0 BU9' : 0 0 '\ G 0 3 0 9A 29 :$E-
0 W 0 0 ?7D-?+Ps I 0 - ¥ 0 V1F 0 - F 0 0 G #[Å\_^12 ÇY 0 0 .12- >Jr1 0 f*,+ % 0 ?7 8 - 0 %9;2JI 1P(;- . M3- {" I Y =ª¯¬¬.§r¨;³² °§jº¨{ !G e- @g s?o,BbslBXsqBXy}ijBI!6 z-39; 3- Y GO# -3 & 0 9?(3-1 0 f(;._^wS')?1293 0 ?758 ÂDÄ]*,+! 1293-12 0 0 zÂC¤*,+ - C -(;=- {N 0 {x7-n7 8 F 0 -? YJ.Åu99/1F 0 -? Ç 5(;J|+ 0 M? 3--T (,%W 0 +- VK? 0 J|+ 0 -? 0 G 0 &D3-HA? 0X0 z1' (;- L- 2I-2 ? I 34%2z 1F33 +1P(; XJt "-99;R7IN3-- ^ G_D+1F Og lhiS9 0 #3-? 0 12 0 0 -:$W G ". { +3 0 K+ - 0 - C? 0 J|+ 0 -? t7 8 -&3- 0 1 - L( 2% G12- 91212- z P9' 0 F*,+ % 0 L 1 - Y#(; 00 ?1 +9fJ -? d7W!
5D;J 12B!21M(;- CJ 0 I*,+ %V +( 0 16 , 0 0 5z- L ?129+ 0 MJ?1 0 I1P(;- ? XJ 0 I*,+ %P +( 0 , 0 = 0L0 I!3 b7J 57XÂK12 0 C:3-1M(; ? CJ 1 6 - 5 0 # +( 0 3,8,B 0 F3- 0 1Á? 3-%O1F- 0 - 0 M? PI 0 0 M12- -1F3 ? 0 *7 (C9; 0 - 0 (;:?P 0 9 J|U!=1F 0 - W 0 V C9J 5z% 3 UV 0 J1M(; ? J 16?7#Â 0W0 2 GfJ 0 F3-? 0 1#B 0 21M(;- ? VJ 1 C 0 (%M- - V 0 G9 0 0 0 I+ 7X8
2.3.3 8 (;Filtering :?M H!e9, ^ f(;W+-
0 3-34%{129H:$#(,% + - MW - 0 *+ 0 0 &" U &J|33-I I? 0 K ? ' I-39; 0 -? JP 0 Y G*,+ % 0 7Ф&129+ 0 { G 0 O3-3^- G-:+3^ {3(;3- # G33D9G 0 ')-3@3(;3 94 P- >5 0 0 =- 0 {#G 0 (3-?Bb , 0 O! 9 0 ')-3=94UI 0 0 K 0 JS 0 0 0 0 0 - 0 9 0 ')-39G47X_KH< +99;? KV*+ % 0 1Z- &:? 2I 0 { 0 - A 0 #3-3-H&<- 5 H! FB 367#898P758"? 0 1M+3 0 - 0 JI3(;3- WJ?1 1 Gf I-Y 0 0 VG:$ +9; ')1P+3 0 - 0 J 0 ? ^9; (34%=I 0 J 367#898 12- P3(; 3 7 8p"$ 0 &1M+3 0 - 0 JG9G 0 ')-3z9G4 SJr1 1 M LI-! 0 0 H:?^M +9; ')1P+3 0 - 0 J 0 ? K9GH 0 '\-3F9G4 B $ Z9;? -(34%I 0 367#898 12- - 59G4 7 8 - #+- 0 - 3-12- G 0 ^43-: 0^0 KJr1 0 -? f 0^0 M(;- '
- =J&F O G#% 3 z2 0 J& G 0 0 0 F3-,?" Jr7
2.3.4 8 U Implementation 2 GzG3 0 - z3-? 0
12 RÃu+ 0 -(;PHU?3-3- ' 0 -:$ 3-% J| 0 = ! "$##%&"$# $#|I? M G12M- D 123- 34% 9 0 FJr?1 ÂK9eg4n}hipJrK99/-1F 0 D 0 - - GON K9
?- ?B3-3->`z#a@kD+ %e(,% ÄS/1293F`^#aJr' 12 0 j*,+ % 0 HC G G 0 V`^#ad ^- e2`z#a5 0 (G 0 0 99/-1F 0 34%E 0 - 0 #*+ % 0 ?7F /1293-?B 0 e*+ %< -+fh5- 0 YG GA3-3 0 {`^#a],+12 0 -(- 12H: D- I-!) (C?(; 0 (KJ|e- 0 P- 0 B ~b?PwX 00 - X M 0 B, 0 &12H:- S&1F?b- 2¤ 34Jr B mW7 NR7 ÂW7NHI O 0 P?+FH{?+ 0 !3-,!",I- ?BX 0 0 - J?1 +99;!D3- J 0 0 V1F 12 +tB 0 M*,+ % I- GzB 0 !/1293-U`z#afj*+ %p- 93%,P:z^!? J 0
Äe(I B M1F 0 - M`z#aO 0 - - 0 z*,+!%- 93%,.: 0 ^
Ä 41
Ir;pH V<t r { ddH¢5 @ EH r A pr t$ f Rp f@. [£V
42
Ir;pH VAt ddH¢5 @ EH r F A d{?pH ' <pG p! HP W
Book
Book Chapter
Chapter
Editor
Editor
Title
John
Name
Title
Author Title
John
XML
Mary
XML
(b)
Chapter
OLAP
Author Jack
IrGpHtzÀ G pH< p | U { tp¢OH 5dH;Fu;V tpH¢>H;2ub KH U {=[ p{HR (a)
43
0 #*,+ %Y A 0 - EI-3H {|9 0 - e L9G 0 0 V3-3-H
1F3-3-%E+ 0 {*+ %E9 0 Y>3-3 0 -? J 1F3-3d9 0 7 h7C¸f±ª)³«7&# 0 - M- U-1293-12 0 M 0 U(,% 0 0 -? 3 +(;u9' 0 ')9#1F 0 !- 0 *+ BGD(,%.?1' (- - 0 C 0 J9 0 0 G 0 +3 0 J?1 9, - 0 9G 0 . /9 - C 0 z*,+ % 0 ?+? 0 z 0 ( ?7
?1293- / 0 %J 0 ^3 0 1 - U /9; 0 3 0 ?+ 0 ^3' 0 1 1F%2+ 1M+=J| 0 D9; G- P? 0 z 0 7 2.4.2 +D 0 !Selectivity
*,+UJ| G3 Estimation 0 - 0 ?+
0 J| 0 I- 0 V+ K 3- 0 :,' 0 %2 0 -1F 0 -? t7S
u g yqidK+?= GPc1 -(;Kad 3jÍ ? 0 ')(G M*,+ %^9 0 -12-T BHI-W1F- 0 - p 0 0 - 0 X(;?+ 0 +(9 0 VJI3 0 ?RB Gf+ V 0M0 J| W 3- 0 : 0 %O ' 0 -1F 0 .JW3 #9 0 *,+ - 7 ^- G ]¬!ªF±?/² . g yn iV ' !(;{ -12-3 0 ! *,+ UJr^9, - .*,+ %. 0 - D ' 0 - - WI3 B7 ?7b 0 -1F 0 - 0 D +1M(; bJ 0 - ? U- = 0 (G 0 G 0 ? 0 - f=-:$ f*+ % 0 - FI 0 eI-3 7 + 0 U3-: 0 ". (;^Jr?+ .- >g xyBRsxBRsHvBGq?qij7 ¤& Y¬!ª ±?/² .Cg xsHid? 3--T 0 ^ 3- 0 -: 0 %= 0 -1F 0 -? .9(' 3-1 J|+ 0 7SN9;43-34%,B?-:$ VC 0 0 3Z G I-3H'jJr *,+ % 0 1BI- 0 b+ 0 d3-3-V 0 I-B
37 0 %. 0 -1F 0 0 0 0 3 +1M(; UJ 0 IF1F 0 ! IJ 1 -! 8 e+ 0 F9 0 J*,+ %A- J|1F 0 -? (;+ 0 1F3-3 0 I-? Bt3-3- 0 I-?3- 0 Bd- 3 + - .23 0 e +(9G 0 0 )¤UN8I!7bwX, - >e*,+ %O? - 0 J 0 FJ|33-I- f 0 9 ¥ nI9 V!#, 0 ' 0 ')3JL9G 0 !
1Æ- 0 F 0 JX +(9G 0 0 0 G:$z1F 0 ! I ¤UND8 S)x JrD 0 I-2 0 G 0 - K ( !# ?B K33d +(9G 0 I?( 0 - - >n 0 G 0 H , 0 { 0C0 V 12z W 0 G 0 9 0 ?+? 0 z( !
?BK GA3-3^@ +( 0 {- G+E(,% 0 +(9G 0 = *,+ % 0 I3- 0 U G@jh$V 0 -1F 0 0 F +1M(; WJC1F 0 MJ 1 (,%{9-- 0 ?? 0 W+ 0 0 -1F 0 zJ| 0 0 I-3 0 M(' 0 - O- @)x^(G O? Y O- G9; 2 +129 0 -? >(;?+ 0 0 {,+ .JW +(9G 0 BC @+ - Y9?((-3-- 0 -O 0 4' 1F 0 -? {J|1M+37V^f9 0 {J&3- 0 ASBRG - =3-3S 0 +(9 0 0 0 G:$U1F 0 ! S- F¤UN8 0 "? A 0 -12?78 + 0 0 -122?1293!/ 0 %f J 0 23-? 0 1 - DI >- 0 z- 0 J 1Æ G - 0 ^ +1M(; UJ3H:? KJ 17
N :$ 3d % 0 12 UJ|^*,+ %- 2 G- /- 29{ 0 (G G:$D(; #-1293-12 0 A(; 0 F? 34')9+9;? Fg h?}BGv$yHiS G 993-- 0 - ') 9;4G.g v?vBdssBdohij7z8 W+ G 34%- 0 ! *,+ V -(;- 0 ^ !/ 0 0 -? d7 3.1 ¤&,?"Y¬!Keygraph ªC±?²/.Wg h?}Bth$sibSearching 993- {-12in9HGraph :$12 0 Databases J 0 V / 0 9V1F 0 - U12 0 Pj3-? 0 1 t !(;^(%D_D-3- ?
g oqHi( V? P W / 0 9P1F 0 ! D3-? 0 1[99;? - Og xn!i 0 WG F -12-3I9; 0 0 -:$K +(9 U- #W ?3- ')9 0 ( ?7K8 + B 0 4K12 0 KHM9-1F-34%#JX- 0 0 J| 0 0 4A 0 9(;:??7]8 4 % 0 1#BCNm^~&ÏDm^ÄUB& =(;
993-- 0 A :? % Jr +(9 #- Z9 0 -
0 ( BC-1Ff 0 (G B^¤&- {G 0 0 (G B ¤ ÂKÏ 4+ 0 0 { GY J 0 UH# ?+ ?75+ 0 !12 = / 0 FJNm^~LÏ^m^Ä@|cO(;Nm^~&Ï^mDÄ3 e9 0 - A 0 ?(Ã 0 =? KH^3 C3-- "- 0 &P 7 K9Ïz~<? 0 - 3 0 = 0 P :? 3S9 0 K- 0 W 0 (G ?7VwS 0 {3 .- G /- 0 P 0 + 0 + z?7 7~L' 0 ?BaNÏz&z+ 0 - G /5 B&9 0 2 E +(9 - 0 9< 0 (G ?7 K9*,+ - =H 9;4G<+ - O ?+3H.!/9 -? G 0 !%1F%@ 0 - 0#0 O H! 9G 0 AE +(9J 0 I3-9d@ 7 K9Ïz~ 9H: 9< A9; 0 -? 0 zG 0 C 0 0 9G 0 &(; 0 0 V 0 zG +(' 9 VJ?1¡ 0 H 0 - PI 0 - Y#- 0 ?7=8 -1293-12 0 0 .- C(G .
7 Ïz%3- 0 g ssHiU- M# % 0 1Á+ 0 # 0 -:?= +( 0 + 0 + V-
0 ( WJI123 +3- zI!=>12?3-+3-2 V9 0 (,%<>9d7ZÏz%3- 0 + F 9- 0 - 0 > GE 3 :? 0 9 dJr1 U 0 (G C 0 9n!7SÄbz92J 0 b 0 ( H - I , 0 I 0 V/') -TK( 0 :$ 0 3-3- 0 K ?!' 9- 0 J 0 K9d7 D-:$ W9 MB 0 G ? 9- 0 ( 0 U 0 - 0 XJ|3-3I- KU%R¥33 0 L9 0 - 5J3- 0 MT!D G +9 0 CU3--12 0 3- 0 Wb?129+ 0 HV9G 0 z- d+ z U 0 V?129+ 0 C^ ?1 +1M(; , G 0 C( 0 9 0 0 -? =J 0 - = +1P(;!.- .? 0 0 # 9- 0 7 8 G ? 9- 0 9 0 V 0 + 0 +3XJ| 0 + WJ 0 29d7=8 2 -123H 0 % J 0 29 D- K ?129+ 0 (,%.?129- 0 4K ?!9- 0 7 N12S -123H 0 %z12 + d?¥ 0 b8 G12 0 C¤&, 62 0 0
+1M(; J^( 0 2- E?1212 <-:E(,% 0 0 0 3I +1P(; !0 0 WÄX+3- {- 0 =?12 0 -W- 0 H0 t 0 W8 :$!' ",%E 12-3 0 % A+ 0 >12 + 0 # -123H 0 %AJW>*,+ % 9OI 0 O +(9OJC# 0 .9t7=8 2 H!> 9 - ^G3 0 e(,%{?129- 0 P 9- 0 J 0 2*,+ %9 I 0 0 ^ 9- 0 JS!9#- 0 V 0 ( ?7 kD+! A- 3-+.I-3 7@F12 0 *,+ - B 0 .1F 0 - e- -1293-12 0 W+ - V993- 0 -? F 9;4G 0 *+ 7 KH&:$
3. Â SEARCHING 95 0 (G = Y(;IN F:GRAPHS ! Y P 0 !# - 3-f3H
3(;3->9@?7 7pUUKzP?3-3- 0 - EJI3(;3-O9 7 7b!12-3 123-+3- !7Y~L% 0$¬!Ì´¯±!»«E° ¬±¯³«§|¨´.&. Jr 0 9>W +(9>1F 0 !- - O 0 #9 7.8 21' 93- / 0 %FJ 0 P +(;u9' 0 ')9F1F 0 - W9(3-1 G= :- JU 0 >3-? 0 12 zI 0 O9; 0 0 3L993-- 0 -? 0 "? %9V - K- P 0 ( XH + W MN 0 -? Mh7 h7 ÂC3 0 ?+?5 +(Gu9' 0 '\9e1F 0 !- F3- 0 12 ^ e(; + >J|"$ %9Y - B& 6- %>? 0 - +' 00 e+ fJP /- 0 *,+ 0 5+ 0 f 9K 0 0 -12U1293- / 0 %M 9;3-34%2- 23D 0 ( 7 8 U"$ %9M 29(3-1]- 2^ 0 ( U - 0 bJ 0 ( -V 0 9 SÃu+ 0 IJ|C"$ % 0 ^ H!- 7
n7 I¬©³¬zªr«¬z° ¬±¯³«°j»±$³¬W¾ ÌIL² ª\¬!¯§|¨´7LCP 0 ( ^J 9 K VG 0 V12 0 3 :? 0 9 ;J|^2 ?3- ' 9V 0 ( X b 0 4Jr% 0 S12? 0 3-: 0 +(9 7 c>C G D+ 34J 0 VG3 0 - 0 *+ &( 2 0 0 + 0 +YJ 0 >3(;3-[9 E9G 0 BW +(9 !7 N- I3," WJr& +(92 0 + 0 + &- *,+ 0 C-6+3 0 B 12? 0 3-? 0 12 , 0 W3, 0 ^9 0 LJd K3(; 3 7 x,7C¦pº¯µP²-±ª\ ¬ ¬!¯Ì§|¨ª)ºW°§rµD»;²¬K°ª¯³ ª¯¬!°7&8 K"$ %9 E(;F:? E4 0 34%Y 0 JC G>? M 0 >- 0 ! 0 -? ]JFA 0 J9G 0 7Á+ 0 12 44
*,+ - .- 3-+G- OI-3 1F%5*,+4 /G+ 0 -:$9 0 :$! 3- 7 D31F tBSc1 g vviI G>33-?+ #g o?oiU99;? Y# % ' 0 1#B3-3-Wad?B 0 I 0 b z*+ %DI 12 0 + 0 +^ 0 (G |I-!#- C123-. KP3V, 0 #3(;3-4 0 .9 .g4n?BGl?lBRq$xiJ|z +:? %!7 atV+ IJ|+D"- IJX- G- 0 . 3- 0 |?+3H!K9G 0 { /9 -? e H! 7Vz! ?V3(; 3 - 0 z9dB;:3-+z /eÎK /&- C+ 0 - /f3-3 0 0 0 G:$M- 12 #? z3(; 3OI 0 GEI 0 0 ?12-:?3-+ 0 G 0 0 - Jr%A ?12 G 0 -? t7[Â 0 !/ 0 - G /<j8 /^- M+ fJrP3-3& VI 0 Y ?12- ' 3(;3-? I G=I 0 . 0 2 0 12-^:?3-+ ? 0 - - 9; ' -2 7#Â 3- "f- /<jad- G /D- G!/ 0 VI 0 + 0 ?- ')3(;3-V 7XÂY9G 0 W- /2jwX- G / Ïz 0 D+H - / K3-3 0 z CG(3-WJ?1 0 ^, 0K0 ?+{3' (; 359 0 t7YÄbE9 0 5*,+!% 0 G 0 0 H 0 2 0M0 F, 0 + 0 PÏz 0 D+?7MÂK3-3S 0 z9 0 f*+ - ^+ 0 M 0 0 - / L 2I= 0 %MG G2V 0 Jd 0 U 0
0 :$! 0 V9 0 =9+ WU%9G 0 0 G 0 F 0 1F 0 ! 0 P*,+ %#9 0 d7z~&+ 0 M 0 D- G!/ ^M+ 3- 0 -:$?B 0 WW9; 0 0 3-34%1F %.12V G 0 0 G 1F 0 - 9 0 7 -3-E N+-+ g ohHiz99;? @Y 0 O 0 + 0 +BI3-3-8&' - /RB 0 U- G /^ 12- 0 + 0 +D 0 (G L 0 G 0 Hb!' (3-PJ?1 :? 3S+3V9 0 e /9 -? 7Â 8&')- G!/{ ^
? 'u 0 12- - 0 -b+ 0 ?1F 0 DI L 0 0 d 9 0 |?+?34% 0 F*,+-:?3- F3 9+>(% 0 (K( 'uN 00 3' 0 1 5I? 0 0 -? 2 9; G 0 f 2(; 0
(Ãu 0 F- 0 ? #3 7~L%Y3H/- 0 0 12- 1Á ' *,+- 12 0 -129;? e? >Ïz 0 D+ BS8&'\- /e >(; ' 0 + 0 G# 0 {12V 62- 0 34%,7C8 %1F%.9 0 122 62- 0 Ïz 0 D+2 f(; 0 0 -122 Ge 9G ?7#W /' 1293- 0 P+ 0 D9; 0 0 G 0 - OF9{JKnHs}}. B 0 V8&') /= -Tz- znh J 0 D T WJ 0 z9 0 (G ?7 %" &-$-) %&"$# $,BC9 0 A- 0 / 0 0 -? tBD- .> G ' ( WÂC¤f3 0 1ZJ|pG G- V±?²|² 0 b,+ JK*,+ % 9#- # 0 ( zJS9 7LÂ 0 JS- 0 0 - P?+3 9 0 = /9 - I- I+2(,% 0 D*,+ %F9t&7 %" &-$-) %"$# $ + z:(3M3- 0 f9 0 P 0 G 0 1F%? 0 f %3- 0 =- ' / 0 F 0 (G ?¥ 0 - M3-3-I 62- 0 G3 0 - {(,%O4 0 34% 3 0 - 0 12? 0 3 :? 0 +(9 zJ 0 12 0 3-: 0 9 7 8p(3-PnD +121FHT 0 KJ| 0 + UJ :$ 3R"$!% 0 D GF"$ %' 9 - 0 *+ 2J| 0 e A9 0 ( B 9; 0 -:$34%,7
D B 0
3 C
1
B 0
B 2
3
C
C 4 E
B 2 B A 4
A 1
5
6
(b)
(a)
Ir;pHt pG t d H @ub H ? AXf p; IHSr H¢ rpG b
A 1
B 2
C 3
(c)
? p <? rXu Rr
0 b- G / 0 I9 0p0 L 0 (G J9 X 0 JG9 0 0 - z 0 9f- M? ? 3-%e H!B&)x?K3 0 ! 0 0 ( 2( ? 0 z +(12 00 #*,+ %. 0 z- G / 0 + 0 z H! 9G?B& @jh$W9;!J|1 / 0 1F 0 - 7{c>.- + 0 129;? 0 U- 0 + d7 3.2.1 2EIndex 9AConstruction GYJ|F< ?BL
=G G533I9 0 0 G 0 0 0 0^0 - ^ 2 GG:$M3- 0 f # - 3- HK+9 0 O 1F33BS7 7v$^? 0 0 :?3+ !7Fc>+ 0 12 J|b3-39 S- 0 & 0 (G ?7X~&+ U :$ 39 0 1F%P ? 0 - 0 I 12C3(;3G *,+ ?B? I+9 0 I')9 0 , 0 EI 0 0 = 12=3(;34')9G 0 E- E{ 0 758 EÅu9 0 ' 9 0 0 -? ÇfJ^9E- 0 . 0 JK3(;34')9G 0 - 0 9tBI z3(;34'\9 0 # IP 0 JS')9G 0 ^ V' +zoj$!7b8 ^"$ % J 0 KG 0 (3-z 0 D :3-+ UJ 0 V3(; 3S9G 0 7^Äb[ 0 - 0 W +1P(; CJb')9 0 , 0 OI 0 >="$ %5G O:3-+K- O!f9d7Mc>MI-3-3 Jr 0 0 0 (3-I 0 &G ? 9 0 J 0 U 0 ( z -?+Do(;!7ad 0 3 (; 0 U +1P(; JR9 b- 2z 0 (G 37at 0 A (; 0 . +1P(; PJz F G 0 #1FH/-' 1P+1 :3- j H J 0 ^ U- 0 P9dB 9; ' 0 -:$34%,7X8 D 0 z1293- / 0 %2J(+-3- 0 D- /= G 0 L9G 0 W9 0 0 - MJ| 0 & 0 (G U A !B I! 0 ^12 12%F 0 - A !7
1'('17'((!#("% $&8!92*) +:),'+@) (2;)3!; ) !<) !*"./*)),".+-)!*".)#2;)*/=)/:)*!*2-) /-) )*!A"%!#$0) "%+ $="%$ 1'1'((( > +-2-!*".) +*)3) "./24)"%"%$ $2*) / "%1'$?'1(( +?2#56)"%!<$ "$ ) /?) !4"%$ 'B'('1('( +?56) !-)$ /*"%')*1 /@() !* 56) + "%$C$ ''A11((>5D!-)-$ 2 '),1+ "%')*(!- ) 562 ) /-$ "1($@'17'(( 56 56$ $ F G8H ''BB'11('( 5656$4$417'7'(1'(1(( 5656$C$4'(117A''1( 56 5D$ $ '17177'(( 5E 823$ ) !-1) +-".()-82-2*) ! ) !<) /*""%$ $
3.2 GraphGrep: A Variable Length Path InV-3-3+dex 0 0 Approach -? Y9+9; ^ PJr,+ V O+ 4 0 f9 z
Key
g1
g2
g3
h(CA)
1
0
1
2
2
0
F I#H
…… h(ABCB)
I-!W XC 0 G:$L3(;3- 7X8 0 *,+ ? 3-T 0 4 0 P9 XI 0 P3(;3-? 7%" &-$-) %&"$# $K +12 0 G 0 0 z IJ 0 V 0 M9 IG:$^ # 0 4 0 -? +1P(; §©?½)¨Gº©,¬z O.3(;3K²-±?¾!¬ ²4½j¨;º©$¬!7c>2 G <§j©?½-»±ªr«.J 3- 0 : A 0 V(;Cz3- 0 ;J A#') XI 0 . 2K(; 0 F ,% 0 .? + 0 -:$P 7 ²-±$¾¬ ²4½»±ªr«.JU3- 0 AE- V=3- 0 J A{9 30 t(;BG 3-') G fjh B-nH7&U I0 !/^12')99G3-?0 B- #-+ 9;z? yj$- !Bd )0¤KPB ÂD 0 &7 - KW3(;3 8 = 0 2(G F129;? 0 zJ %" $-) %"$# $,¥=nH^(+-3
Ir;pHKJRu; H p 8 6 L HpR D pfGH YIr;d& pu;C2r vub pNM pG R & d pe p r¢ pH C 2? 3.2.2 8 F*,+ Filtering %e9>-the V9GDatabase 0 #(+-3f 0
z ?!9- 0 G 0 Jb9G 0 !7Ic>zG3 0 0 W 0 ( M(%.129G- 0 zG ' ?!9- 0 J 0 F*,+ %I 0 0 ?!9- 0 J 0 2 0 (G ?7
45
N % 0 1 ÂK993-- 0 -
Âb8d/K9 D`z # a 3 `K
NN KKÏz9%9 3-KÏz ~09 DD?3- +333 at N 12- 0 + 0 +' Ï^ 0 Nm^~LÏ^m^Ä D 3 8&'\- / N 12- 0 + 0 +' Ï^ 0
zÏ 0 (G 3 # ,%.8d # ,%.8d # , % K9 +D 2 K9 # , % K9 +D - (C, 0 ' K K99 +D 2 +D - (C, 0 ' K9
wS 0 ')
u /- -3 0 !'\+ 0 1 at 0
0 1 N+(')
0 1 ÄX:$ %.adJ +3-3 LL &_D ÄX:$ %=_D n ÄX:$ %=_D wS12 0 L _D N?12K_D wS12 0 L & ÄX:$ %=_D wS12 0 L && (C, 0 +3-3 _D ÄX:$ %=_D n _K _K _D _D (C, 0 +3-3 _D & N?12K_D Î&H(3-
c-3' # 0 - && LwLw ¤¤ && ?BÂKwLÏ L¤ 'u8 && wLwL¤L¤ '\8 &_D wL¤L'\ 8
reG | U . 5GH E' pf¢p f?^Ir Gp2| d p<t ! 6 p pYRrH GY ? ÐXH ; ) p pH K p e' pZZG ;Ð tpH¢S dp 6 p p H r R GH { r? H5 GH <[ pt4MS t¢ p M r p SH[ [L G |r? . =b d R f p p Gr u;-pKG GH< G4 r$ r G K % S p <u;-p t? d I G K {Sp f pA r Gr K |' ZH dprH=H GGH H ; 9 . &HtP¢p f6 p ; LH RP H ; WF p= ? ?
Â<9dB$JrLI-! 0 3 0 I:3-+U- 2 0 b 9- 0 b3- 0 0 U 9; G V:?3+I 0 G ? 9 0 J 0 K*,+ %,B - &- PI 23," zJ| 2 / 0 +(921F L 0 !t7S !/1293-?BX- 0 =*,+!%O95- 5-?+l#I 0 vB 0 9 V(;& GeH&- -?+^y^3 0 !.+ 0 (;+ 0 % z 0 ? 0 - 0 U3(;34'\9 0 FÂK~U¤ ÂW7$3 0 - 0 I 0 (G 0 "$ 3-- 0 -12C 0 K -TKJ 0 D 0 (G 7b8 K 1F- - 9 µ2±Ì. 0 - @? #=12. +(9 F1F 0 - 0 *,+ %,7
B 1
2
A
3
B
3
0
C
B
1
B
0 C
2 A (a)
lp=4 A*BCA* CB (c)
Ir;pHtVu;&Æ dpH¢=GH LMuX H p dp &MSUH
V pY L u;H@u. p GpG d 2fr G vr ] G |.|tt G > r p ; r p dS pL rXb| !|#2r H pe f! f YHH R d{f p;
3.2.3 ÂIJ 0 X3 0 Finding ! B$&USubgraphs 3-,?"MJr&3-3 0 Matching 1F 0 - with D +(Queries 9 X-
0 1F- - {9 7>8 .( ! MJ^{9 0 ') 0V0 H:? 3 0 ^J 0 ^*,+ %=z129;? F- 0 W *,+ UJH:$ 8 39' 9- P3(;34'\9 0 BI-!= ^3- 3-3R»±ªª\¬!¯¨°BGJS3- 0 3- W V-?+Vl$!7 +D:? 39 I1F%F,+C 0 DJr?3-3-HI- . ¥
') U- 0 UH:$ 399- z9; 0 d7b
u P:? 399- z Wjh?!B 23- 0 C12H:$#4Jb 0 , ^ 0 0 - 0 W 12V') M-
0 VH:$ 399- =9; 0 RG 3-34%,B;3-- 0 zV12H:$4JL*,+G3 ') Cz 0 J|+ - H:$ 399- P9;? 0 -? 7 t r;7Lad 0 + I ! 0 z 0 9 0 1F 0 ! 0 V*,+ %=-
-?+Vlj$ I 0 0 z9& - -?+Vyj$!7
n7IU? + 0 :?K3(; 3-')9 0 B 0 K3 0 CJpW9 00
KI 0 E0 L V 0 WJ 0 W / 0 9G 00 5?7 7 ÂD~ ¤ ~KBGI 0 hB- D?129; - 0 0 &29G 00 ! ¥ ÂD~ ¤ G¤ ~U!7 x,7U
\JGK S( p 0 - S- 3+W- 0 & 0 9 00
JX :$ %F( O V V¤@- -?+VlH!7 h7I8 z 0 V:- 0 - %3-V99; 0 I-¥&- 0 (; - .J 0 P 0 9G 00 ! OJ 0 P!% 3 Gf 0z0 #J 0 V3 0 9 00 J 0 W!% 3= 0 z 0 #3 0 9G 00 #(;z 0 -3BG K- #-+WlH!7
n?7IN3- 0S0 0 JG9G 0 S- j-?+Coj?p1FL 0 - 0 9G 00 ! tJ 0 b*,L+ %Mj-?+LlH!¥pÂD~U¤ Â n } h n n x h n ,BR¤ ~ jh }$ jh x,7 x7I¤&?1P(- %E3-- 0 Jr1ÂK ~U¤ Â I 0 %E3-- 0 J ¤ ~Æ4J 0 0 4>') 2- - W*,+G3 0 0 0 '
FJ G 0 F 0 ') FL- M*,+G3 0 0 J|?+ 0 O') PJ ¥zÂD~ ¤ ÂK¤ ~ n } h nH jh }? n } h n jh x? n x h nH jh }$ n x h n jh x ,7 h7 (K12H:$D3- 0 DJ?1 ÂD~U¤ ÂC¤ ~4J 0 %? 0 - *,+3p'
.- ')H:$ 399- O9;? 0 -? f 0 {9;? 0 -? -
jh IMx3-I- 0 D G e 0 12- n 9;:$?x 3 :?h 0 -?VnH 2 %(;jh H :$3}?H! U!77ÂD8 ~ ¤ ÂK0 ¤ C~E +(M 0 +n 0 } + h pn-! B
cO#+ 0 #9 0 59 0 0 -? @J 0 .9 0 O3-,"EJr , + bJ 0 U*,+ %,7 +D 34% 0 9 0 XJR! 0 H 9{I? W')9G 0 # 0 D 9; G 0 0 V9G 00 CJ 0 *,+ %#HV 3- 0 { #?129=I 0 0 W*+ %,7&ÂCJ 0 ! 0 '\9 0 0 O 3 0 tBK e 0 4Jr%H:$!399 <'\9 0 3-- 0 GO ? 0 0 0 1 |12H:- #H:$!39 0 (+-3O 1F 0 !- Y +(9d7 #H:$!399 Y >nHF [)x?F 942J^3-- 0 2 P?1M(- Y4J 0 0 e3- 0 2 ? 0 - 0 {° ±µF¬
8 =1F 0 - f3-? 0 1 9; G M 0 . +1P(; WJD*,+ % 9{9G 00 0 G 0 0 .(;V1P(- ;{- D 12 IG 0 46
462+3 0K0 . 0 12- zJr 0 P:$!?W ?7-(C?+?34% 9;",' - Bt 0 - z4 0 34%{9?9; 0 - G3 0 0 M*,+ %# T 0 0 1FH/1M+1 :3- VJ 0 V C- 0 W*,+ %,7 8 V3?! B 0 1F33- dB 0 ?+ 0 - P3 0 -? -9A- F 0 '\9; G 0 7
\ . !3R4J A{- 0 C1F/-1P+1Æ +1M(; J :- 0 123(;3B 0 P 0 0 -12P1293- / 0 %Jr 0 1F 0 !' - A DI 0 3 (;- 0 2 -TFJ 0 0 (G WHJ 0 0 ^3 0 - 7
1
0.1
1000
2000
4000
8000
16000
0.29
0.35
0.37
0.56
1.02
0.32
0.41
0.45
0.64
1.2
2.12
3.91
7.21
15.93
33.6
Ir;pHE d p G"! t K p|F; ; d>"!$ ^ d p p ;Hr? p|> p M d f f G?d r @2 Á { p < G r f | frHr?H. £.epG|F? £ |[ r$ r 2r # p[ $ H?ÐpG?Æ G> p@ dprY£.< £ %# & p pG A| p|? p p p M r p G> G
|p z G2 pO7 '(#= ? rp p ! ; . G£. t G£
2 D * 1 B
10
0 0 9 0 J 0 D*,+!%29=(; 0 & 2I-3 I I ? 0 ?129;? 0 BSÃ+ 0 =&eOJr $'&/(0) +#,7 /1293-?B 0 - ? 0 O?129; 0 VJ 0 9>- Y-+=q 0 9 0 ÂK~U¤ 0 D ?3-V zÏP7
0 A
100
3.2.4 kD+ %WTechniques 9 SI I-for 3HQueries LUGwith G3Wildcards M(,%W? -
.
1000
3 C
IrGpHR p tp¢ÆGH f deZ 2 p XHr? !> p X0W rX r dA [ X r d@f¢ p|F . dH<| Z0 p p X0WÐ X r d d D P dHf|2@pG{X0WA pf dO rX p b ] M pHf|2@pG{X0W p d?
8.21
16.78
33.48
70
167.1
- ^99; 0 -? 3 0 0 M*,+ % -T7VÂK ^!/9; 0 tB O +( 0 0 3-34%.I 0 #3H? B(+ 0 0 3- % 7
-? 3W9 - 9(3-12 #I 0 [993- 0 -? 0 @ 0 A1F G?12 0 BD 3-+G' - V129+ 0 - 0 0 -:$C3-? + B,+ -:$D*,+ - B 0 1293- / 0 %.Jb9G 0 - F- { 0 ( 7Ic>z:- ?12&3 -3 +(9M1F 0 ! 0 *+ B12? 0 34%WG:- 0 2PI 0 # 0 9#hMJX?+C*,+ %=9, - Jr12 ";7
3.3
u g4n}?sHSubgraph i G"?" Matching +:$ %$ 0 ? 0
8 #1F 0 - f3-? 0 1 !(;<(;:?- F .JrF! ?129;? 0 7W8 ¤ 0 O9+ 0 J 0 W 0 0 0 1F 0 ! P129;? 0 ? 0 0 + 0 0 & G 0 L1F 0 7pÂK W 0 % - 0 P¤ H 0 {9+ 0 - D:3-#1F 0 #4J 0 z- D9G 0 JI3- 0 O*,+G3 0 0 PI-3H Íp:?3+ V- 0 2*,+ %K(; ' 0 e 0 G 0 HW ? 0 #I 0 #I-3H 7D8 W9G 0 - 0 G 0 92 !"$W+ zD9 0 V 0 0 :$! 3PJ 0 Y9d7 8 - e 0 9 1F% (;>?9 0 -12T (,% 1F- 0 - - 0 0 0 -:$M 3 +M1F 0 - KJ 0 W 0 (G 9 C - - P G 0 z9# 34%.-J 0 DI-3' tÍ 2:3-+ 2 0 ! 0 G E*,+G3 0 0 . 0 0 9G 0 (; 0 0 D 7
1
7
2
3
6
(a)
Ir;pHYGG2uRM tpH¢5GH
&-$-) %" #'$U U G+ 0 W +' 21 !3G /9; -12 0 X? 2_^¤&
Ug oyit 0 (G & 0 - - V+9 0 nyB }?}}O12?3- +3- 7ec>=+ 5{ad- +/f " 0 0 <*+-99; I 0 n/DKTO9; 0 -+1
F9, 7 8 >_z¤&
. 0 (G 9 CG:$z :$ V +1P(; JLx} :$ 3d9 :$X+9 0 Cx?o}C 7dc>9; 0 3-34'\ 3,"V*,+ %- 0 12SJr :-{*,+!% -T PnhB 0 nl?q2 !Bt 0 (G M -T n?B }?}} 'CnyB }?}?}9 !B; G :?3+ zvBG en}?^ V-?+2n}$!7 ÏD-QR! 0 :3-+ KJ - G+ 0 M*,+ %.+ - 0 -12?¥UJr 0 L 1WxD*,+ %,B 0 U1F 0 ! z L 3- 0 1Æ9; Jr12 b(; 00 XI
n}>129G<I 0 vBII- . ? - 0 0 I 0 0 0 12F1293- / 0 %O 34% 7e
\ Y? 0 -? dBb- 0 =!/1' 93- .:$ 4Jr% 0 00 *,+ % 0 -12=- 3- F- 0 . -T J 0 0 (G BU Y /9;? 0 3 - 7 (C33 0 0 0 V +1P(; Jb9G 0 UI 0 - -T 0 0 G:$ 0 2(; 0 0
3.2.5 8d^:3-+GExperimental 0 0 9; Jr1FResults UJ%&"
5 (b)
4
2uXM pfGH
Â] -1293- 0 0 -3S +12 0 -? e3 0 1 0 2G G 0 V, ' + ^J *,+ %#9 - O. 0 =9 j-?+ n?n!B?- 0 C? 0 U3-39;? -(3-L1F9 d(; 0 & 0 b J 0 0 	 V G 0 #"#I 0 V!> ! 0 e1F9e W 1F 0 d7SÂK3-3 0 D1F9 U (;D9 0 =+ - P.°ª)±ª\¬ ½)°j»±$³¬ ¯¬\»¯¬!° ¬!¨ª)±ª§º¨ 0 ?¥K L9 0 XC9G-bJ;1F 0 z:$!' 0 - GP9G 0 .Jr1 0 D, 0 I 0 2P3-HJS9 0 CP1F9 (; 0 0 0 f9 7 9G 0
1F 0 t7 +D 3-%> 0 - <3H:? 9;? 0 fe +(- ?12' 9- 1È(; 0 j-?+.nx?!7M8 M?1293!/ 0 %J +> O3-? 0 1Á- z /9; 0 3Bd(+ 0 0 - 0 M(; 0 " I
3- 0 1 0 K9?(3-1 Jp +(9=- ?129- 1 - 9H:$
0 (;z_DwX')1293- 0 Pg v$xHij7 47
root
(1,4)
(2,5)
(2,6)
root
(1,5) (2,7)
(2,4)
(2,6)
(1,6)
(1,7)
(1,4)
(1,5)
root
(1,4)
(1,5)
(1,6)
(1,7) (1,_)
(2,7)
(2,6)
(3,6)(3,7) (3,5)(3,7)(3,5)(3,6)(3,6) (3,7)(3,4)(3,7) (3,4) (3,6)
IrGpHZ > V p@e SX0W p ; Gz > | / df.Hb? Mp; r K \H f z GHH E ep
(3,7) (a)
(2,4) (2,6) (2,7) (2,_) (3,4) (3,7) (3,_) (b)
Ir;pH@ H d>HY GE AHG' Z p M | G |/E@uR H d>H Z G? pZt¢ ÀJ f ] r E \b H d ' G p¡d ¢ # | Z r Gr E H d f' HHReH ' p p r LWG f= pVY d' r¢d pe |p = \ ? <rM <; pY pYY p? . LHR= |d \ ? p{ p{H ' LR r¢G
8 H:?&(; W1F ,%V 00 129 0 0 K+ 0 L?1M(- G 0 3 ? 0 J ÂC¤ *,+ %9, - .- f9 zz"? %9f ' - 78 %E <(;#3 4G F99/-1F 0 ?B& / 0 BU G !/ 0 3- 0 12 7AÂK99/1F 0 =3-? 0 12 g yBCxoBUh?oBUv?hB qn?Btn}n idG:$D9;34% ?123; ?1293- / 0 %(+ 0&0 %=HD 0 ?+' 0 0 G>. 0 3+ 0 -? d7#ÄX/ 0 Gf / 0 3' 0 12 IM GF 0 K 0 J|zG:$^!/9; ' 0 3b& 0 ') 2 ?1293- / 0 %5g4n vBSv?lBXs}By?hBSovBXoqBSl?xB&n}$xi)7
\ / 0 3-? 0 12 =1293-%5 = 0 -? 0 ! *,+ Jr . ?- %f 0 .9t7=8 3-? 0 12 V1293-%e 0 J|+ ' 0 - 0 V12 + 0 I -12-3 0 %2J 0 I9 7b !/1293-?B$ ? 0 Jr+ 0 -? 21F%W(;K G P( 2 1F 0 -IL % 0 0 - 0 Jr1F 0 - 0 0 Jr1¡? =9Y 0 0 7Y +KJ ?+ Bb99/-1F 0 23-? 0 12 W 53 (;F+ fJ|P ?- % 0 z9 7 (K 3 :? 0 &"P F(; J|+ G- g x}BxnBhn?BhyB hqBpy$s,BSosBdl?qBq?oBdq?lHi)7M8 P12? 0 9;?9+3z!/ 0 j G{ /' 0 K +(9{1F 0 - .3-? 0 12 VP( f+- 0 - 0 K 0 0 ') 9GD9 0 0 -? 0 0 G 0 9;? G 0 W +(- ?129 1#7 À f e Gr 57mD3-3-1F @g q?}i&9 0 > 53' 0 1 J|= ]¬Ë$±?³ ªK +(9E1F 0 - f( E? 0 f°ª)±ª\¬ °j»±$³¬=° ¬±¯³« É §|ªr«>¾±$³ 0ª¯±?³ 0§|¨´=3-? 0 1¡
0 5- 0 Y {- 0 0 e 0 34%1M+ 0C0 V +( 129- 1 ? G 0 ^?3tBG(+ 0 BG e' 0 dBV9;? -(3-^1F99- z1P+ 0 /- 0 J|W±?²|² 0 C+ 1F 0 ! :? 0 - 7=ÂK V= +3 0 B 0 23- 0 1¡9+ 0 0 !'\ 12z 62- 0 34%. 0 P C3-:$ 3L V-+nhj$!7 ¬Ë$ ±?|³ ªI +(=L 9rE G1Fr 0 ! - { H3-H7U_K 0 3- 1# 75 Y8 g oq-iX 90 -12 ? BL0 #( > 0 §|¨G'½ 0 ? 0 0 0 ') 9Ge 9 0 0 0 e9- 0 0 W3-? 0 1#Í K9? 7CÄL!{ z- 0 0 ') H!# 9' 0 K:? 0 /=- M0 0 G C(; # 0 !K1F 0 !2I 0 # :? 0 /F-
C3- 0 t7X
\JpM:? 0 /2- 0 W(;z3- 0 tB
0 - z1F 0 0 #= +3-3X:$ 0 /- 7P ? 0 - W -? 0 0 =1F 0 - e(; 0 0 e:$ 0 - 7E8 =? 0 Jz{9GH 0 3 1F 0 - W- 0 D +1 J 0 K? 0 UJ 0 D1F 0 F:? 0 - 7b J|+ 0 - 2:?3-+G 0 0 U9 0 31F 0 - ^(,%M +1212- D 0 b 0 0 KK3- X(;+ Gz 0 -1F 0 PJ 0 L? 0p0 D1F 0 0 X1F- ' - W:$ 0 - L- 7b8 0 C .- !/9 0 W 0 0 &J| I- 0 #:3-+G 0 -?+nh(G!7 4. c>CGCONCLUSIONS :$IJ|, + F9-1F-34%2AND
=9 00 FUTURE ')1F 0 - zWORK ( =3-?'
0 12 zJ|MJ| 0 - 0 W Gf9 7#8 .3-?' 0 12 M?+3E(;+ 5Jr=- 0 +99; 0 Jz*,+! ? 0 0 0 %9; BRz ?+3(;P+ { zF9 9, zJ| Ã ')3-"$ 3- 0 12 Vg sHij7&+ 0 +D ".- 0 - I3.- 3+ ¥
48
u129H:$ 0 9; Jr1F JV / 0 - Y"$ % 0 # H!' 3-? 0 12 2?7 79! "$##%&"$# $K G{"$ %9{ H!' V3-? 0 12 D7 7&%" &-$-) %"$# $X 0 0X0 %P 2(;C J 0 b"$ % P H! V b3-"$I,??3-?7&# %PJ 0 3-? 0 12 2.1P( ?34%E9GH3-3-3-T(3- I3-3d 3-z 3-37 Ï^:$3-9<- G / 0 00 0 12FJ|F 9G#?9 0 -1F3-34% 0 - Y3-3D9G 0 21F%5(;12 0 G <- = tB&(+ 0 0 - DÃu+ 0 9GH 0 ')!3=9G4 C1F%F(; 0 ,23- 00 3-H!7 Ï^:$3-9>9 0 -3-34%Y12 - J|+3&- 0 F12 + W?
0 # G9 # 99/1F 0 e*+ %@9, - 3-? 0 12 0 +99; 0 - / 0 1F 0 - 7 Ï^:$3-9V&Jr12! "KJ|p 3- 0 -: 0 %^ 0 1F 0 -? ^J|S*,+! ? 0 K G=9 UI 0 I-3H 7 Ï^:$3-9MJr12 "=Jr 0 + H! 0 9G 00
- H:$ %=- 0 C G.9 Vg h?hBGqvB;q$s,Bpn}?}ij7
g4nhHiVÏP7G~&(;? B;ÂV7G~ H 0 BGÂW7 +M7; G 3T ? dB M7;ÂV7 -3BR&7 (CT T?3-BG w7 (C-+T ' D+ 33-7R8p` '&8 V8p 0 `z#aO ?- ?7
\ ¯º³¬¬©§|¨´°Mº¼^ªr«¬ #º¯ 0°«º!»>º%¨ ¨¼º¯µ2±ª§jº¨ ¨ª\¬j´¯±ª§jº¨Oº¨{ªr«¬( #¬¾ B 9G Cy?y ohBtx}}n7 g4nv2i M7~ H G (V7f7~&+ 0 3-3j7N+(9=- 129- 1#B 1F 0 - W3 0 -? 3p 0 + 0 + K G=1F/-1F3R3-*+ 7 ¨¼º¯µ2±ª§jº&¨ ¯º³¬!°°§r¨´ 3¬!ªª\¬!¯°B;v¥ l?h lvBSnq?oy7 g4nHsiMNR7~&$BGÏM7;¤&1P(;!3- tBGf7G&7G G G T?BÏP7 3 +tB;7 (K(-?B7RN-12? tB Gf7RN 0 !J +t7 `DkD+ %n?7 }¥ ÂC `z#aOkD+ %.ad +G? GH:-3(3-M 0 00 9t¥ " "HUUz7 Ch7 - "8 (M"/*,+ % "7 g4nyHiWwS7~&+ 1F d7N12- 0 + 0 += 0 7
u%
U¯º³!¬¬©§|¨,´°Mº¼ ªr«¬^Ê p ¸ '!b¸#"L·V)½ '!bÊ*S+½ !LÊ ,- ̵D»º°§|µ º¨ U¯§|¨;³ § »;²¬!°Vº¼K·W±ª)±$¾±° ¬ Ì°ª\¬!µP°B;9G? znnHo nHx,n?BSnqq$o,7 g4nHoiWwS7~&+ 1F dBNR7~K7Ïz: ? tB M7 M7 K3-3-( GRBG G ÏP7;N+-+t7ÂZ*,+ %=3 ?+G?W .9 0 -12-T 0 -?
0 ! *,+ LJ|I+ 0 + 0 +F 0 7
u ¯º³¬¬©§|¨´°Vºu¼zªr«¬ Ê p. ¸ !L¸#"L$ · ¨ª\¬!¯!¨G±ª§jº¨G±?/² bº¨¼¬!¯¬!¨G³¬Pº¨ ¸f±¨;±´,¬!µF¬!¨ªUº¼K·W±ª)±B9G? Ks}?s snyBSnqq?y7 g4nlHiWwS7~&+ 1F dBc[7G tBG GNR7c>- 0 t7GwS 0 ? 0 - 0 C- # 12 0 + 0 + . 0 + 0 + 0 (G 7G
\
¯º³¬¬©§|¨´°Mº¼^ªr«¬DÊ p. ¸ !L¸#"L· '!LÊ*# '!LÊ ,0 ̵K»º°§|µ º¨ U¯§|¨G³ § »;²¬!°Vº¼ ·W±ª)±$¾±° ¬ Ì°ª\¬!µM°BG9G znHxq nh?lBSnq?ql7 g4nqHiWwS7~&+ 1F dBf7G&7 T?B GÏP7N+-+d7mD Gk^ab¥  *,+ %=3 ?+?W G3-?(PJ|C 12- 0 + 0 +. 0 (G ? . 0 + 0 +3R+ - d7 3·K¿ º¯!¨G±?² B qnH!¥ oy nn}Bdx}?}}7 g x}H2i M7~&+ "$?7ÄXC 0 29#1F 0 ! ¥ +D 0 G+ DJ 0 z+ G 34% P 0 J|+ 0 -? t7 ¯±¨°!±$³ ª§jº¨°Pº&¨ C±ªª\¬!¯¨eÊC¨G±?² Ì°§r°V±¨;©P¸f±$³«,§|¨R¬ ¨ª\¬ ²|² §´,¬!¨G³¬!B;x,n$jq$!¥ qnHo q$xxBXnqq?q7 g xn!2i M7~&+ "$z G M7ÂK3-3- 1F d7
u / 0 9#1F 0 - J|C 0 + 0 +3d9 00 ? 0 -? d17 C±ªª\¬!¯! ¨ C¬³º´¨§rª§jº¨ 3¬!ªª\¬!¯!°Bn?v,!¥ xv$s x?shBXnq?lh7 g x?xiMNR7GNR7¤&GU 0 ?B;NR7ÂK( 0 (;?+3jB 7c1#7 (K9 0 - P G*+ %- PG I . 12- 0 + 0 + 0 7
\
¯º³¬¬©§|¨´°Mº¼^ªr«¬ ¨ª\¬!¯¨;±ª§jº¨;±² bº¨¼¬!¯¬!¨;³¬Pº¨#·V±ª)± ¨´§r¨R¬¬!¯!§r¨´BG9 Iv nhBnq?ql7 g xhHiMNR7GNR7¤&GU 0 W W7 ^H'u?3-- G7d - Jr+3 ! V 0 0 -? #- 0 + 0 + 0 7
u%
U¯º³!¬¬©§|¨,´°Mº¼ ªr«¬^Ê p ¸ '!b¸#"L$ · ¨ª\¬!¯¨;±ª§jº¨;±/² bº¨¼¬!¯¬!¨;³¬Pº¨ ¸f±¨;±´,¬!µF¬!¨ªUº¼K·W±ª)±B9G? Kxy h?oBnq?q$o,7 g xviMNR7NR7¤&G 0 BGÂV7 (DÃH1F tB W7 ^'u3- BR G 7c@?1#7G¤&G ?V 0 0 - #- - H!-3-34% 0 + 0 +.- Jr1F 0 d7
u%
U¯º³!¬¬©§|¨,´°Mº¼^ªr«¬zÊ p¸ '!L¸#"b$ · ¨ª\¬!¯¨;±ª§jº¨;±?/² bº¨¼¬!¯¬!¨;³¬Pº¨¸f±¨;±´,¬!µ2¬!¨ªIº¼ ·W±ª)±B9G? Iv$qh s}vBSnqq?y7 g x?s2i S7G¤& tB W7ÎM7$??- tB;&7 z dB_M7 z?+ B;N;7 + 0 +",- dB (V78D7_KB G.ÏP7N-:? 0 :?7 ¤&?+ 0 - 0 I-1F 0 U # 0 ?7
u%
U¯º³!¬¬©§|¨,´°Mº¼^ªr«¬ ¨ª\¬!¯¨;±ª§jº¨;±/² bº¨¼¬!¯¬!¨;³¬Pº¨·W±ª)± U¨,´§|¨R¬¬!¯§|¨´B 9G Ksq?s y}vBdx}?}n?7
Ï^:?3-?9 +99; 0 JrL 1F 0 -U / 0 - ¥S 124' G!/-(3 /-(3-*,+! 2g syiL- fI-f9 0 ')-3{3 0 ' -9 2 A*,+ - 21F%5(;12# 0 '\ G 0 :$ G 0 '\ 0 X3 0 9 L- P 0 K9 7
H" z FÂK(;?-B K2 D-3-B V 0 - D!(; 0 B-D+4%+
0 GACKNOWLEDGMENTS N G > >N ;G Jr 0 4V 0 (+ 0 -? V 0 :-+ 9G IJ 0 ! "$##%&"$# $W9Ãu 0 7
5. cO
6.g-n!iWNRREFERENCES 7ÂK( 0 (;?+3j7kD+ % 124') 0
+ 0 += 0 7
\
¯º³¬¬©§|¨´°Mº¼^ªr«¬¨ª\¬!¯!¨G±ª§jº¨G±?²bº¨¼¬!¯¬!¨;³¬Pº¨ ·W±ª)±$¾±° ¬d «¬º¯!ÌBG9 zn nlBnq?q?o7
g xiWNR7ÂK( 0 (;?+3jBw7~&+ 1F tB G=ÏP7;N+-+t7;·V±ª)±º¨ªr«¬ #¬¾ ¦t¯ºµ I¬ ²-±ª§jº¨°^ª) º R¬!µP§r°ª¯³ ª¯¬©F·W±ª)±.±¨G© 1K4 ¸ 3X7G?
V+J|1F dBRnq?q?q7 g hHiWNR7ÂK( 0 (;?+3jBÏP7GkD+G BG7R K+?tB7c?1#B 7 ab7c- 7G8 Vad3*,+!%F3 +GzJ| 12- 0 + 0 +. 0 7 ¨ª\¬!¯!¨G±ª§jº¨G±?² º¯¨;±?²pº¨#·z§´§rª)±?² 3X§¾ ¯±¯§)¬!°Bpn?nH!¥ y?l l?lBSnqq$o7 g viWNR7ÂK( 0 (;?+3d G=ÎM7ÎD +d7 (C?+3K9G 0 *,+ - I 0 0 - 0 7 º¯¨;±²º¼ bºµK»Gª\¬!¯P±¨;© Ì°ª\¬!µ ;³ §j¬!¨;³¬!°BRsljh$!¥ v,xl v,s?x,BXnq?qq7 g siWNR7ÂK34' zG3--J|B M7ÎM7$$?- dB;_W7 z+G B7;f7GwS 0 3B ÏP7GN-: 0 :?B GL P7c>+t7GN 0 + 0 +3à ¥L 9-12 0 -:$KJrI 6- 0 `z#ae*,+ %F9 00 =1F 0 - 7,
u
¯º³¬¬©§|¨´°Mº¼^ªr«¬ ¨ª\¬!¯¨;±ª§º¨;±?² bº¨¼¬!¯¬!¨;³¬Pº¨ ·W±ª)± ¨´§|¨;¬¬!¯!§|¨,´BRx}?}$x,7 g yH9i M7ÂK3-12G1F. GNR7 +M7ÏD+QR+G7ÂZ3-- H 91212 99?J| 0 ^ 0 9 1F 0 - P9(3-1#7 ¯±¨° ±?³ ª§jº¨°Mº¨ I±ªª\¬!¯¨ ÊC¨;±² Ì°§|°V±¨;©P¸f±$³«§|¨;¬ ¨ª\¬ ²|² §´,¬!¨;³¬!BtnHs)s?!Bpnq?qh7 g oiWf7ÂK3 0 - 3d f7G7G "3-- d7ÄX62 0 3 0 ! J `z#aO,+12 0 &J|D 3- 0 :?V- 12- G 0 #J - Jr1F 0 - d7G
\
¯º³¬¬©§|¨´°Wºu¼Vªr«¬ ¨ª\¬!¯¨;±ª§º¨;±?² bº¨¼¬!¯¬!¨G³!¬Mº ¨ G¬!¯2Ì 3p±¯´,¬z·W±ª)±¿K±°¬!°B;9 Ksh yvB x}}?}7 g lHiWNR7ÂK12!' &BNR7G¤&BGaX7ÎW7NR7ap" 1F G dB .ÏP7 N-: 0 :7G -12T 0 -? #J 0 z9G 00 #*,+ - 7
\
¯º³¬¬©§|¨´°Mº¼^ªr«¬zÊ p ¸ !L¸#"L$ · ¨ª\¬!¯!¨G±ª§jº¨G±?² bº¨¼¬!¯¬!¨G³!¬Mº¨#¸f±¨;±´,¬!µF¬!¨ªUº¼K·W±ª)±B9G? Iv$q?o s}?lB x}}n7 g qHiWNR7ÂK12!' &BNR7G¤&BG G=ÏP7;N,-:? 0 H:78d 9G 00 . 3H/ 0 -? t7G
u%
U¯º³¬¬©§r¨´°Mº¼^ªr«¬ ¨ª\¬!¯!¨G±ª§jº¨G±?² bº¨¼¬!¯¬!¨G³!¬Mº¨ L˪\¬!¨G©§|¨´·W±ª)±$¾±° &¬ ;¬³«,¨;º?²-º´ÌBtx}}$x,7 g4n}i (V7G~ TH' & 0 7GÂC3 0 12 UJrC 0 - 2 H! ¥L +:? %,7 '! ¦pº¯µMB;xhjhH'\v$!¥ hv slBSnq?lq7 g4nn i (V7G~ TH' & 0 K GJ M7 M7 D 0 7GG 0I0 / 0 - J|K ?+3HK!/9 -? KD+ 0 1F 0 ? . - ?
0 - 7 º¯¨;±²º¼^ªr«¬zÊ p¸Bv?hjy?!¥ qnHs q?hyBXnqq?y7 g4nxHi (V7G~ TH' & 0 K G.~K7 (C-(;4')_D 0 7R¸eº©,¬!¯!¨ ¨¼ º¯!µ±ª§jº¨ I¬!ª¯!§j¬!®±?² 7;ÂC¤U wS "ÂK- 'jc> 3- %,B nqq?q7 49
g h?qHiMf7 '\aX7G! G T^ GM7ÎL3-- 0 ?7ÂZ9- 0 12 0 -^?1M(- - P1F/-1P+1Ð ?1212? . +(9# G 12 -1P+1 1212? +9; 9t17 I±ªª\¬!¯¨ I¬³º´¨§|ª§jº¨ 3¬!ªª\¬!¯!°Btosh o?slBdx}?}n7 g v$}HiWÂW7 B M7 ^3-3-B (V7 D+? B; G.ÂW7wb+3-:4 0 7 ~& 0 ')1F 0 . 0 -:3RJ|C 0 + 0 +.-1F 7 ¯±¨°!±$³ ª§jº¨°Pº&¨ C±ªª\¬!¯¨eÊC¨G±?² Ì°§r°V±¨;©P¸f±$³«,§|¨R¬ ¨ª\¬ ²|² §´,¬!¨G³¬!B;xh)o?!¥ o}$o onlBpx}}n?7 g vn!izc[7G~C7G"$ C (V7~ T' 0 7 ¨¼º¯µ2±ª§º¨ ^ C¬!ª3-¯3Bt§)¬!n®q?±?q?² x I7 ·V±ª) ± ª¯!³ ª¯¬!°P±¨G©ÊK² ´$º¯§|ªr«µM°7GwS 0 - g v,xiMf7 ^H %# GÏM7? ? t/7 bºµK»Gª\¬!¯!°W±¨G© ¨ª¯±?³ ª)±$¾ §² §|ªÌ IÊ §j©,¬zª)ºFªr« ¬ d«¬º¯Ìºu¼ U½ bºµD»;²¬!ª\¬!¨;¬!°°7R1F #¤&?129 ,%,BRnq?oq7 g v$hHiMNR7 D?3# ÂV7 (K $à d7GÂZ+ 0 # -? 12 0 3-? 0 1 J|C91F 0 - 17 ¯±¨°!±$³ ª§jº¨°Wº¨ C±ªª\¬!¯¨ÊC¨;±?² Ì°§|°V±¨G©¸f±?³«§|¨R¬ ¨ª\¬ ²|² §-´,¬!¨;³¬!B nlv$!¥ h$o?o hl?lBXnq?q?y7 g v?vi (W7 D?31F G7c?1#7Ïz 0 D+ ¥LÄX G(3-- *+ %2J|1P+3 0 -? G9 0 -12-T 0 -? . 12- 0 + 0 + 0 (G 7G
\
¯º³¬¬©§|¨´°Mº¼^ªr«¬ ¨ª\¬!¯¨;±ª§jº¨;±?² bº¨¼¬!¯¬!¨;³¬Pº ¨ ¬!¯2Ì 3p±¯j´,¬^·W±ª)±P¿K±° ¬!°BG9? Kv?h?y v?v$sB nq?q?o7 g v,sHi M7 W7 D 0 &7c[78p?1297- G=%$?+I121FH¥ ÂZ ! 99$ 0 123-- 0 !/ 0 7
u%
U¯º³¬¬©§r¨´°Wº¼ ªr«¬ ¨ª\¬!¯!¨G±ª§jº¨G±?/² bº¨¼¬!¯¬!¨G³!¬Mº ¨ G¬!¯2Ì 3p±¯´,¬z·W±ª)± ¿K±° ¬!°BG9G? Kh?hq hv$yBnql$o,7 g v$yHi (W7 M7 D+ 0 - 7 K9Ïz~K¥G3-- F G.*+ %- 9 I- 0 ( 7
u
¯º³¬¬©§|¨,´°Wº¼Vªr«¬ ¨ª\¬!¯¨;±ª§jº¨;±?/² bº¨¼¬!¯¬!¨;³¬Pº ¨ ¬!¯*Ì 3d±¯j´,¬z·V±ª)±P¿K±° ¬!°B 9G Kxq?o h}?lBSnq?qv7 g v,oiMf7 K% B;7wS B; G.ÏM7ÎW7 D+! 0 7 9')- 0 =?(à 0 0 ( z1237
\
¯º³¬¬©§|¨´° º¼^ªr«¬zÊ p ¸ '!L¸"L·V)½ '!LÊ*S)½ '!bÊ ,# ̵D»º°§|µ º¨ U¯§|¨;³ § »;²¬!°zº¼D·W±ª)±$¾±° ¬ Ì°ª\¬!µP°B;9G? IvnHo v,xHvB nq?q}7 g v$lHiW8D7;¤K7 D d7G·z§|°!³ ¯¬!ª\ ¬ C¬ ²-±Ë$±ª§jº0 ¨ R¬³«¨§ G¬!°7 +K/Jr=mD -:$! 0 %.wX Bdnqq?}7 g v$qHiM¤K7;f7 DQR1F Gf7;7 +MÍ Ï^? 3-37GwS 00
1F 0 - M 0 7 º¯!¨G±?²º¼^ªr«¬^Ê p¸{Bxqn!¥ y?l q$s,B nq?l?x7 g s}Hi (W7 D+# 8D7GN"$ 7GN 0 ! 9;? 0 ?+?=J| 0 +V+9- 2 .1F/-1F3R3-*,+ 17 ¯±¨°!±$³ ª§jº¨°Pº&¨ C±ªª\¬!¯¨eÊC¨G±?² Ì°§r°V±¨;©P¸f±$³«,§|¨R¬ ¨ª\¬ ²|² §´,¬!¨G³¬!Bdnn$n?n!¥-n?nyl n?nl}Bbnql?q7 g sn!iW7G??""$32 GwS7 z-3-9;3- d7GmK - 9J| *+ %- P 0 + 0 + 0 / 0 G3- 7mD -:$ 0 %=J D3- - "B Ï^9GH 0 12 0 JX¤&?129+ 0 KN ?B (C9; 0 ¤L'nqq?y'\lhB _D"H+ :$"Ã1MÃ?(; "^"$?nq3 "q? #y ;9d:?7 -30 12(33-W7 0 00 9d¥ " "UUz7 7 3- - "7 g s?x2i M7ÎM7$?? tB +M7 V9 0 "B (V78D7_DB GÏM7 N-:? 0 :?7;+3 0 4')Ï^-12 G3d +( 0 - M 3- 0 -: 0 % 0 -1F 0 -? t7
\
¯º³¬¬©§|¨´°Mº¼^ªr«¬ ¨ª\¬!¯¨;±ª§jº¨;±?² bº¨¼¬!¯¬!¨;³¬Pº ¨ ¬!¯2Ì 3p±¯j´,¬^·W±ª)±P¿K±° ¬!°BG9? Dhl$o h?qlB nq?qq7
g xyi27;¤& dB&7 z dB_M7 z?+ BG GN;7G+ 0 +",- G d7 N 3 0 -: 0 % 0 -1F 0 .JrK(;,?3- {*,+ - 7
\
¯º³¬¬©§|¨´°Mº¼^ªr«¬zÊp¸ !L¸#"L·z½+ !LÊ*S½+ !LÊ , ̵D»º°§rµ º¨ ¯!§r¨;³ § »;²¬!°^º¼D·W±ª)±$¾±° ¬ Ì°ª\¬!µM°BG9G xny x?x?s,Bdx}}?}7 g xoHizc[77G¤&- 0 1F B7 z 00 3- BG G.f7Gw 0 ?+d7N 0 + 0 +3 1F 0 - P- #129+ 0 !U: - #+ - P9?((3-- 0 - 3/ 0 d7 ¯±¨°!±$³ ª§jº¨°Mº¨ C±ªª\¬!¯!¨ÊC¨;±?² Ì°§|° ±¨G©¸f±?³«§|¨R¬ ¨ª\¬ ²|² §-´,¬!¨;³¬!Bdnojl?!¥ oHv$q oyvBXnqq$s,7 g xli (V7;¤&3B (V7 D-GH tB; w7
u G%"R78tz9G 00
1F 0 - . +( 0 1F 0 - P- # 0 12- - 0 - Az3-? Ad\' 0 -12?7
\
¯º³¬¬©§|¨´°Mº¼^ªr«¬zÊ p¸{+½ ÊK¸ ̵D»º°§rµ º¨#·^§|°!³ ¯¬!ª\¬zÊK² ´$º¯§|ªr«µM°B9? ^xHv,s x?sHvB nqq?q7 g xqiMf7wS7G¤&? K ÂV7 +M7 3-T dB K9ad?¥L :- +G3RJ|1F3-- 1 J|C3d3-4J|z+ -? d17 U¯º³¬¬©§r¨´°Wº¼ ªr«¬zÊ p ¸ !LÊ*S+½ !L¸#"L·z+½ !LÊ ,- ̵K»º°§|µÈº¨ ¯!§|¨G³ § »;²¬!°Vºu¼D·V±ª)±$¾±° 2¬ Ì°ª\¬!µP°BG9 Kv?}v vnyBnq?q}7 g h}iVÏP77G¤&,?"# G.ab7~K7 K?3!7;N+( 0 + 0 +^- H:$ % + - 12- -1P+1 -9 0 -? #3- 0 G.(G"+ G " I3-?7 º¯¨;±²º¼KÊC¯ª§ &³ §j±² ¨ª\¬ ²r² §´,¬!¨;³¬ I¬!° ¬±¯³«B n?¥ xhn x?ssBXnqqv7 g hn iWab7G¤&3-3BRw7??B;¤K7RN ?B #f7ÎL 0 7ÂC
62 0 3 0 1 Jr 0 z- !/ 0 1F 0 - PJbH 9 C+ - 2P ? 0 / 0 +G3 0 J|1F 0 -? 3d1237
u
¯º³¬¬©§|¨´°Mº¼^ªr«¬ ¨ª\¬!¯!¨G±ª§jº¨G±?² bº¨¼¬!¯¬!¨;³¬Pº¨ I±ªª\¬!¯!¨ C¬³º´¨§rª§jº¨B:$?3-+12^hB9G? znl} nlvBSnqq?y7 g h?xHiVÏP7G¤& -3 #¤K7G¤K7 D 0 3-(t7;ÂC 62 0 3-? 0 1 J|D9- ?129- 1#7 º¯!¨G±?²ºu¼zªr«¬zÊ p¸{B nHonH!¥ sn yvBSnq?o}7 g hhiWab7Ï^ 9;?B M78p:?? dB G (W7ÏP7 z- 7G- G- Jr*+ 0 +( 0 + 0 + U- #!12-3t129;?+ 7
u
¯º³¬¬©§|¨´°Mº¼^ªr«¬ ªr&« ¨ª\¬!¯!¨G±ª§jº¨G±?/² bº¨¼¬!¯¬!¨G³!¬Mº¨ V¨Gº É ²¬©´,¬z·z§r° ³º®¬!¯Ì=±¨G©·V±ª)±2¸{§r¨§|¨,´B9 Ch?} h?yB nqq?l7 g hviWÂW7ÏD+ 0 dBf7&7 GT?BÏP73- +dBÂW-7 M7at:,%,B .ÏP7GN+-+d7Â[*,+!%F3 +GzJ|K`z#aX7 bºµD»Gª\¬!¯ V¬!ª É º¯ 0°BRhn$n?n!'ny$!¥-nnHs?s nny?qB&nq?q?q7 g h?sHiMNR7Ï&Ãu?"$BÏP77G¤&,?";B; G.ab7~K7 K?3!7GÂC 129--3 0 +G%=JX?1F- ." I3?V G 0 I(; 0 0 +( 0 + 0 +z- H:$!%,17 ¯±¨°!±$³ ª§jº¨°Mº¨ V¨Gº É ²¬©´,¬P±¨G©P·V±ª) ± ¨´§r¨R¬¬!¯!§r¨´B;qv,!Btnqq$o7 g hyiMf7ÂW7Äb J 7 'uNR7+d7 9- 0 z12 + J|D-1F?V 34% - 7 ¯±¨° ±?³ ª§jº¨°Mº ¨ Ì°ª\¬!µM° ¸f±¨ L±¨; © SÌ$¾¬!¯¨R¬!ª§j³ °Bn vjh?!¥ h?sh h?yhBXnqlv7 g h?oHiW7G Bf7;ap+1W%,B Gf7ÏD?127
\ / 0 1F 0 - + - +3t 0 " 7
u ÄI7 D3- 1F G#aX7 _M7 V 3B 0 1B C±ªª\¬!¯! ¨ C¬³º´¨§rª§jº¨e§|&¨ U¯±$³ ª§j³¬ '
¸{² ª§ »;²¬ I±¯±$©§´µP° bºµD»±¯±ª§|®¬ ª©§)¬!°W±¨G© DÌ$¾ ¯§j© Ì°ª\¬!µP°7;_K 0 D33 GtBtnqqv7 g hliMf7&7; T?BÏP73- +dB;7 V BÂW7 P7at:,%,B .ÏP7GN+-+d7¤ 0 - 0 ^(;? 0 I 0 # 0 +G3¥ ÄS/9;! UI 0 McO(') 0 ^1F G12 0 % 0 1#7
u
¯º³¬¬©§|¨´°Mº¼^ªr«¬zÊ p ¸ !L¸#"L$ · ¨ª\¬!¯!¨G±ª§jº¨G±?² bº¨¼¬!¯¬!¨G³!¬Mº¨#¸f±¨;±´,¬!µF¬!¨ªUº¼K·W±ª)±B9G? Ivn v v,x?s,B nqq?l7 50
g shi2M7ÎM7$$- dBRaX7ÎW7NR7ap" 1F G dB8D7G3-BGÏP7 N-: 0 :B G=ÏP7ÎD- 0 7GkD+ %- M 0 " 4 0 - 7G
\
¯º³¬¬©§|¨´°Mº¼^ªr«¬^Ê p. ¸ !L¸#"L· ¨ª\¬!¯¨;±ª§jº¨;±/² bº¨¼¬!¯¬!¨;³¬Pº¨¸e±¨;±´,¬!µ2¬!¨ªIºu¼D·V±ª)±B 9G? Vnhh nv?vBnqq?q7 g sHv2i M7ÎM7$$- dB (V78D7G_KB ÏP7N-: 0 :?7 N+( 0 - M 3- 0 -: 0 %. 0 -1F 0 -? t7G
u%
U¯º³¬¬©§r¨´°Wº¼^ªr«¬ Ê p ¸ '!L¸"L·V)½ '!LÊ*S)½ '!bÊ ,- ̵D»º°§|µ º¨ ¯!§|¨G³ § »;²¬!°Vºu¼D·V±ª)±$¾±° 2¬ Ì°ª\¬!µP°BG9 ^xHv$q xy}Bnq?qq7 g ssHiM¤K7;ÂV7$12 BÏP7c>- ? B 7Ï^3 ,%,7G·W±Ì?² §´H«,ª d«¬º¯Ì¸f±¨±?²4½|·W±Ì?² §´H«,ª . 7Ï^%3--? 0 ¤&12-3
u J|1F 0 -? {N,% 0 12 B,UUz7 %3- 0 7 1#Btx}}?}7 g sy9i P7 V T GL M7N-:R7G3- /(3-V*+ - IH:$ 12- 0 + 0 +. 0 7
\
¯º³¬¬©§|¨´°Mº¼^ªr«¬DÊ p¸ '!bÊ*S+½ !L¸#"L·z+½ !LÊ ,# ̵D»º°§rµ º&¨ U¯§|¨G³ § »;²¬!° º¼K·W±ª)±$¾±° 2¬ Ì°ª\¬!µM°BRx}}n7 g soHiWw7 z-3-9;3- d7G8dz1F 0 - P9(3-12 I 0 993-- 0 - 0 0 + 0 + 0 !/ 0 0 (G 7 (C9; 0 ÂC'nq?q$x'\yBGmK -:$ 0 %FJ D 3 - "B- 3 tBtnq?q?x7 g sliWw7 z-3-9;3- J M7# -37 (K 0 :?3tJ?1 - H!-3 0 / 0 C(,%F9 0 3d9G 00 ! 7
u
¯º³¬¬©§|¨,´° º¼^ªr«¬ ªr«.ÊC¨¨±?1² ¨ª\¬!¯¨;±ª§jº¨;±?²tÊ p ¸ ! bº¨¼¬!¯¬!¨G³!¬Mº¨ C¬!° ¬±¯³«{±¨;©P·M¬!®¬ ²-º»GµF¬!¨ª §|¨ ¨¼ º¯!µ±ª§jº¨ I¬!ª¯!§j¬!®±?² BG9? Dx,nv x?xxBSnq?q?h7 g sqiWw7 z-3-9;3- J M7# -37;kD+ %=912 0 -:$ Jr
¯º³¬¬©§|¨,´°Pºu¼zªr«¬zÊC¨¨±² 0 ') 0 + 0 +. 0 7
u ̵D»º°§rµ º¨ bºµ2¾ §|¨G±ª)º¯§j±?² C±ªª\¬!¯!¨¸f±ª)³«§r¨´B9G xnh x?x?s,BSnqqv7 g y}iWw7 z-3-9;3- J M7# -37 +K + 0 z 3-+ -? t7 ÊK ¸ ./bºµD»ª .-B xv)x?!¥ hv?} h$syBXnq?q?s7 g yn iWw7 ^- G tBG7;N;7ÎK 00 !B G#~C7 (V7
\%, 7ÄX 0 1F 0 - 3-9G +12 -^ 3- 0 -: 0 %. 0 ^9 zJI-3H 7
u%
U¯º³¬¬©§r¨´°Mº¼^ªr«¬^Ê p. ¸ '!b¸#"L$ · ¨ª\¬!¯¨;±ª§jº¨;±² bº¨¼¬!¯¬!¨G³!¬Mº¨#¸f±¨;±´,¬!µF¬!¨ªUº¼K·W±ª)±B9G? Kxl?x xq?hB nqq?y7 g y?xHiW8D7c 7at+ B M7; 0 3-3B;~C7RN+(1F dB~K7Î& ?B NR7ab7ÎL G (; B G#N;7~K7 R -";78 VÂCkDm^ 0 12 3d G#3-?(7G
\
¯º³¬¬©§|¨´°Mº¼^ªr«¬ ªr« º¯ 0°«º»Yº¨#·W±ª)±$¾±° ¬ U¯º´¯±µMµP§|¨,*´ 3p±¨,´±´,¬!°B 9G? VnHso nHo?s,Bnqq?h7 g yhHi M7ad:7G 0 z? 0 z -: 0 -? JS1FH/-1F3t ?1212?
+(9 IJ 0 &24 0 C+ 4 0 .9 7 b±?²-³º?² °Bq¥ hvn h?svBbnq$ox7 g yviMkM7add G.~K7G,? d7
u /- P G.*,+ %- M`z#a> 0 J|K ?+3HK9 0 . /9 -? 7G
\
¯º³¬¬©§|¨´°Mº¼^ªr«¬ ¨ª\¬!¯¨;±ª§jº¨;±/² bº¨¼¬!¯¬!¨;³¬Pº¨ ¬!¯2Ì 3p±¯´,¬z·W±ª)±P¿K±° ¬!°B 9G? Kh?yn h$o}Btx}}n7 g y?sHiW7Gad3?? B;ÄU7G# 0 B; G7ÎK3-3 +:?7;N,%1P(;?3 ? 0 - (%= ' 0 ?3- 0 +(9#1F 0 ! (; 0 .?-? #?à %.9 7 ¯±¨°!±$³ ª§º¨° º ¨ I±ªª\¬!¯!¨ÊC¨;±² Ì°§|°V±¨;©P¸f±$³«§|¨;¬ ¨ª\¬ ²|² §´,¬!¨;³¬!B xhn}?!¥nnh?o nnv?hBx}?}n?7
g y?yHiVmM7# (; K M7G.%, 7GN+6P/H% ¥LÂ 12 0 2J|D ')3- z 0 - H! 7G
\
¯º³¬¬©§|¨´°Mº¼ ªr«¬ °ªLÊC¨¨±?²;Ê p¸e+½ ÊK ¸ ̵K»º°§|µ º¨#·z§|°!³ ¯¬!ª\¬ ÊK² ´$º¯!§rªr«µP°BG9 Chnq h?x?oBSnq?q}7 g y$oiMNR7G# 0 # #&7_D:$ d7N 0 + 0 +=, +12 0
U¯º³!¬¬©§|¨,´°Mº¼^ªr«¬ 0 Jr1F 0 C(G . #`zNab7
u% ªr« º¯ 0°«º!»Yº¨·V±ª)±$¾±° ¬ ¯º´¯±µPµM§|¨*´ 3d±¨´±´,¬!°B 9G Cl?} q?lBnqq?q7 g y?lHiV_M7# ,!BGÏM7G7G¤&,?";BG Gab7~K7 K?3!7;N 0 + 0 +3 c>(. #+ - 2P9'\( .- H:$ %. % 0 1#7
u
U¯º³!¬¬©§|¨,´°Mº¼^ªr«¬D¦&²-º¯§j©$±PÊC¯ª§ &³ §j±1² ¨ª\¬ ²|² §´,¬!¨;³¬ C¬!° ¬±¯³ « ̵D»º°§|µPBGx}}n7 g y?qHiW7;* D+ 7c1#7;kD+ %F?9 0 -12T 0 -? Jr `z#ab7
u%
U¯º³¬¬©§r¨´°Mº¼^ªr«¬ ¨ª\¬!¯!¨G±ª§jº¨G±?/² bº¨¼¬!¯¬!¨G³¬ º ¨ G¬!¯2Ì 3p±¯´,¬z·W±ª)±¿K±°¬!°B9G KhnHs h?xyBSnq?qq7 g o}HiWÂW7 +M7; G 3T ? dB M7GÂV7-3BR G.8D7R-3-7 kD+ %- 0 DcO3.c^cO(d7 ¨ª\¬!¯!¨G±ª§jº¨G±?² º¯¨;±?² º¨#·z§´§|ª)±² 3S§j¾ ¯±¯§)¬!°Bpn?nH!¥ sv y?oBnq?q$o,7 g on!iWÂW7 +M7; G 3T ? G#w78D7cO,t7 - M?+3H 1293-^9G 0 I- 9 0 (G 7 'ÊC ¸ ./bºµD»Gª .B xvjy?!¥-nHxh?s nHx?slBbnqq$s7 g o?xHi M7G-"3+ G=ÏP7N+-+d7¤&? 0 12 0 G.*+-:?3 JS`DwS 0 # /9 -? 7
u%
U¯º³¬¬©§r¨´°Mº¼^ªr«¬zÊ p¸ '!L¸#"b·V)½ '!LÊ*S)½ '!LÊ , ̵D»º°§|µ º ¨ U¯§|¨;³ § »;²¬!° º¼K·W±ª)±$¾±° 2¬ Ì°ª\¬!µP°B;x}?}?x7 g ohHiW8D7;-3-F ÏP7N+-+d7
u G /F 0 + 0 + UJ|C9G 0 /9 -? 7G
\
¯º³¬¬©§|¨´°Wº¼zªr«¬ ¨ª\¬!¯¨;±ª§jº¨;±?² bº¨¼¬!¯¬!¨;³¬Pº¨#·V±ª)±$¾±° &¬ d«¬º¯ÌB9G? Dx?oo xq$s,BSnq?qq7 g oviMNR7 M7.% 2 GÂV7Gat?9;T!'uat?9;T7;¤& 9 0 +G3p9 1F 0 - ¥b G!/-(3^3-? 0 1 G. /9; -12 0 7 º¯!¨G±?²º¼ bË!»¬!¯!§rµF¬!¨ª)±²S±¨;(© d«¬º¯¬!ª§j³±?²tÊC¯ª§ &³ §j±² ¨ª\¬ ²|² §´,¬!¨G³¬!Bv¥n}$o nHxyBXnqq$x,7 g o?si (W7.%, B (W7c-3- ? tB; GÄU7 (W7 ^ ,";7G~ %,
9# 0 - 0 ?7G
\
¯º³¬¬©§|¨´°Wº¼zªr«¬ ªr« ¨ª\¬!¯¨;±ª§jº¨;±?/² bº¨¼¬!¯¬!¨;³¬Pº¨ µ±´,¬^ÊC¨G±?² Ì°§|°z±¨;© U¯º³!¬!°°§|¨,´Bnqq?l7 g oyHiV_^ 0 - G3p¤ K
u 0 0 + 0 ?7 00 9d¥ " "UUz7 7 -d7 ?H: "7 g o?oiMNR7_D 0 :;B7ÏP7mK3-31F dB7ab7c- !BG GN;7GN;7 ¤&GU 0 ?7 (K9 0 0 -:$D?(Ã 0 ¥&¤& - 9 0 0 -? UJ 12- 0 + 0 +RB- H!3d 0 7
u
U¯º³!¬¬©§|¨,´°Mº¼^ªr«¬ ¨ª\¬!¯!¨G±ª§jº¨G±?/² bº¨¼¬!¯¬!¨G³!¬Mº¨#·W±ª)± U¨,´§|¨R¬¬!¯§|¨´B9G Koq q?}Bnqq$o,7 g olHiW&7_K:$ G.8D7;N!,& 0 ";7ÄX/9 :?V G= 62- 0 9G 00 ! 3 ?+G? IJ| 0 ') 0 + 0 + 0 7
u
U¯º³!¬¬©§|¨,´°Mº¼^ªr«¬^Ê p ¸ '!b¸#"L·V)½ '!bÊ*S+½ !LÊ , ̵D»º°§|µ º¨ U¯§|¨G³ § »;²¬!°zºu¼D·V±ª)±$¾±° 2¬ Ì°ª\¬!µP°BG9 nv,s nsyBdx}?}}7 g oqHiV_M7_D-3- ? t7 ¯!§|¨G³ § »;²¬!°Vºu¼DÊC¯ª§ L³ §j±?² ¨ª\¬ ²|² §´,¬!¨G³!¬!78 -??B wS3-FÂK3 0 BG¤ 3-4J| BSnq?l}7 g l?}Hizc[7 W7wb-3BRf7G7Ï^? ??+?BG Gf7G7;N G! ? d7 8d~ ÂDNÄU¥ÂZ 0 ( ^J9%3-? 0 K- J|1F 0 -? t7
u
U¯º³!¬¬©§|¨,´°Mº¼^ªr«¬ $¨G© ¨ª\¬!¯!¨G±ª§jº¨G±?² º¯ 0°«º!»Yº¼ ?»¬³ §)¬! ° BG8 +"+(GBG?9G dBGx}}?}7 51
g q$siW7G8D7Gab7cY B~K7ÂW7N9-BÏM7;NG B 71;G B G¤K7 ' M7;¤& 7;ÂC+ 0 1F 0 =- H:$ %=Jb 0 -:$ 12 0 4J| I- 1M+3 0 -93-- (C_^ÂZ ? %= 0 + 0 + 7
u
U¯º³!¬¬©§|¨,´°Mº¼^ªr«¬ $¨G© ¨ª\¬!¯!¨G±ª§jº¨G±?/² bº¨¼¬!¯¬!¨G³¬Pº¨ V¨;º É ²¬©´,¬D·z§|°!³º®¬!¯Ì.±¨;©P·W±ª)±P¸{§|¨§|¨´B9G? Ko} osB nq?qy7 g q?yHiW7G8D7Gab7cY BÏP7N B M7G7 'uNR7G¤&G B;ab7 (C3- tB 71;G B M7wS 0 37;N 0 + 0 +3R1F 0 ! G - H:$ %F- .,+12 0 0 ( 7
u& ¯º³¬¬©§|¨´°Wº¼Dªr«¬ Ê p. ¸ !L¸#"L$ · ¨ª\¬!¯!¨G±ª§jº¨G±?/² bº¨¼¬!¯¬!¨G³¬Pº¨ ¸f±¨;±´,¬!µF¬!¨ªUº¼K·W±ª)±B9G? Ksy} sy?hBSnqq$o7 g q$oiW7G8D7Gab7cY B 7 R B M7;¤& B; G.ÏM7;NG 7 - 99/-1F 0 ^9G 00 U- #+ G4 0 %3- 9 7 C±ªª\¬!¯!¨ C¬³º´¨§|ª§º¨BGh$s)x!¥ v,oh v?l?hBpx}?}$x,7 g q?lHiW7G8D7Gab7cY B 7 R B GJ M7 ')c 7R¤&4 t7G8 99/-1F 0 ^9#1F 0 ! M9?(3 1#7
\
¯º³¬¬©§|¨´° º¼^ªr«¬ ¨ª\¬!¯¨;±ª§jº¨;±² bº¨¼¬!¯¬!¨G³!¬Mº¨ C±ªª\¬!¯¨ C¬³º´¨§|ª§º¨B:$?3-+12zxB9G Dxlv xl?lBpnq?qv7 g q?qHiMf7c> BG7RNR7ÎK 00 !BG G~C7 (V7
)%, 7N 3 0 -: 0 % 0 -1F 0 -? #- 0 z9 zJX3-9G +12 - 3 0 7;
\
¯º³¬¬©§|¨´°Mº¼^ªr«¬ ¨ª\¬!¯!¨G±ª§jº¨G±?² bº¨¼¬!¯¬!¨;³¬Mº¨·W±ª)± ¨´§|¨;¬¬!¯§|¨,´B9? Vny?q nl}Bnq?q?o7 g4n}}iV`M7cY BG78D7;aX7cY BÏP7GNG GBG~K7ÂW7GN9-B NR7Ï^-" 0 +3-+dB
!7 (C-??+ 0 ? BR GL 7;G 7GÂC+ 0 ?1F 0 - H:$ %=Jb 0 -:$z12 0 4Jr C- 0 V12 -? 3 12?3-+3 7
\
¯º³¬¬©§|¨´°Mº¼^ªr«¬ ¯© ¨ª\¬!¯¨;±ª§jº¨;±?² bº¨¼¬!¯¬!¨;³¬Mº¨ z¨;º É ²¬©´,¬K·z§|°!³º®¬!¯Ì.±¨;©M·W±ª)±¸{§r¨§|¨,´B 9G Cl?q q$s,Bnqq$o,7 g4n}n i (V7c-3- ? # GÄI7 ^ ,";7G~ %, #129G 0 -(3- 0 % 123;J|D91F 0 - 7 C±ªª\¬!¯ ¨ C¬³º´¨§|ª§º¨ 3¬!ªª\¬!¯!°Bno¥ xyh x?oyBXnq?qy7 g4n}?xHiWÂW7c> P G#f7 L?+t7ÄX 0 ?9,%. - 0 zJ G?1 9 UI 0 #993- 0 -? 0 P 0 + 0 +3t9G 00 !
? 0 -? t7 ¯±¨° ±?³ ª§jº¨°Mº¨ I±ªª\¬!¯¨{ÊC¨G±?² Ì°§|° ±¨;©P¸f±$³«§r¨R¬ ¨ª\¬ ²|² §´,¬!¨G³!¬!BGo)s!¥ sq?q y}?qBXnq?l$s,7 g4n}hiMNR7c>+ .mM7G# (; 7G 0C0 !/ 0 - 23-3I- 7 bºµPµM¨§j³±ª§jº¨°Vº¼^ªr«¬DÊ p¸{BGh?sn}$!¥ l?h qnB nq?q?x7 g4n}viV`z#aO8dÏ^4QS7 00 9d¥ " "UUz7 3-9G&" 7 (1#7 ?L1 " z7 J "ÂCkD "H/123 0 4QS7 g4n}?sHiMf7 G"?" 7 K9 0 0 -z12 0 - 0 (G
¯º³¬¬©§|¨´°Mº¼^ªr«¬DÊ p¸ !L¸#"L· !LÊ* 0 %,7
\ '!LÊ ,- ̵K»º°§|µ º¨ U¯§|¨;³ § »;²¬!°Vº¼K·W±ª)±$¾±° ¬ Ì°ª\¬!µM°BG9G? Dxh} xv,x,BSnqq?}7 g4n}y2i 7R BÏM7;NG B 78D7;aX7c> 7 ÂK99/-1F 0 0 z1F 0 ! P- 0 z9 ^JX:?H(3- 3 0 . dÍ 0 H 7 º¯¨;±²pº¼CÊK² ´$º¯!§|ªr«,µP°Bdnyn!¥ hh y?yB nq?qv7 g4n}?oH2i 7R B (V7N 0 0 1F dB GÏP7NG 7 +D 0 0 - 2- 0 z(; 0 & #+ =3(;3- 0 7 ¨¼º¯µ2±ª§jº&¨ ¯º³¬!°°§r¨´ 3¬!ªª\¬!¯°B;v,x,¥nh?h nhqBXnqq$x,7
g ln i (V7 (K12 .
!7ÎW7 (K1F"- G t7_D? 3- 9G 00 1F 0 !- P- 0 7 º¯¨;±²Sº¼^ªr«¬^Êp¸B h?q)x?!¥ xq?s hnyBXnq?q?x7 g l?xHiWÂW7GN Jr3-+# GL 7G+d7 0 V12 +^(; 0
00 -(+ 0 F3 0 -? 39 UJ|C9 00 ? 0 -? d7 ¯±¨° ±?³ ª§jº¨°Mº(¨ Ì°ª\¬!µP° S¸f±¨ &±¨;© SÌ?¾!¬!¯¨R¬!ª§³ °Bpnhjh?!¥ h$sh hy$xBXnq?l?h7 g lhiW8D7RN!3- C G&7_^+1F dBÂC99/-1F 0 0 1M(; WJrD*,+ %- M`z#aO 0 7G
u%
U¯º³¬¬©§r¨´°Wº¼ ªr«¬zÊ p ¸ ! º¯ 0°«º!»Yº¨ 1K4¸ 3±¨G© ¨¼º¯µ2±ª§jº¨ I¬!ª¯!§)¬!®±² B; 0 B K?BG?+34%#x}}?}7 g lviVÏP7GN GBG7G8D7Gab7cY B M7GN tB GL 71;G 7 Âb8d/ K9t¥bÂK99/1F 0 D H!- 2- #+ 0 7;N+(12 00 tBx}?}?x7 g l?sH2i M7GN+tB M7 z+ B G.ÄI7 (C+ G 0 7ÂK+ 0 ?1F 0 -
U¯º³!¬¬©§|¨,´° 0 0 Jr1F 0 JS`^#a>, +12 0 7
u% º¼^ªr«¬ º¯ 0°«º!»Yº ¨ ¬¾ ¨¼º¯µ2±ª§jº¨e±¨G©·V±ª)± ¸f±¨G±´,¬!µF¬!¨ªBtx}}n7 g lyiW~K7GN+(1F tB8D7c[7ad+ BGN;7GaX7ÎL (; B G NR7~K7 t? ";78 VÂCkDmDÂZ99? 0 2*,+!%- P3-- 0 0 K- (Ãu 0 ')- 0 0 (G 7;
u ¯º³¬¬©§|¨´° º¼^ªr«¬ ¨ª\¬!¯¨;±ª§º¨;±?² bº¨¼¬!¯¬!¨;³¬Mº¨·V±ª)± ¨´§|¨;¬¬!¯§|¨,´BG9G? Kl?} lqBnq?q$s,7 g l?oHiW~K7N+(1F dBN;7~K7 t? -";B8D7,c[7ad + B N;7ab7 ÎL G (; 7 +K 0 %9; U- 0 zÂCkDmDÂZ 0 P1237
u%
U¯º³¬¬©§r¨´°Mº¼^ªr«¬ ªr « º¯ 0°«º»Yº¨·V±ª)±$¾±° ¬ ¯º´¯±µPµP§r¨*´ 3p±¨´±´,¬!°B;9G? znnHs nh?sBSnqq?h7 g lliVÏP7GN+-+d7ÂK .:? :!ZJS 12- 0 + 0 +. 0 7 '!bÊ* '!bÊ* V¬ É °¶|Ê p¸ »¬³ §±?² ¨ª\¬!¯¬!°ª ¯ºH»Yº¨#ÊCª)ºµ2±ª)±±¨G( © bºµK»Gª)±$¾ §² §|ª( Ì d«¬º¯!Ì!¹BRxqB nqq?l7 g lqizc[7 M78 GL 7;N;7+d7ÄS') 0 - - ?129- 1 Jb 00 -(+ 0 =3 0 G3p9 IJr 9G 00 # G3-% - 7 ¯±¨°!±$³ ª§jº¨°Wº( ¨ Ì°ª\¬!µM° ¸f±¨ L±¨; © SÌ$¾¬!¯¨R¬!ª§j³ °BRq¥ o?s?o oy?lBXnq$oq7 g q}iW7mD3-3-1F t7ÂK 3-? 0 1 J|K +(9- 129- 1#7 º¯¨;±?²pº¼Vªr«¬^Ê p¸{BGxh¥ hn v,xBSnq$oy7 g qn iMNR7mD12!%1F7ÂK =-? 129;? 0 -? {99? 0 0 9#1F 0 !- P9?(3 12 17 ¯±¨°!±$³ ª§jº¨°Mº¨ C±ªª\¬!¯!¨ÊC¨;±?² Ì°§|°V±¨G©¸e±$³«§|¨;¬ ¨ª\¬ ²r² §´,¬!¨;³¬!Bpn})s!¥ yq$s o}hBSnq?l?l7 g q?xHiVÎM7ÎD +t7 (#% %R¥b1 ¤& 0 `^#ab7
u
¯º³¬¬©§|¨´°Mº¼^ªr«¬zÊ p ¸ !L¸#"L·z+½ !LÊ*S+½ !LÊ , ̵D»º°§rµ º¨ ¯!§r¨;³ § »;²¬!°^º¼D·W±ª)±$¾±° ¬ Ì°ª\¬!µM°BRx}?}n?7 g qhiW7G8D7GaX7c> B 7? ? B 7R B G=ÏP7GNG G7G % 0 1 J|K99/-1F 0 0 z1F 0 - 7 ¯±¨°!±$³ ª§jº¨°Mº¨ V¨;º É ²¬©´,¬M±¨G©·V±ª)± ¨´§r¨R¬¬!¯!§r¨´B yv$!¥ s?sq son?BXnq?qv7 g qviW7G8D7GaX7c> BG~C7GÂV7;NG94B G=ÏP7GNG G= !7 I±ªª\¬!¯!¨{·z§|°!³º®¬!¯ÌF§|¨¿I§jºµº?²¬³ ²-±¯K·W±ª)± ;ºº?² ° R¬³«¨§ ¬!°W±¨;©PÊ »?»;² §j³±ª§jº¨°7 +K/J|.mD -:$ 0 %.wS B _D! L";BRnqq?q7 52