ISSN 0249-6399 ISRN INRIA/RR--5256--FR+ENG
a p p o r t
d e r e c h e r c h e
Thème COM
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
The Effect of New Links on Google PageRank
Konstantin Avrachenkov — Nelly Litvak
N° 5256
July 2004
Unité de recherche INRIA Sophia Antipolis
2004, route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex (France)
Téléphone : +33 4 92 38 77 77 — Télécopie : +33 4 92 38 77 65
./10324657084:9;0*<>=@?:57A6B3CD0FE7/G=IHKJMLCDNONQPSR9O4T=75UEIV
WYX[ZT\^]`_acb#dfehgGikjlZT\^]:imonp\^\`q[r[stmuvrpjwi
xzy{n}|~]jb>eGWa
>u}[7nvylj G]yl]:mwX[]ywmwX[]r73pvv df}qgvvvd Uu}v]:i
IT6[vv x3u}p]Tuvr[$stinvr[]cnv@jlX][yls rms[ ]moy{sjl]y{stu`upmmonpy{ [sr[`jln¡X[stmwX¢£nhnvv ]£y{uvr[Gi¥¤¦]§
Uu}v]:i¨IxFuvv]:u}r[£muvr§U]¥srDj{]y{[yl]jl]: uvi@uQyl]:©pq]rmg£nvGªDstils«j{sr[£u¤¦]§uvv]M§hguywu}r [nv\¬ikq[ylQ]y
uvr ^jlXhqis«jyl]]Tmoj{iMjlX[]®Unp[q[tu}y{s«j~g`n}¯u¤¦]§°uvv]p¨I¤¦]®ikjlq [g j{X[]>]±7]:m²j¥nv8r[]¡ g$moy{]Tu6j{]T ^ sr[Gi
npr³¢£nhnvv ] x3u}p]Tuvr[1¨¤¦]^ Gsti{moqi{ij{n-¡Xu}j®]o´hj{]r u-u}p] muvr³monprDjly{nv¯sj{i£x3u}v]:u}r7¨®µ>ilsr[
j{X[]`upikgh\Gj{n}jlstmuvru} gGiksti¡][y{n6ªDst G] ils \^] mnvr [s«j{snprij{Xu6j£ikX[n6¡¬sMr[]¡ s r[Gi§[y{sr°§U]Tr[]o¶j{i
j{nu·¤ ]T§Ku}p]°u}r ¦sj{ir[]TspXh§Unpy{ics r¦jl]y{\$in}x3u}p]Tuvr[¸nvyjlX[]Tg Gn¸r[nvjT¨º¹[q[yljlX[]Tyl\npyl]p»¯¡¥]
ilX[n6¡¼jlXUu6j£jlX[]Tyl]`]o´Gs ikj{i£u}r³nvGj{s\$u}F sr[hs r[ikjlywu6j{]pgv¨>¤¦]monvrUmo q G]j{Xu6jcu°¤¦]§ u}p]§U]Tr[]o¶j{i
Qy{nv\ sr[Gi srilst G]-sj{i`¤ ]T§½monp\\ q[r[sj~gKu}r KnprKjlX[]n}jlX]y XUu}r Ks yly{] ]ª6uvrpj`s r[Gi7]ruvs ¾]-jlX[]
¤¦]§·uvv]:iuvr jlX[]Tsy¤¦]§¸mnv\\ q[rs«j{s]:i¨
¿¸ÀDÁ1Â{Ã Ä 6ÅFv ¢£nhnvv ]v»IxFuvv]:u}r[1»@>u}r[¦a®r]µ>7 u6jl]p»za®[jls \uvMƯs r[hsr¸ehjlywu6jl]Tvgp»Ib¸u}y{vn6ª
mwXUu}s ri
ǯÈÉIÊwË:ÌÍÈ:βÏ;Ð8ѲÏ;Ê{ÌÍÉÓÒËÔÕÔÖÊw×ÙØÚÎkÛIÔÕÉ~ÜѲÉIÌÍÈÉ@Ý6Ú6ÊwÚ×~ÞßÊwÔ}ÐÍË:àà}βÏO̯ÎwÒvÌÍÈ:É3áIÉÓÌ;ÈÉ~Ï;ÔßÊwÚ:ÜÐIâFÏ;ÑoÊwÚÞÕãkÊ{Ì;ÞÕβÚÒ Î²Ï¯ä×kÞÕÉ~ÚoÌÍÞÝ×
å@É~ÐÍÉkÊwÏO×ÙÈ`æ á@çâzè7Ë:ÚÜÉ~Ï8ÌÍÈÉFѲÏÍÊwÚo̯é3ê3ë°ì:íÓîQï²ð²ñ¥ÊwÚÜÌÍÈÉFò6Ï;É~Ú×ÙÈcâFÏ;ÑoÊwÚ:ÞÕãlÊ{Ì;ÞÕβÚcó7êFôQõ3ó$ËÚÜÉ~Ï8é7ÊwÚcêFβѲÈ>ѲÏÍÊwÚoÌ
ÚÎöñ²ïw÷oø²ø²ùFõ¥ö
ú ôQáIå@ôüûýäTβàÈÞßÊûIÚÌ;ÞÕà}βÔÕÞÕÐlþð²ñ²ñw÷þ,å@βËTÌÍÉÿÜÉ~ÐDË×~ÞÕβÔÕÉkÐkþFöë[ö²ø:þ ñ²ì²ñ²ð:þ ò6ÏÍÊwÚ:×kɲþ ÉÓîÊwÞÕÔ
öû:Ï;Êw×ÙÈÉ~ÚØ²ÎFÐ;βàÈÞßÊ:öÞÕÚÏOÞßÊ:öÒ Ï
ùIÚ:ÞoÉkÏOÐÍÞÌüÖ£ÎwÒ1ÇhÛ8É~ÚoÌÍɲþDõFÉ~àDözûIààÔtöÊ{ÌÍÈDöÕþvò}Êw×~ËÔÌüÖÎwÒ1ó7ó@ä}þvë[öâ¥ö1Îð:íTþwï²ñ²ñ>ûFó·óUÚÐ;×ÙÈÉ~ÜɲþpÇ@È:É
áIÉÓÌÍÈ:ÉkÏOÔßÊwÚÜÐkþ}ÉÓîÊwÞÕÔ [áöDÞÌwÊwØÊ{Ì;ÈDöË:ÌüÛ8É~ÚoÌÍɲöÚÔ
x3u}p]Tuvr[®]:i~j3q[r^ G]TiI[y{srUmos u}qG´mylsjlZTyl]:iIil] nvr ]Ti{©Dq[]ti3¢£nDnpv ]Mnvyw Gnpr[r[] ]TiIuvv]Ti
¤¦]§@¨3x3uvv]T>u}r[^U]TqGjojly{]s rDjl]y{[yoj®monp\\^]® uQy:©pq]rm]® G]:iªhstiksjl]:i q[r[]£u}p]¤¦]§°uvy¥qr
q[jls stilu}jl]Tq[yu}Tu6j{nvs yl]p»p]jyl]Zoj{]£ Gnprm® u`Unp[q[tu}y{s«j£ q[r]£Uu}v]®¤ ]T§¯¨ npqioj{q Gs nvri]±7]j G]Ti
rnvq[ªp]Tu}q[´s ]rizilq[yz ]x3u}v]:u}r G]>¢£nhnvv ]v¨npqiz GstilmqGjlnpri7|~qi{©pq!"©Dq[]TGUnpsrDjMq[r[]Uu}v]7]qGj
\nG Gs¶]y¥iknpr^x3u}p]Tuvr[1¨Izr$q[jls stiluvrDj#u}rUu} ghil]uvilgh\^[jln}j{s ©Dq[]p»}r[npqi3Qnvqylr[sti{iknpri3]:iMmonpr Gsjls nvri
ils \^]:i©Dq[s¯\nvrDjly{]rDj>ils¯ ]Tir[npq[ªv]:u}qG´s ]ri>u}[7nvyljl]Trpj> []Tiuª6u}rDjwu}v]:i"q[r[]uvv]c¤¦]§¸]oj>uvqG´
Uu}v]:i>ªpnvstiks r[]:i¨xzqs iT»¯r[npqi£\^nprDjly{nvri£©Dqs 3]o´Gsti~j{]`q[r]ikjlywu6jps]`nvGj{s\$u} ] j{uv§[sti{ik]T\^]TrDjc G]
s ]ri©Dq[s¯ylnv¶[jl]cu}qG´qiluvv]Ty{iYugpuvrDjY G]:iYs ]rUiu}q·ik]Tsr· G] ]q[ymnv\\ q[rUu}qGjv»G]oj>©Dq]rºy{]ª6u}rmwX]
[]TiY s]Tris ru}[ylnp[ylsTi$ruvstil]rDj]:iYqGjls sti{u6jl]Tq[ywi Gq·¤ ]T§º]j]Tq[ywimonv\\`q[ru}q[jTiT¨
% Ä : Â '& ° ¢£nhnvp]p»Dx3u}p]Tuvr[1»D>u}r[a®r[]£µ1 [u6j{]v»[eDj{y{u}jps]®nvGj{s\$uv]c oj{uv§[ s i{ik]T\]rDj G]
1 2
F -Fo`
eGq[ykQ]Ty{i nvrKj{X[]43ÓrDjl]Tylr]ojQy{]T©Dq[]Trpj{g¦qil]il]Tuvy{mwXK]rvs r[]Tijln¸¶rU u}p]Tii{u6j{s ikQghsr¸jlX[]Tsy©Dq[]y{gv¨
5>n6¡¥]Tªv]TyT»pjlX[]Tyl]cu}y{]®j~gDs mTu} g$Xhq[r [yl]: [invyjlX[npqi{u}r [inv@yl]T]Tª6u}rDjUu}v]:iYuªuvstu}§]®nvr°j{X[]c¤ ]T§¯¨
WYXhqiT»M s ikjls r[³jlX[]T\ sr u³ylnpU]Ty`npy{ G]Ty stiu mylqms uvuvr rnvr6Íjly{sªhstu}j{uvil1¨ WYX[]ºnvy{spsruvst G]Tu
nvY¢£nhnvp]`[y{]Til]rDjl]: ³s r 87'7:9°§hg<;yls r ]ju}>=0"?Ms i®j{nº sti~juvv]Ticupmmonpy{ [sr[-jlnjlX[]Tsyx3uvv]T>u}r[
¡Xs mwX·y{]o]:m²j{iUnp[q[tu}y{s«j~gn}Muu}p]v¨WYX[] x3u}p]Tuvr[°sti> G]¶r[]T ·s rºjlX[]Qnv n6¡s r[$¡Yugv¨A@®]rn}jl]
§hgCB jlX[]-jln}jwu}¥rDq\ §7]y nvu}p]TinprKjlX[]¤ ]T§½u}r []o¶r[]°jlX[]DBFEGBXDgh7]y{s r[¦\$u6jly{s´CH#uvi
Qnp n6¡iT¨ ehq[[7npil]·jlXUu6j°uvv]JI XUuviLKNMPOKnpqGjlpnvs r[Ks r[GiT¨ WYX[]TrRQTSVUXWZY\['K s]sti$nvr[]¸nv
j{X[]³npqGjlpnvs r[ sr[Giu}r XQTSVUFW^On}j{X[]y{¡s il]v¨N3Ù u u}p]³ Gnh]Ti-r[n}j-XUuªv]npqGjlpnvs r[s r[GiT»jlX[]
ylnp§u}§[s s«j~g°stiil[y{]Tuv ºu}\npr[$u} ¯u}p]TinvIj{X[]¤¦]§¯»Uru}\] gv»,Q S_U W`Y/[\Bz¨a3Ór·npy{ G]TyYjln$\$u}p]cjlX[]
Xhgh7]y{s r[ºvywu}[Xmnvr[r[]:m²j{]T 8»7s«j£s i£uvi{ilq[\]T ºjlXUu6j£u°y{uvr Gnv\ ilq[ykQ]Ty>pnD]:i¡sjlX³ilnv\]ylnp§u}§[s s«j~g
j{n°u}r¸u}y{§[sjlywu}y{g$¤ ]T§¸u}p]c¡s«j{X·jlX[]qr[s«Qnpyl\, Gsti~j{yls §[qGj{snpr¯¨¥WYXhqiT»GjlX] x3u}v]:u}r°s i> G]o¶r]T ¸uvi
uºikj{u6j{snpru}y{g· Gs ikjly{s §[qGjls nvr n}Yuºb¸uvylpn6ªmwXuvsr ¡X[npil]i~jwu6jl]iluvm] sti>j{X[]$ik]j£nv¥u} 3¤ ]T§ Uu}v]:i»
uvr -jlX[]cj{y{uvriksjls nvrº\$u6j{yls´-sti
b
HNWdcHfedghYiRc\j.g.Y\[/Bjlknm o~8p
¡X]y{]qk sti>u\$u}jly{s«´º¡X[npil]u} @]rDj{yls ]Tiuvyl]]:©pqUu}8j{n$nvr[]p»rBKs iYj{X[]rhq[\`§U]Tyn}z¤¦]§¸uvv]TiT»[u}rU
c<sNgtOrm Y"j>sti jlX[][ylnp§u}§s s«j~g n}r[nvj>|~q[\[s r[³jln uy{uvr Gnv\uvv]<oQsjs i`mwX[npil]r§hg¢£nDnpv ]$jln
§7]LOruv:w:p²¨°WYX[]-¢£nhnpv ]`\$u6j{yls´
b
Hs i i~j{nhmwXUuvikjlstm}»@uvU]Tyls nG Gs mv»Iuvr ¦sy{yl]: Gqms§[ ]v»IiknºjlX]y{]$]o´Gs ikj{iu
qr[s ©Dq[]y{n6¡Sªp]Tm²j{nvy>xKikqmwXjlXUu6j
x b
HyWdxzm{xzY WyY:m o;'p
¡X]y{]DY s iuºmonpq\^r¦ªv]:m²j{nvy£n}¥npr[]TiT¨ WYX[]y{n6¡ªv]:m²j{nvyx i{u6jlstikQgDs r[Ro;:p>stimuv ]T ux3uvv]T>u}r[
ªp]Tmojlnvy:»Dnvyiks \[ g°xFuvv]:u}r[1¨3ÙIuilq[ykQ]TyQnp n6¡iYu Xhgh7]y{s r[$¡sjlXº[ylnp§u}§s s«j~gnc£u}r |~q[\ijln
uy{uvr Gnv\ uvv]¡sjlX°ylnp§u}§[s s«j~g|Yzi|c}»}jlX]rLx}SImTu}r$§7]>s rpj{]y{[y{]ojl]: $uviuikj{u6j{snpru}y{g ylnp§u}§[s s«j~g
j{Xu6jj{X[]ilq[ykQ]TyYs iu}ju}p]Iw¨
3Ór¦nvyw G]y®jlnºv]T]q ¡sjlXKmonpri~jwu}rDj®\nG Gs¶Umu}jls nvri£nvMjlX[]^¤¦]§Ki~j{ylqmojlq[y{]v»@¢£nhnpv ] q[1 [u6j{]Ti
sj{i®x3u}v]:u}ru6j®]:uvikj>nvrm]U]Ty>\nvrDj{X¯¨mmnvyw Gsr`j{n°[q[§stmo g¸uªuvstu}§]s rGQnvy{\$u6j{snpr¸¢£nhnpv ]
ikjls zqik]:iiks \[ ]^7n6¡]ycs«j{]ywu6j{snpri®jln¸monp\^qGjl]^jlX]°xFuvv]:u}r[1¨eh]ªp]ywu}3[y{nv7npi{u}ti!= }»Ih»IG»~h»
:G»7v}»7:h»7 0/?zo;ik]T]®uv iln u}r$]´hjl]rUiks ªv]£ikq[y{ªv]Tg uvU]Ty¥§hg$Æ@uvr[vªhs ]>uvr -b·]Tgv]y =7/?pXuªv]>yl]:mo]rDj{g
§7]]Tr¸[qGj®Qnvy{¡uvy{ -jln-upmm] ]ywu6jl]cj{X[] x3u}p]Tuvr[mnv\[qGjwu6j{snpr¯¨WYX[s i>yl]:ik]:u}ywmwXº [sy{]Tmojls nvrmuvr¸§U]
y{]Du}yw G]T ¦uvi`uilghikjl]T\UnpsrDj nvªDs ]¡¨ a®r mnvrDjlywu}y{gv»FX[]Tyl]°¡]$jwu}v]u¸qil]y 7nvs rDj n}ªhs ]¡ u}rU
j{ylg^j{n^uvrik¡]yjlX[]£Qnp n6¡sr ©Dq[]Tikjls nvri 3¤X[]rº Gn^r[]¡S s r[Gi§7]r[]¶[jYjlX[]£¤¦]§ºu}p]Qy{nv\ ¡X[stmwX
j{X[]g¦]\$uvru6j{]8 ¤X[]r Gn·j{X[]°uvv]:icQylnp\ j{X[]-i{u}\]$¤ ]T§ monp\^\`q[r[sj~g³§7]r[]¶[j Qy{nv\ÿjlX[]-s r[
myl]:u6j{snprT|3~ijlX[]Tyl]cnpGjls \$u}¯ srDs r[$ikjlywu6jl]Tvgr
WYX[]¥u}7]y@s iInvy{puvr[s¾T]T £uvi¯Qnv n6¡i 3Ór`eh]Tmojls nvr [»T¡]ikjlq Ggu©Dq[]:i~j{snprcjln¡Xu}jI]´Dj{]r uu}p]
mTu}rmnvrDjly{nv}sj{iFx3u}p]Tuvr[1¨@WYX[]r srj{X[]]Trilq[sr®eh]Tmojls nvr!0¡¥]©DquvrDjlsQg®j{X[]yl]Ts \sruvylg£u}ruvgGils i
nv@eh]Tmojls nvr-c¡sjlX$j{X[]X[]T-n}@ehX[]Tyl\$u}rr6Ób·npyly{stiknpr6ͤ¦nhnG G§[q[y{gq[1 [u6j{sr[Qnvy{\ q[tuu}r $ []y{sªp]jlX[]
]´G[yl]:ilils nvr-nvFr]¡¬xFuvv]:u}r[u6üjl]TyjlX]uv [ Gsjls nvr·nvFr[]T¡ s r[Gi¨a3Óreh]:m²j{snprº$qUiks r[°uvilgh\Gjlnvjlstm
uvru} gGiksti¯¡]nv§Gjwu}s rru6j{q[ywu}hmonvrU Gs«j{snpri@jlXu}j3ilX[n6¡s7ur]¡ gmoy{]Tu6j{]T s r[s iI§7]r[]¶Umostu}hnvyFr[nvjT¨3Ór
eG]Tm²j{snpr·`¡] G]\nvrUi~j{y{u}jl]£jlXu}jjlX[]Tyl]c]´hstikj{iu}rºnv[jls \uv¯ sr[hs r[$i~j{y{u}jl]Tvgv¨z¹Fs ru} gp»G¡¥]c[y{n6ªhs []
mnvrmqUiks nvris reh]Tmojls nvr·[¨
K -) ^F )º)%) F &½²I 'S)%+,)
WYX]Yx3uvv]T>u}r[ G]¶r[]: `s r o;'p3m]:u}y{g []7]r [iMnvr^§UnvjlX^srmnv\s r[u}r `nvqGj{vnpsr[£ sr[Giznv7u£uvv]v¨
WYXhqiT»6j{X[]]Tupiks ]Tikjz¡ugcQnpyMucu}p]j{nmwXu}r[p]¥sj{iMy{uvr[hsr[cstiFjln\nG GsQgjlX]nvqGj{vnvs r[£s r[GiT¨;] n6¡
¡]°ilXu} ilX[n6¡ j{Xu6j jlX[]-x3uvv]T>u}r[³mTu}rK§7]°¡ylsjkj{]r upiu·[y{nh [qm²j nvYjlX[y{]]j{]y{\i¡X[]y{]$nvr[ g
npr[]$j{]y{\ []7]r [i^npr nvqGj{vnpsr[¸ s r[Gi¨C3Ùj`¡s Yu} n6¡ qUij{n³]Tikjls \$u6j{]°jln ¡Xu6j^]o´hjl]Tr u³u}p]
mTu}rºmonvrDj{ylnpsj{ix3u}p]Tuvr[1¨FWIn j{X[sti¥]Tr 8»G¡]>¶Uy{ikjy{]TmTu} j{X[]£Qnv n6¡s r[`qik]Qq[1]o´G[y{]Ti{iks nvr°QnvyjlX[]
x3uvv]T>u}r[J=ÕG»r7»¯ 0\?
x<W YiCc
B Y !iRcH\u o0:p
Æ@]oj8SVU G]Tr[n}j{]u}rCgI ml]jM] ]\]TrpjnvIj{X[]\$u6jly{s´ W !iRcH! ¨ >u}\]Tgp»G¡¥]cXuªp]
S_U W#" S !iRcH! "U'm I ml] WNY:muu(umhBzm oQ,p
¡X]y{]" $sti¥jlX[]qK,6ÍjlXºmonv q[\r-nv¯jlX]£st G]Trpj{s«j~g$\$u}jly{s«´%7¨ n6¡»G G]o¶Ur[]£u^ Gstilmyl]jl]6;j{s\]cu}§ilnvy{§[s r[
bu}y{vn6ª`mwXUu}s r'&)(*m,+zWdOmY'm uu u.-®¡sjlX-jlX[]cikj{u6j{]®iluvm]/&8OmYau uu m.B0-p»h¡X[]y{]j{y{uvrils«j{snpriM§7]oj~¡]]Tr
j{X[]i~jwu6j{]TiY'm uuumhB³uvyl]£monvrU Gqm²j{]T §hgjlX[]c\$u6j{yls´4cH»Gu}r -jlX]cikj{u}jl] O stiYu}§ilnvy{§[s r[¨3Ư]j21 S §U]
j{X[]rhq[\ §7]ynvFªhstiksj{ij{n$i~jwu6jl]] WyY:muu umhB¦§7]oQnvy{]u}§ilnvy{Gj{snpr¯¨F¹nvy{\$u} gp»
1*UW43
5
*76!8:9<;>=@?
6 UBA m ] WNY:muu umhBzm
¡X]y{]
9C;ED
A
G]r[nvjl]:i8jlX]s r Gstmu6j{nvy8Qqrm²j{snpr¯¨3ÙjFs i@]Tupikg®jln>il]]MjlXu}j@jlX]ª6u} q[] S_U s i¯jlX[]monvrU Gs«j{snpru}
]´GU]:m²j{u}jls nvr¦n}F1 U vs ªv]r³jlXu}jjlX[]$s r[sjlstu}Mikj{u}jl]$sti I{¨$Æ@]ojG S_U §U]j{X[]$[y{nv§uv§[s sj~g·jln·yl]:uvmwX jlX[]
ikj{u}jl]]°§U]Qnvy{]cuv§ilnvy{Gjls nvrºs«FjlX]srs«j{s uv@i~jwu6j{]s i>Iw¨µ®iks r[jlX]i~j{ylnpr[°b¸u}y{vn6ª$[y{nv7]ylj~gv»G¡]muvr
rn6¡*]Tikj{uv§[ s ilX-j{X[]cQnv n6¡sr[ G]:monv\7npils«j{snpry{]Tilq[jT¨
H ÄJIMÄ )KüKÄMLON )$+%,.- +/rLQP+ %:IW`Y'm uuumhBf%"R/TSEU
x}SW YiRc
B
8S(SVWXzYAeZY 5[\^]
[,_\a`
G U.Sbdc
e m IWNY:muu umhBzu o;'p
H įÄJf 3ÙjQnp n6¡i¥Qylnp\ ot0:pjlXu}j
x S W YiRc
B Y !iRcH!E"
S W YiRc
B Y
5
U 6 U.S
u oO:p
¹q[yljlX[]TyT»¯¡]Xuªv]hg g1 S W Oji(8 Wy]j$W YikG U.S »@uvr qiks r[ºjlX]ikjly{nvr·b¸uvylpn6ª·[ylnpU]Tykj~gp»8¡¥]
mTu}rº¡ylsjl]£Qnpyu}rhgDKl Y
g g1!SW Kmi( 8 WX]j W g g1!SW K m,1!S0l Yni( 8 W]j
W g g1 S l Y^i(%8W]rjg g1 S W Ki(%8W]'m>1 S l Y"jWoG U.Sg g1 S W Ki(%8W I.ju
_¥npril]T©Dq[]rDj{gp»hQnvyu}rhgnI ml] WyY:muu um.BIWX]U»[¡]cXuªv]
U.S Wzg1
S i(%8W]jW#G U.S
g1 S i(8WdIjW#G
U.S SSu
eGq[§ikjlsjlqGj{sr[j{X[]tuvikjY]:©Dqu6j{snprs r oO:p¡]cs\\]T [s u}jl] g-np§Gj{uvsrRo;:p²¨
WYX[] G]:monp\^7npilsjls nvrQnvy{\ q[tuDoÍ'p¥y{][y{]Til]rDj{ijlX]xFuvv]:u}r[nvIuvv] IMuviu`[y{nh [qm²jn}IjlX[y{]]
\`q[jls [s ]ywi¡X[]Tyl]ºnvr[ gKjlX]·jl]y{\ SS []7]r [i°nvr j{X[]¸nvq[jlvnpsr³ sr[Ginv®uvv]|I{¨f5]Trmo]p»§hg
mwXUu}r[psr[^j{X[]nvq[jlvnpsr$s r[Gi»7uu}p]muvr·mnvrDjly{nv@s«jwi>x3u}p]Tuvr[°q[·j{n-u\ q[jls [ ]Oupm²jlnpy S(S W
Y/[ g.Y$iTG SS j$s Y'm ghY$iXc'j
Ù»8¡X[]y{]G S(S s Ormc 3s icu-[ylnp§u}§s s«j~gjlnºy{]ojlqylr§Uuvmwjln|IYikj{uvykj{sr
Qy{nv\ I{¨>n}j{]`j{Xu6jj{X[]$q[[7]y §Unpq[r ghYiFc"j oOu}[yln´Gs \$u6jl]Tg<0¨Qnpyqc W uv:w:p>stiXuvy{ nvy
ywu6j{X[]yrn}jUnDilils §[]cj{n°uvmwX[s ]ªp]®§7]TmTu}qil]s rj{X[stimupik]u^u}p] I7nvs rpjwiYjlnuvv]:ijlXu}j>u}y{]£ s r[hsr[
npr[ g$jln Iw¨ehqmwX·uUnpstmog-\uvv]:i>Iu}r sj{ir[]TspXh§Unpy{istiknp u}jl]T -Qy{nv\ j{X[]yl]:i~jnvIj{X[]¤ ]T§¯¨
3Ùuvv]<I$ Gnh]:i°r[nvjXuªp]¸nvqGj{vnvs r[ s r[Gi»Yj{X[]r SSstiªv]y{g mnDik]jln j{X[]³ n6¡]y°§7nvq[rU v»
ils rmo]`jlX[]Tyl]^sti£uv\nDi~j£r[nºmwXUu}rm]jlnºy{]ojlqylr³Qylnp\ I§Uuvmw·jln|IY§U]Qnvy{]^uv§ilnvy{Gjls nvr¯¨*;stu}rmwX[s r[s3]oj
uv;¨}=Õ8?7qUik]: -umsywmoq[sjuvru} gGikstizj{n`ikjlq [g^s r []oj{uvsUjlX]>s rGq[]Trmo]£n}¯uvv]:iM¡sjlX[npqGj¥npqGjlpnvs r[ sr[Gi
oO]:uªv]:i»h [u}rv sr[^r[nG G]:ipnvr-jlX[]x3u}p]Tuvr[n}Iu`¤ ]T§ºmnv\\ qr[s«j~gp¨zWYX[]u}qGj{X[nvywinv =Õ\?¯muv\^]®jln
j{X[]°i{u}\]^mnvrmqUiks nvr jlXu}j [u}rv sr[·muvqil]Tiu·monprikst G]Ty{uv§[]`nDilics rKy{uvr[hsr¨WYX[]^Qnvy{\ q[tuRo;'p
X] ijln°©Dquvrpj{s«Qg°jlX[sti npi{i¨
¤¦]$r[n}j{]jlXu}j]ªp]rKu-j{X[y{]]oQnp s rmoy{]Tupik]^n}jlX[]°x3uvv]T>u}r[¸\s vXDjr[n}j§7]°monprikst G]Tyl]: ³uviu
ils vr[s¶UmuvrDj®s \^yln6ªp]\]rDjT»8ilsrUmo]$¢£nDnpv ] \]Tupikqyl]:ij{X[]$xFuvv]:u}r[·npr u° nvDu}y{s«j{X[\s m`ilmTu} ]D= :\?ͨ
3ÓrjlX]£]Trilq[sr^il]Tmojls nvri¡]£ilX[n6¡SX[n6¡ u ¤¦]§ºu}p]£ilX[npq[ qil]®sj{ii{muvy{m]>y{]Tilnvq[ywmo]:iMj{n`s rmyl]:uvil]
sj{i>xFuvv]:u}r[1¨
+ )`-- )I( *!#$% &ÿ'S) %+ )`-
Æ@]oj3qiFmonvrUikst G]y3u¤¦]§`u}p]¡sjlX K 8 nvt XhghU]Tyl srhiFu}rU K
r[]T¡gmyl]:u6j{]T cXhghU]Tyl srhiT¨@¤sjlXnvqGj
npi{i3n}1v]Tr[]ywu} sj~gv»6¡]Yupililq[\]jlXu}jMjlX]u}p]¡sjlXr[]T¡ s r[GizXuvi3s r G]´u}rU j{X[]uvv]TiFj{n6¡uvy{ i
¡Xs mwX·r[]T¡* sr[Giuvyl]c7nvs rDjl]T ºXuªp]csr [s m]TiYQy{nv\ `j{nLK
e Yp¨MWYX[]r¯»[jlX[] up [ Gsjls nvrºn}3r[]¡¼ sr[Gi
mTu}rº§U]y{]Du}yw G]T uviYnpr[]cy{uvr[$q[1 [u6j{]n}FjlX[]XhghU]Tyl s r[°\$u6j{yls´
b
HNW Hfek"
m ol~"p
¡sjlX
W K
K Y
K $ ]
5S6 " S
i|Q
m
uvr ¡X]y{]nK<W K 8 efK
»Q
sti®jlX[]¶Uy{ikj£y{n6¡n}\$u6jly{s´ H¨3Ór =:\?3jlX[]°uvqGjlXnvywi>qil]q[1 [u6j{sr[
Qnpyl\`q[tu}]`jln·uvmm] ]ywu6j{] j{X[]$xFuvv]:u}r[mnv\[qGjwu6j{snpr¯¨;gy{]Tikjly{s mojls r[ºnvq[ywik]Tªp]Ti>jlnºjlX]mTuvil]`nv
ywu}r^npr[]£q[7 u6jl]p»G¡¥]£u}y{]£uv§[ ]jln7]ylQnvy{\ u \nvy{]®mnv\[y{]X[]Trilsªp]®u}rUu} ghilsti¨3WYX[]£r[]o´hjYjlX[]Tnvy{]\
yln6ªhst G]Tiq[1 [u6j{srQnvy{\ q[tu}]®QnvyYj{X[]x3u}v]:u}r$] ]\]rDj{iT¨
ÀhÄ
À N zK
&_ ! +"}+"t % B P+ %:S. + 'aD At &nT!h*}
)$+%,.- +/r/ !+ %'R\TS Unt A/&&("z,% P'+"t % &(+:
b
x W x
Yi
$ ]
$ YAe
$
]
$ ]
S6 8S
i
>
o9:p
b
xrUWdxU eXx
$ ]
$
$
]
$ ]
S6
S_U$i U
Yi
$ ]
$
YAe
$ ] $ ]
S6 8S
i
, m ]Wm uu umhBzu o7:p
H įÄJf >[[ ghsr[j{X[] ehX[]Tyl\$uvr6Ób¸nvy{ylstiknpr6Ù¤ nhnG G§[q[y{g^q[7 u6jls r[Qnpyl\`q[ u|=/?¯j{n qi c b H! »[¡¥]
mTu}rº¡ylsjl]
iCc
b
H! W iCcH eXc
!iRcH! " iCcH
YiCc
!iRcH
!
" u
WYX]r¯»[yl]T\ q[jls [ gDs r[^jlX]u}§7n6ªv]£]T©Dqu6j{snpr§hg
Y Y u}r ºqilsr ot0:po»G¡¥]p]oj
b
x<W xLex
c qiRcH!
YiRc
!iRcH
!
" m
uvr ºmonvrUik]:©pq]rDjl gv»
b
x Wdx
Y
YiCc
qiRcH
!
" m okT:p
b
xrUWdxU eXx
c !iRcH
!
" U
YiRc
qiRcH
!
" m ]Wrmuu(umhBzu okv8p
¤¦]]ª6uvqu}jl]cr[]´Djc
iCcH! "U®Qnvy ] WyY:muu(umhBz»
c
FqiCcH " U W c
@" U W c K
K Y
K $ ] 5S6 " S
i|Qj
" U W K
K c
K $ ] 5S6 " S
2" U iRcQj
" U
eGsrm] cH`W i 7»8¡¥]^Xuªp]!cQ
W
iT"
»8¡X[]Tyl]
sti>j{X[]º6Ói~j£yln6¡nv\$u6jly{s´ »8u}rU
X]rm] chQ
"UWo
Ui "
"Uv¨MWYXhqiT»G¡]v]oj
c iCcH "UW K
K c
K $ ] 5S6
8SVU$i g
Ui "
"U"j
u
eGq[§ikjlsjlqGj{sr[·j{X[]°u}§7n6ªv]`]o´G[y{]Ti{iks nvr³Qnvyqc
nicH
!
"U'ml]<W Y'm u(uumhBz»¯s rDjln o~::p£u}r o~p8po»¯¡¥]
np§Gj{uvsrRo9,pYu}r Co 7,p²¨
WYX[]$y{]Tilq[j{ics rWYX[]npyl]T\ $u}y{]^s rKs r[]$¡sjlX¦Qnvy{\ q uRo;:p²¨n3ÙYu}p]·$q[7 u6jl]:ics«jwinvq[jlvnpsr
s r[Gij{X[]r¦sr³jlX[] G]:monv\7npils«j{snpr¸Qnvy{\ q u°Qnvyx
nvr[ gºjlX[]il]Tmonpr \`q[jls [s ]yc¡s 3§7]^u}±7]:m²j{]T 8¨
3Órj{X[]r[]T¡iksjlqu}jls nvr¯»pjlX][y{nv§uv§[s sj~g Gb
>
j{ny{]ojlqylr^jln u}p]>i~jwu}yljls r[cQy{nv\ jlX[stiMuvv]p»vstiMvs ªv]Tr
§hg
b
G
>
W
K!i K
K G
,
e cK $ ] 5S6 G S u
eGq[§ikjlsjlqGj{sr[j{X[sti]o´G[y{]Ti{iks nvrsr
b
x W b
>
>
x W Yi G
>
Yi
b
G
>
x m
¡]>p]oj¥jlX[]£q[1 [u6j{sr[`Qnvy{\ q uLot9:po¨ n}j{]j{Xu6juvmTmonvyw Gs r[j{nDo9,pzj{X[]£y{uvr[hsr[ n}@uvv]£s rmoy{]Tupik]:i
¡X]r
YAe
c
K $ ] 5S6
8S
i
,
MfOrm ok:'p
¡Xs mwXºs i]T©Dq[s ªuv]TrDjj{n
Y
K $ ] 5S6
G S
M G
>
u
5>]rm]v»UjlX[]`u}p]°s rmoy{]Tupik]:isj{i®y{uvr[hsr[$¡X]rsj®y{]oQ]Ty{ijln°uvv]:ijlXUu6j£uvyl]`mwXu}ywuvmojl]y{s ¾]T §hgºu
XspX¦ª6uvq[]nvFG S
¨-WYX[]:ik]$\`qi~j§7]jlX]$u}p]Ti£jlXUu6jy{]oQ]yjln·u}p] Y$nvyu6j ]Tupi~j§7] nvr[·j{n·jlX[]
i{u}\]¤¦]§-mnv\\ qr[s«j~gp¨5>]y{]§hg^u¤ ]T§-monp\^\`q[r[sj~g`¡]\]Tuvr°uik]jn}¯¤¦]§$Uu}v]:i3jlXUu6ju ikq[ylQ]y
mTu}rºyl]:uvmwX-Qylnp\nvr[]cj{n$u}r[nvjlX[]Tysr·uyl]T u}jls ªv]Tg°il\$u} 8rDq\ §7]yn}zikjl]Ui¨
Æ@]ojcqi>rn6¡monvrUikst G]y>Qnvy{\ q[tu ot7:po¨£¹Fs y{ikjT»1¡]`il]]j{Xu6j£jlX]^ Gs±1]y{]rm] §7]oj~¡]]rjlX[]^nvt u}rU
j{X[]cr[]¡ y{uvr[hsr`nvIuvv]$]stiY[ylnpUnpykj{snpru}Ujln xb ¨ >u}jlq[ywu} gv»GXhghU]Tyl sr$yl]Q]y{]rm]Ti¥Qylnp\uvv]Ti
¡sjlX½X[spX ywu}r[hs r[Xuªp]-u¸vy{]Tu}jl]Tys\upm²j^nvr nvjlX[]Ty uvv]TiT¨³¹q[ykj{X[]y{\nvy{]v»FjlX]x3u}p]Tuvr[ nv
Uu}v]]$s rmyl]:uvil]Tis«
c
K $ ] 5S6
8S_U*M
U'm ok 0:p
3ÓrU G]]: 8»[sFj{X[stis r[]T©Dquvsj~g°X[np [ijlX[]Tr·jlX[] s r[-q[1 [u}jl]§hg°uvv]nY ]Tup [ijln$X[s vX]y[y{nv§Uu}§[s sjls ]Ti
nvy{]TupmwX[s r[·u}p]*]¸Qylnp\(uvrDg u}p]^jlXu}j Xuvi u·u6j{X j{n4]ªhstuºu}p]JYv¨-WYXhqiT»Is r¦Qnvy{\ q[tu o;:p²»
j{X[]°j{X[s y{ \`q[jls [s ]y^¡s srUmoy{]Tuvil]°u}rU KjlX[]ºik]:monpr \ q«j{s[ s ]y ¡s ¥]Ts«j{X[]y^srUmoy{]Tuvil]°npy y{]\$u}s r
j{X[]iluv\]c []7]r Gs r[nvrº¡X[]jlX[]TyYjlX[]Tyl]cstiu`Xhgh7]y{s r[°u}jlXQylnp\ ]§upmwjlnq]$Uuvi{iks r[`jlX[y{nvq[pX
Uu}v]*Yp¨>n}j{]jlXu}js8il]ªp]ywu}[ s r[GiMu}y{]uv [ []T §hg`Uu}v]*YYj{X[]r$sj¥\s vXDjXuv[7]rjlXUu6j¥ilnv\]uvv]Ti
y{]Tm]s ªv]£r[]¡ s r[Giu}rU - nhnpil]£s rºy{uvr[hsr[u6jYj{X[]iluv\]®j{s\]p¨ehqmwX·iksjlqu}jls nvrºnGmmoqy{iY¡X[]Trºu^r[]T¡
s rmnv\sr` sr°s imyl]:u6j{]T -ils \ q[j{uvr[]npqik g$¡sjlX¸ik]Tªv]Ty{uvUnvjlX[]Ty s r[Gi»G¡X[stmwXºUnpsrDjYjlnksy{yl]T]Tª6u}rDj
Uu}v]:i¨3WYX[]upikgh\Gjlnvjlstmcu}ruvgGils is rj{X[]r[]´Dj>il]Tmojls nvr·u} n6¡iqijln^Qq[yljlX[]Tymotu}y{s«Qg$j{X[stis i{ilq[]v¨
-IcF ) ) &$I
Æ@]oj>qUiu}[gjlX[]`uvilgD\Gj{n}j{s muvru} gGikstijln$Qnpyl\`q[tu}]no9,pu}r ot7:p¡X[]Tr<ccs i®ikq$ms]TrDjl gmo npil]cjln
npr[]u}r jlX]>b¸u}y{vn6ªmwXuvsr^s r Gqm]T ^§hgjlX[]Xhgh7]y{s r[\$u6j{yls´H s i3s y{yl]: Gqmos §[ ]v¨3WYX[]uvilgh\Gjlnvjlstm
uv[[y{npupmwX-u} n6¡i¥qij{n []y{sªp]£ils\[ ]cru6j{q[ywu}8monpr Gsjls nvrij{Xu6jilX[n6¡Ss3u`¤ ]T§·u}p]®¡sjlXºr[]¡ g
myl]:u6j{]T s r[Giu}r sj{ir[]TspXh§Unpy{i§7]r[]¶[jQy{nv\ j{X[]Til]cr[]¡¼s r[GiT¨
ÀhÄ À c S< Tt&UF&\G /G+" &(Pr+%, +\DK
&r8<'P+ %:
&m u(uu(m K
eY -C0 nA+/t + " +" /S U UBPrE &_ n+/ >HN R.S&()
*+ /a/&&/z,% " "t"r
aq
>
M Ye
$ ] $ ]
S6 S
zqd. +/l / &_r8&:Y m u(uumY K
eY -n}d. +\
)$+%,.- +/r4h P+ %:Y
q
U*M Y e
$ ] $ ] S6
S6 U SVU t E. +"t"D }R&_r8 &,Y m u(uumY K
eDY - }d. +\
)$+%,.- +/r4h P+ %:>]B. t q:&m u(uu(m K edY -
q
M Y e
$ ] $ ] S6 S
ad. +/l/C*f&_ &:Y rmuu(umY K e Y -L}d. +\
)$+%,.- +/r4h P+ %:r MfK
edY
E SVU4*t +": mP+/+ %:l B. Pr+%,$I P+ %:>]Gc$WNY^
H įÄJf ¹Fs y{ikjT»I¡¥]\$u}p]^u·mwXuvr[v]^n}Yª6u}y{s uv§[] c W Y/[ g.Ye! Tjl»I¡s«j{X" GM Oºs r³j{X[]Qnvy{\ q u-Qnvy
qgtc/juvi¥Qnv n6¡i
qgtc/jW !iRcH!W !i
Y
YAe#
H!WNghY e# j nqi gtH i j\u
WYX]r¯»3¡]°qil]$jlX[]yl]:iknpªp]rDj Æ@uvq[y{]rDj ik]Tyls ]Ti]o´Gu}rUiks nvrKQnpyjlX[]·b¸u}y{vn6ª mwXu}s rv]Tr[]ywu6j{nvyLoOil]]
]p¨U¨» = »WYX[]npyl]T\ 9[¨ÕG¨0/?p
qgtc/jW qiRcH WNg.YAe$ TjB n!i gtH i Tj7 ! W`ghYAe# TjB
Y
&%
e(' e 3
5
$d6
$ ghi*Y'j
$ ' $ lm
¡X]y{]
%
WNY x stiYj{X[]]y{vnG Gstm£[y{n}|~]Tmojls nvr·u}r )'stiYjlX[]` G]ªhstu6jls nvrº\$u6j{yls´nvIj{X[]`b¸uvylpn6ªmwXUu}s r
s r GqUmo]T §hg H¨3ehs rm]¡¥]mnvrilst G]yu£¶Ur[s«j{]>ikj{u6j{]®b¸uvylpn6ªmwXu}s r¯»}j{X[]>uv§Un6ªp]Yil]y{s ]Ti3XupiMur[npr6;T]y{n
ywuv [sqinv3mnvrhªv]Tylp]rm]v¨
Æ@]ojIqUi¯r[n6¡¦[y{n6ªv]3jlX]z¶ywi~jIikj{u}jl]T\^]TrDj@n}hjlX]MjlX]nvy{]\·¨3Ùj@s i@]r[npq[vXcj{n>ilX[n6¡³j{Xu6jz_¥nvr Gsjls nvr$
pqu}ywu}rDj{]]TijlXUu6j
YAe
c
K $ ] 5S6 S
gtc/j i
>
gtc/j M O
Qnpyu} ccikq °ms]Trpj{gmo npil]®j{nnvr[]p»[nvyY]T©Dq[s ª6u} ]rDjl gv»[Qnvyu} * °ilq °mos ]rDjl gmnDik]£jln¾T]y{n¨
YAe
c
K $ ] 5S6
S
glc\j i
,
gtc\jWNYAe
Y
K $ ] 5S6 + Y x
e(,TS
e#- g. j0/di ghYAe# j + Y x
e(,
>
e#- g. j0/
WNYAe
Y
K $ ]
5S6 , S
i$,
>
iCx
e(- g1 Tj
eGsrm]|S_UWNg , UU$i$,S_U"j [/xUcQnvyIW]J=9/?Ù»G¡¥]XUuªv]
Y/e
c
K $ ] 5S6
S
glc\j.i
>
glc\jWyY/e
Y
K $ ] 5S6
g0,
, i S x
j.i,
, ix
e - g. jW`Y'ix
YAe
Y
K $ ] 5S6
|S
u
WYX]r¯»Gj{X[]monpr Gsjls nvr
YiCx
YAe
Y
K $ ] 5S6 S
MfO
stiY]T©Dq[s ª6u} ]rDjYjln
>
M Yae
Y
K $ ] 5S6 S m
ils rmo]
, W`Y\[/x
¨
>]o´hj®¡][y{n6ªv]cjlX] ik]:monpr ·i~jwu6jl]T\]rDj>n}3j{X[]j{X[]npyl]T\º¨YWIn°[y{n6ªv]£jlX[]^ik]:monpr ·i~jwu6jl]T\]rDjT»7s«j
stiY]rnvq[pX-j{n°ikX[n6¡SjlXu}j£_¥nvr Gsjls nvr¸^s \^s ]Tij{Xu6jQnpyu`psªp]rn]ns & rmuu(umK
e Ya-
c
K $ ] 5S6
8S_U'gtc\j i U'glc\jaMfO
Qnpyu} ccikq °ms]Trpj{gmo npil]®j{nnvr[]p»[nvyY]T©Dq[s ª6u} ]rDjl gv»[Qnvyu} * °ilq °mos ]rDjl gmnDik]£jln¾T]y{n¨
c
K $ ]
5S6
8SVU'glc\j i U'glc\jW
Y
K $ ] 5S6 + Y
xrU e ,S_U e#- g. j0/ iFg.Y e# j + Y
xrU e , U e#- g. j0/
W Y
K $ ] 5S6
,TSVUi#,
UiGxrUAe(- g1 TjW
Y
K $ ]
5
S6 S6 U g0,TS_Ui$,
UiGxrU'j}e
Y
K
g0,U U$i",
U$iCxU"je(- g1 Tj
W Y
K $ ]
5
S6
S6 U
g0,U Ui SVUxrUi$,UUAe#
UxrUiCxU"j e Y
K g.
UxU$iCxU"je(- g1 Tj
W
xrU
K VX $ ]
5
S6 S 6
U
g1
U$i |S_U$iFY'j}e g.
U$iFY'j
be
e(- g1 Tj
WYX]£tu6jljl]Ty]o´G[y{]Ti{iks nvrs iY7npilsjls ªv]£Qnvyuv¯ilq °mos ]rDjl gil\$u} * U»s«
$ ]
5
S6 S 6 U g1
U$i |S_U$iFY'j}e g.
U$iFY'jaMFOrm
¡Xs mwX°sti¥]T©Dq[s ªuv]TrDjjln$_¥nvr [s«j{snprºG¨3WYX[]£[y{nDnv8n}3_¥npr Gsjls nvr40 s i¥ªv]Tylgiks \stu}y¥jln jlX[]£[y{nhn}OiMnv
_¥npr Gsjls nvricuvr º[¨
>mnvr [s«j{snpri£n}WYX]nvy{]\ÿXuªp]`ªp]y{g¸mo ]Tu}yc[y{nv§Uu}§[s stikjlstm s rDjl]y{[y{]ojwu6jls nvrUi¨^WYX[]Til]srDjl]Tyh6
yl]j{u6j{snpri§U]:monp\^]c]Tªv]r\nvy{]>j{y{uvrikUu}y{]rDjs rjlX[]mupik]c¡X[]Trnpr[ g$nvr[]cr[]T¡* sr[-s iup [ G]T ¯¨M¹[nvy
s rikj{uvrmo]p»}srj{X[]mupik]Ynv1uilsrv ]r]¡ s r[_¥npr Gsjls nvr·Yj{uvv]:iFjlX[]YQnpyl\
>
M e Yv¨3WYX[] u}jh6
j{]yM\]:u}riMjlXu}jMjlX[]®uªv]ywu}p]¥Uu6jlX°Qylnp\ uvv]>£j{nu}p]ikXnvq[t §U]®ikX[npykj{]yu}jM]:uvikj§hg`npr[]X[np
j{Xu}rºj{X[]uªv]Ty{uvv]>y{]oj{q[y{ru}jlXºQy{nv\uvv]cjln$sj{il]~¨_¥npr Gsjls nvr¸^§U]:monv\]:i M Yv»G¡X[stmwX·s i
uv¡YugGiFjly{q[]v¨3WYX[stiMstizr[nvj¥ikqyl[y{stiks r[uviz¡]hr[n6¡½jlXu}j¥u}r°up [ Gsjls nvrn}¯uilsr[p]>r[]¡ s r[^UnpsrDj{sr[
j{n-u$¤¦]§Uu}v]uv¡YugGiYsrUmoy{]Tuvil]Tis«jwi>x3u}p]Tuvr[Go;ik]T] ]v¨¨ » =Õ8?p²¨5>n6¡¥]Tªv]TyT»upi\]rDjls nvr]T ¸u6j®jlX[]
]Tr ¸nvMjlX[]`[y{]ªhsnpqi£ik]:m²jls nvr@»U¡] ¡nvq[t ¸ sp]j{nr[nvjl] jlXu}j®s¥u°uvv]^moy{]Tu6j{]Ti®ik]Tªv]ywu}Ir[]¡ s r[Gi»
j{X[]uvv]Tizjln6¡Yu}yw [iF¡X[s mwX^j{X[]Til]r[]¡ srhiMUnpsrDjM\spXDjr[n}juv¡YugGiF§U]Tr[]o¶[jQylnp\jlX]>uv [ [s«j{snpr^nv
r]¡ srhiT¨3W@ncmotu}y{s«Qg£j{X[s i3st G]:u[»}uvi{ilq[\]j{Xu6jFjlX[]Yr[]T¡ sr[Gizuvyl]¥§U]T]rmoy{]Tu6j{]T npr[]§Dgnpr[]v¨I¤X[]r
ilnv\]uvv]psªp]TiMu s r[ j{nnvqyMu}p]v»p¡¥]¡s 1u} ¡Yughi3§7]r]o¶[jMQy{nv\ sjT¨z5n6¡]ªp]y:»}s«¯u}üjl]y¥UnpsrDj{sr[
j{nqiT»FjlX[sti Uu}v]°uv iln¸ sr[Gijln³\$uvrDg n}j{X[]y`u}p]TiT»I¡X[stmwX¯»3nvr uªp]ywu}p]v»¯Xuªp]$ªv]Tylg¦npr[¸u}jlXi
§Uuvmw·jlnºnvqyu}p]v»1jlX]r¦s«j\spXDjc]Tªv]Trpj{qu} g [u}\$u}p] npq[yy{uvr[hsr¨ WInºilq[\\$u}y{s¾T]v»8s rmonp\sr[
s r[Gi£uvyl]^]Til7]Tmostu} g¸ªuvqUu}§[ ]`sjlX[]Tg³u}y{] y{]Tm]s ªv]T Qylnp\#Unp[q[tu}ycuvv]Ti®j{Xu6ju}y{]` []T Gstmu}jl]T ³jln
npq[y¤¦]§¸monp\^\`q[r[sj~gv¨
WYX[]Tyl]¥s iFu>ikjly{s Ds r[>ils \^s tu}y{s«j~g£§U]j~¡¥]T]r^_¥npr Gsjls nvri¥ 0Qylnp\WYX[]npyl]T\¬>u}r mnvr [s«j{snpri ok:'p
uvr ok 0,p® []y{sªp]T s r jlX[][y{]ªhs nvqi£ik]:m²j{snpr¯¨5>n6¡¥]Tªv]y:»1sr jlX]upikgh\Gj{n}jlstm^muvil]v»1j{X[]°monpr Gsjls nvri
nvzs\[y{n6ªhsr[^j{X[]`x3u}p]Tuvr[-uvyl]]´hyl]:ilil]T ºs r·jl]y{\$invF\]Tuvr·¶ywi~j>Uuvi{iluvv]£jls \]Tiywu6j{X[]yjlXuvr
\]:u}rºrDq\ §7]yn}3ªhs ilsj{iY§7]oQnvy{]u}§ilnvy{Gj{snpr¯¨
°F ) &¦&T-$% 8F)cI%
Æ@]ojFqi3ikX[n6¡Kj{Xu6jIjlX[]Tyl]]o´Gsti~jwi@s rOupm²j3u}r npGjls \$u}Ds r[hs r[®ikjlywu6j{]vgp¨F_¥nvrUikst G]y3uUu}v]AIW`Y'mu uum.B
uvr °upililq[\]j{Xu6j>IzXuvi¥ sr[Gijln`jlX[]£uvv]TiAI
m uuumhI $ ¡X[]Tyl]I
W I3QnvyYu} WNY'mu uu mK1¨zWYX[]Tr$Qnvy
j{X[] ¢£nhnvp]£\$u6jly{s´
b
H»[¡]£XUuªv]
SSW`Y e c
K $ 56
S(Se
Y
B
g.Y$iCc/jkY 5[\^]
[,_\a`
U.Sm ok,p
¡X]y{]
SVU£s ijlX[]®\]Tu}r°¶y{ikj¥Uuvi{iluvv]Yjls \]>Qy{nv\ uvv]$IFj{n uvv]A]^u}rU LcstiMj{X[]c¢£nhnpv ]>monpri~jwu}rDjT¨
WYX] nv§[|~]Tm²j{sªp] r[n6¡sti®jlnºmwX[nhnpil] K¸uvr <I
m uuu mhI $ ilqmwX¸j{Xu6j
S(S§7]Tmnv\]Ti£uvi£ik\$uv3uvi®UnDilils §[]
uvr -mnvril]T©Dq[]TrDjl g x S WyY/[
SS §U]:monv\]:i¥upi¥tu}y{v]£uvi¥UnDilils §[]p¨z¹[y{nv\Po~T,pMnvr[]cmuvril]]j{Xu6j SS s i
u^ sr]Tu}yQq[rUm²jls nvr·nv
U.S iT¨b·nvy{]n6ªp]y:»vnpqGjlpnvs r[` s r[GiQylnp\ I Gnr[nvju}±7]:m²j
U.S iT¨zWYXhqi»G s r[hsr[
Qy{nv\ IYj{nL]»@nvr[]muvr³nvrguv«j{]y£jlX[]$mnD] °mos ]rDj{ics rj{X[]yls vXDjh6ÙXuvr ³ils []`nvo~T,po¨`>i£¡Yuvicu}tiln
rn}jl]: s r¦eh]:m²j{snpr¦G»1sj£\]:u}ri®jlXUu6j£jlX[]^n6¡r[]y£n}jlX[]^u}p]!IXupi®uªv]Tylgº s«jljl ]mnvrDjly{nvFn6ªv]Ty>sj{i
x3uvv]T>u}r[1¨3WYX[]§U]:i~j¡XUu6jX[]}ikX]cmTu}r¸ Gnstijln$ sr[-nvr[ g°j{n^npr[]iksjl]]cilqmwXjlXu}j
U SW
U &
U.S -:u
>n}j{]jlXUu6jo;ikqyl[y{stiks r[v grpIjlX[]£x3u}v]:u}r`nvT] [tugGizr[n y{nv ]X[]Tyl]p¨FWYXhqiT»D¡¥]XUuªv]j{X[]Qnp n6¡sr
ikj{u}jl]T\^]TrDj
ÀhÄ
À
n PTl +"&&r\,%4 .+" %aU$ + SQP+ %: q + /n/&UD/ %,/ %4&r
Pr/Tt %L4+ S Pr+%,zJ+n n +/ Pr+\ +%,!lnhS+' L %"+/&<Pr+%,
a>mnvq[ywik]p»s ry{]Tu} sj~gv»7s«j£s i®r[n}j®[y{upm²j{s mTu}¯j{n- srºnpr[ g-j{n-nvr]u}p]v¨5>n6¡¥]Tªv]TyT»Gj{X[] \]:ili{u}p]
Qy{nv\(jlX]u}§7n6ªv]j{X[]npyl]T\s ijlXu}j`nvr]°Xuvijln s r[¦jlnUu}v]:ij{Xu6ju}y{]$yl]T]TªuvrDj`u}r §U]Tnpr[¸jln
j{X[]>i{u}\]Y¤ ]T§°monp\^\`q[r[sj~gv¨3ÓrDjl]Tyl]:i~j{sr[pgp»6jlX]> Gstilmqilils nvr^nvrnvGj{s\$uv sr[hs r[ikjlywu6jl]TvgUu}yljlstu} g
]´G[ uvsrUiIu ~y{upm²jlstmuvup Gªhs il]upmmnvyw Gsrjln£¡X[stmwX¯»}u>¤¦]§ils«j{]¥n6¡r[]TyFilX[npq[ ªDs ]¡½X[s i X]y3iksjl]uvi
u£il]ojzn}7u}p]TiFu}r `\$u}s rpjwu}s r`u£vnhnG s rDjl]Tyh6Ùs r[ikjly{qm²j{q[y{]uvr j{n®y{]oQ]TyFjlncX[sti6X[]yzmonp ]Tuvvq[]:i = T/?ͨ
3ÓrU G]]: 8»hs«jQnv n6¡iQy{nv\ nvq[yYu}y{vq\^]TrDj{izj{Xu6jilqmwX°7nv s mg^¡s 1m]ylj{uvsr[ gsrUmoy{]Tuvil]j{X[]£x3uvv]T>u}r[
nvFuv¯Uu}v]:isr¸u^vy{nvq[@¨
& -Fo
x3uvv]T>u}r[°nv3u¤¦]§¸Uu}v]csti G]¶r[]T ·§hg-jlX[]s rmonp\sr[$ s r[Giq[·jln°u\`q[jls []cOupm²j{nvy:»[¡X[stmwX
mTu}r°§7]cmonvrDj{ylnp ]T §hg$uv [ [sr[`nvy¥yl]T\^n6ªhs r[npqGjlpnvs r[ sr[GiT¨3¤ ]ci~j{q Gs ]T $s r []oj{uvs7j{X[]®mTuvil]>¡X[]Tr
npr[]¤ ]T§`uvv]uv [ [i3il]ªp]ywu}Dr[]¡ s r[GiFuvr []y{sªp]T ]´[uvm²j3q[1 [u6j{sr>Qnpyl\`q[ uv]Qnpy@j{X[]x3u}v]:u}r7¨
µ®iks r[°upikgh\Gjlnvjlstmu}ruvgGils iT»[¡]nv§[j{u}s r[]: ºils \^]rUu6jlqy{uv@monpr Gsjls nvriYj{Xu6j£ikX[n6¡¼szu°¤ ]T§¸u}p]
¡sjlX¸r]¡ gºmyl]:u6jl]: ºs r[Gi>uvr ·s«jwir[]TspXh§Unpy{i§7]r]o¶[j®Qylnp\jlX]Til]r[]¡ s r[Gi¨Y¤¦] monprmo q G]j{Xu6j
XUuªDs r[·r[nnpqGjlpnvs r[·s r[¦s i u¸§uv ¦7nv s mg uvr ¦jlXu}jjlX]°§U]:i~j`Unpstmog s ijln srjln³u}p]Ti£Qy{nv\
j{X[]ciluv\^]£¤¦]§·monv\\`q[r[sj~gv¨Mehq[y{[y{s ilsrv gv»hu r[]T¡*s rmonp\sr[`s r[°\s vXDjY§U]cr[nvjYu`vnhnG $r[]T¡iYs«Iu
Uu}v]®jlXUu6j7nvs rpjwiYjlnqivs ªv]Ti\$u}rhg°nvjlX[]Tysy{y{] ]ª6u}rDjYs r[Giu6jYj{X[]iluv\]®j{s\]p¨
+,6 F-
=? !"$#&%%'( !*)+#&%o;}pp:px3u}p]Tuvr[-_¥nv\[qGjwu6j{snpr
uvr jlX[]³ehjly{qm²j{q[yl]·nv®j{X[]·¤ ]T§³3´G7]y{s\]rDjwi$u}r vnpylsjlX\iT¨z3ÓrxzylnGm]]T [sr[Din}£jlX[]
p6ÍjlX|3ÓrDjl]y{ru}jls nvruv7¤¦nvy{t ¤st G]¤¦]§³_¥nvr[Q]y{]rm]v¨
=/?-,.#/%021#&%#3546 789#3546 7:90;=<>)?)?#3A@. 7zoÍ}pp'p3Órikst G]x3u}v]:u}r7¨7>_Yb WIy{uvriT¨3Ór6
j{]y{r[]oj£W@]:mwX[r[nv nvpgv»3Ór·[y{]Ti{i¨UikXnvyljl]yªp]ywiks nvrXuvi>u}tikn°uv[U]:u}y{]T sr·j{X[] xzy{nGmo]T]T Gs r[piYnv
j{X[]$v6;j{XD3ÓrDj{]y{ru6j{snpru}1¤¦nvy{ º¤st G]¤ ]T§³_¥nvrGQ]Tyl]Trmo]p¨
=0"?-,.9#&%:$ 7CBDE<>FG 7H4IJKL!"#32MN ?%'OP#&%$E'QH N ok 7'7:9:p7WYX[]x3uvv]T>u}r[>ms«jwu6j{snpr
ywu}rDs r[TF§yls r[vs r[nvyw G]Ty¥j{n^jlX[]¡]§¯¨7eDj{uvrGQnvyw µ>r[s ªv]ywils«j~g°WI]TmwX[rs mTu}¯]TUnpykj:¨
='?8N)?R$8 >S H%'UT5%VFQ%QWX ;@. To~ 7:7v,p@b¸u}jly{s«´`_¥nv\[q[j{u6j{snpriT»"0}yw ]T ¯¨\;Yuv«j{s\nvy{]v»
b<@!1}npX[ri>5np[hsriT¨
=/?Y[Z;<>%Y\ -WX @* ]%'_^#&9)+%'5:$ *oÍ}vv,p$_¥nvrhªp]y{v]rUmo]·ruvgGils i$nvu}rs\[y{n6ªv]:
x3uvv]T>u}r[ºu} vnvy{sjlX[\·¨ npykj{X _u}y{nv srUuehj{u6j{] µrsªp]ywiksj~gWI]TmwX[rs mTu}@]TUnpykj£_®e_ 6ÙW>}"6
DG¨
="?-^!L :$ ]S- <>)?#K )Q N S 74%%#&%E5DWX %' 8)+R$$8 AS o;vv'0,pM3´ 6
nps«j{sr[ jlX[] ;nGmw$eDjly{qmojlq[y{]>nv8jlX[]®¤ ]T§°Qnvy_¥nv\[qGj{sr`x3u}p]Tuvr[1¨DeDjwu}rGQnpy{ °µ>r[s ªv]ywils«j~g
WI]TmwXr[s mTu}¯]TUnpykj:¨
=V~\?-^!L :$ ]S- <>)?#K )Q N S 74%%#&%E5DWX %' 8)+R$$8 AS o;vv'0,pM3´ 6
j{y{uvUnp u}jls nvr b¸]ojlXnh i>Qnpy£mTmo]T]Ty{u}jls r[x3u}p]Tuvr[_¥nv\[qGjwu6jls nvrUi¨3Ór xMylnGmo]T]T Gs r[Di>nvMjlX[]
\6ÍjlX|3ÓrDjl]y{ru}jls nvruv7¤¦nvy{t ¤st G]¤¦]§³_¥nvr[Q]y{]rm]v¨
=9"?-^<;!"<>% /8 .%' :%<>)?)2 FG ]¹Fsrs«j{]¦b¸uvylpn6ª _¥Xu}s riT»WYX[]³µ>r[sªp]ywiksj~g eG]y{s]:i°s r
µ>r G]Tylpy{up Gqu6j{]cbu6jlX]\$u6j{s mTi»Muvr >npikjlywu}r ¯»[xzyls rm]ojlnpr¯» ®»¯87vv»
=7"?-F%E#&)?)+< 7N%' 4<<> VWX o;vv:0:p|@>]T]7]y<3ÓrUikst G] x3u}p]Tuvr[1¨YxMyl]T[yls rDjT»
>nvyljlX³_u}y{nv s ru^ehj{u6j{]µr[s ªv]Ty{ils«j~gp¨[mm]Gj{]T jln^jlX]*3Órpj{]y{r[]oj>b¸u}jlX[]T\$u6jlstmi®}npq[ylrUu}ͨ
= T"?F%E#&)?)+<$ 79%'(4<<> QWX oÍ}vv,p¥µ1 [u6j{sr-x3u}v]:u}r$¡s«j{XJ3Ùjl]ywu6j{sªp]£>"6
pyl]Tpu}jls nvr¯¨ 3Ór¸xzy{nhm]]: Gsrpin}FjlX[]$80/6ÍjlXº¤ npylt ¤s G]¤¦]§³_¥nprGQ]y{]rm]v¨
= v?F%E#&)?)+< H%' 4< <> WX }o;vvv,pF]npy{ []y{sr[®QnvyMjlX[]x3u}p]Tuvr[[y{nv§[ ]\·¨
c_YeGµ _>eU_WI]TmwX[r[stmuv¯]7nvylj£_>e_ 6ÓWv"6wT[¨
= :/?FQ<>< WX B- WX 78N)?R$8 S 7%'$<>%#$D:$ o;vvv,pz¼¹upi~jW@¡n"6~eDjwu}v]>pnvy{s«j{X[\
Qnpy®_¥nv\[qGj{sr°xFuvv]:u}r[1¨[eDjwu}rGQnpy{ ºµr[s ªv]Ty{ilsj~g-W@]:mwX[r[stmuv¯]7nvyljT¨
= 0"?4I)?<> WX ]%' 4I)?<> ^ 7o;vv:0:p>q[\]y{s mTu}_¥nv\[qGj{sr[ ¡sjlX¼bzWÆ@;£»
e3~®bK¨
= '? B*9J9<>9!G%.46 AF" 7 o~ 7:7} pb¸u}y{vn6ªC@>]:mostiks nvr xzylnGm]Ti{ik]:in@®s i{moy{]oj{]ºeDj{nhmwXUuvikjlstm4@®gDrUu}\s m
xMylnpvywu}\\sr[U»h¤s ]gp¨
= :/?£XDjljl jlnhnv §u}y:¨vnhnvp]p¨mnv\
= T"?£XDjljl 6¡¡¡¨il]Tuvy{mwX[]Tr[vs r[]T¡u}j{mwX¯¨monp\
Unité de recherche INRIA Sophia Antipolis
2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France)
Unité de recherche INRIA Futurs : Parc Club Orsay Université - ZAC des Vignes 4, rue Jacques Monod - 91893 ORSAY Cedex (France)
Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique 615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France)
Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France)
Éditeur
INRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France)