• Aucun résultat trouvé

Groups of Adjacent Contour Segments for Object Detection

N/A
N/A
Protected

Academic year: 2022

Partager "Groups of Adjacent Contour Segments for Object Detection"

Copied!
34
0
0

Texte intégral

(1)

HAL Id: inria-00096663

https://hal.inria.fr/inria-00096663v2

Submitted on 21 Sep 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents

Groups of Adjacent Contour Segments for Object Detection

Vittorio Ferrari, Loic Fevrier, Frédéric Jurie, Cordelia Schmid

To cite this version:

Vittorio Ferrari, Loic Fevrier, Frédéric Jurie, Cordelia Schmid. Groups of Adjacent Contour Segments

for Object Detection. [Research Report] RR-5980, INRIA. 2006. �inria-00096663v2�

(2)

a p p o r t

d e r e c h e r c h e

ISRN INRIA/RR--5980--FR+ENG

Thème COG

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Groups of Adjacent Contour Segments for Object Detection

Vittorio Ferrari — Loic Fevrier — Frederic Jurie — Cordelia Schmid

N° 5980

September 2006

(3)
(4)

, +.-/

01324265874195;:=<>7476?@741BA+C5819DE:+<GFH7I19<J7KA+:=7I<>L.<>7I13DNM@O7I13<;AQPR587IL.<>S919?UTD'VWX19L

Y[Z]\_^a`%bcBdfehgjilknmo\4^a`4kqp_rGsGtvuwmxuwyzk

{+|xr~}`_mq€Q‚ƒ

ƒq„~…]…@rG|omq†j`(|x`4p‡Z]`4|xp‡Z]`ˆt8‰=Š~‹JŒGNeŽgl`4…jmo`4^%@`_|GGG‘(e!’]“B…v„~sJ`4k

”–•.—4˜_™'š]›G˜Gœž

`"…]|o`Ikn`4t>m%„–yz„G^au Ÿ¡iNrGy[kxp_„GŸ `_¢9u¡tl£6„G|ou¤„~t>m¥Ÿ rjp_„GŸ+knZ¦„~…@`ay§`4„'mx¨]|x`4k¥y§rG|x^a`4†©li©p‡Zv„Gu tvk

rGy

k

p_rGt]tv`4pªmx`4†¬«[|xrG¨]sJZ]Ÿ¡iXkmx|x„Gu sJZ>m"p_rGt>morJ¨]|­ko`_sG^a`4tJm‡k¯®

k

‚¥g]°ª«[„~t¦†XmxZ]`_u¡|­¨vko`Ky§rJ|­rGj}`Ipªm–p_Ÿ¡„Jkok

†]`/mo`Ipªmxu rJt±

k

‚¥gN„G|o`a„~]Ÿ¡`morEp/Ÿ¡`4„~tvŸ iK`4tvp/rj†j`R…]¨]|x`Ry§|x„GsG^a`_t>mxkr~y„~t²rGj}`4p/m¥@rG¨vtv†]„~|xiG«¬³u moZvrG¨jm u¡tvp_Ÿ ¨v†]u t]s´t]`4„G|oli´p_Ÿ ¨jmomo`4|4±.µKrG|x`_r'£J`_|I«ªmoZ]`4irG¶@`4|H„~t„~mnmx|x„Jpªmou¡£G`+p_rG^a…]|xrG^au¤kn`@`/m³`_`_t(u¡tjy§rJ|o^"„'mxu rJt

p_rGt>mo`4t>m´„~tv†|x`_…@`4„'m‡„~]u¡Ÿ¡uwmiJ«]„~tv†E`4tvp/rJ^R…¦„Gkxk„a³u¡†j`(£'„G|ou¡`/mi­rGy.Ÿ¡rjp_„GŸHknZ¦„~…@`kmx|o¨vp/mo¨]|x`4k4±  `%„~Ÿ¤kor

†]`/·vt]`a„–mo|‡„~tvkoŸ¡„~mou¡rGtN„Gtv†²kop4„~Ÿ¡`%u¡t>£'„G|ou¤„~t>m¥†]`4kxp/|xu …jmxrG|¥`_tvp_rj†ju tvs–mxZ]`asG`_rJ^a`/mo|xu¤p%p/rJtj·vsJ¨]|x„~mou¡rGt¯rGy

mxZ]`ko`_sG^a`4tJm‡k[³uwmxZ]u¡tE„

k

‚¥g8«]^"„~¸lu¡t]s

k

‚g`4„Jkni­mor"|x`_¨vko`Bu tEr~mxZ]`_|[y§|‡„~^a`4³¹rJ|o¸jk4«Gy§rJ|`/º]„~^a…]Ÿ¡`„Gk

„R|x`_…]Ÿ¤„Gp_`_^a`_t>mrG|„J†]†ju mou¡rGtmorau¡tJmx`_|x`4knm…¦rJu t>mxk4±

 `©†j`4^arGtvknmo|‡„'mx`KmoZ]`©Z]u¡sGZ»…@`_|oy§rG|x^"„~tvp_`¯r~y

k

‚¥g¼³uwmxZ]u¡t½„Ukou ^a…]Ÿ¡`N]¨]m…@r'³¹`4|ny§¨vŸkoŸ u¤†ju¡t]s~¢

³u¡tv†jr'³rGj}`Ipªm­†j`_mo`4p/mou¡rGt¾kxp‡Z]`_^a`G±»Y[Zv|orJ¨]sGZ`/ºlmo`4tvknu¡£G`E`4£6„GŸ ¨¦„'mou¡rGt¦k_«u tl£JrGŸ¡£>u¡t]s²`_u¡sGZ>m­†ju¡£G`_|‡ko`

rJj}`4p/m­p/Ÿ¤„Gkxkn`IkR„Gtv†^RrJ|o`mxZv„~t¿“_À>G©u ^"„~sJ`4k4«Q³`Á“I°Rkmx¨v†jiXmoZ]`E`_£JrGŸ¡¨jmou¡rGtÂr~y¥…¦`4|ny§rJ|o^"„Gtvp/`K„Gk

mxZ]`†j`4sG|x`_`(r~y.y§`4„~mo¨]|x`p/rJ^a…]Ÿ `_ºjuwmi

k

£'„~|xu¡`4kq„Gtv†E†j`/mx`_|x^Ru¡t]`BmxZ]`@`4km´†]`_sG|x`_`JæG°[koZ]r'³ÄmoZv„~m

k

‚g

ko¨]vknmx„Gt>mou¤„~Ÿ¡Ÿ iKrJ¨jmo…@`_|oy§rG|x^Åu t>mx`_|x`4knm¥…@rGu¡t>mxk¥y§rG|(†j`_mo`Ipªmou¡t]sKkoZv„~…@`/¢Æv„Gko`4†Np/Ÿ¤„Gkxkn`Ik_ÃH’>°´p_rG^a…v„G|o`RrG¨]|

rJj}`4p/mq†j`/mx`4pªmxrG|[mxramoZ]`B|x`4p/`4t>m4«]knmx„'mx`/¢Ær~yÇ¢9moZ]`_¢Æ„G|nmkoilknmo`4^ȏli–É¥„~Ÿ¤„~Ÿ„Gtv†Y|xu sJsJk¥ÊÀGË9±

ÌKÍ>Î8ÏxÐ%Ñ ™'Ò.—Gœ Ÿ¡rjp_„GŸ8y§`4„'mx¨]|x`4k4«]knZv„G…¦`†]`4kxp/|xu …jmxrG|‡k_«lrJj}`4p/m†]`/mo`Ipªmxu rJt

Ó©Ô3Շ֠×ÇØÙ‡ÚzÛ=ÜÞÝß6àÞÛÝÛá_×9Ùx×3ÜÞÕªáÜÞÔHÙnâ‡Ù‡ÜÞàãهä6àÞÛ+Ùx×.凿ªç‡è]é9êìë/è6ênç/åoí_æ_î>é¤ïªè_ð/î‡ñxïªò‡ó4ç‡è/æ

(5)

’

+ ,

H"Q-/

-ìtBmxZ]`+Ÿ¤„Gknm¬y§`_³ÁiG`I„~|‡k_«_moZ]`Q…]|orJ]Ÿ¡`_^ÄrGy>|x`4p_rGsJt]u/.4u tvsrJj}`4p/mp/Ÿ¤„Gkxko`4k8Zv„Jk¬|o`Ip/`4u £J`4†¥sG|xr'³u tvs„~mnmo`4t>mou¡rGt«

u¡t²¦rGmoZÁ£'„~|xu¡„GtJm‡k¥r~y[³Z]rGŸ¡`u¡^"„~sJ`ap_Ÿ¡„Jkokou ·¦p_„~mou¡rGtXʒj«Š]«=“4j«Q“_À]«=“6ŠIË9«.„~tv†©rG]}`4pªm(Ÿ¡rjp_„~Ÿ¡u0.4„'mxu rJtXÊސj«

Àv«´“4‘]«¹’]“/Ë9±¿Y[Z]`¯^"„'}rJ|ou miUr~yB`/ºju¤kmxu tvs;^R`_moZ]rj†]k–¨vko`KŸ rjp_„GŸqu¡^a„GsG`K…v„~mxp‡Z]`Ik­„Gk­v„Gkou¡py§`I„'mx¨]|o`Ik_±

 Zvu Ÿ¡`moZv`4ko`q³¹rJ|o¸%³¹`4Ÿ Ÿvy§rG|QkorG^a`rG]}`4pªmp/Ÿ¤„Gkxkn`Ik_«Gko¨vp‡Z­„Jk=^ar~morJ|ovu ¸J`4k=„~t¦†"p_„~|‡k4«~r~mxZ]`_|Qp_Ÿ¡„Jkoko`4kQ„~|x`

†]`/·vt]`I†ali%mxZ]`_u¡| 122 «j„~tv†"„G|o`[mxZ]`_|x`/y§rJ|o`@`/momo`4|¹|x`_…]|x`4ko`_t>mx`4†Rli ! y§`I„'mx¨]|o`Ik´®z`G±sv±.Z]rG|‡kn`Ik_«

rJ|Q^¨]sJk‡°ª±3-ìt–ko…]u mo`´rGy¬moZ]`4u |[ko¨]vknmx„~t>mxu¡„GŸ@kxp/rJ…¦`J«JrJt]Ÿ iap/rJ^a…v„~|‡„~]Ÿ¡iy§`_³¾³rG|x¸lk´Êj«¦“I’j«]Gl«j~‹6Ë8Zv„6£J`

m‡„Gp‡¸lŸ¡`4†–moZ]`p_Ÿ¡„Jkokn¢9Ÿ¡`_£J`_Ÿ@Ÿ rjp4„~Ÿ¡u/.I„'mou¡rGt…]|xrG]Ÿ¡`_^Ȩvknu¡t]s"p/rJt>morG¨v|¹y§`I„'mx¨]|o`Ik_±

-ìtmoZ]u¤k"…v„G…¦`4|a³¹`E…]|x`4ko`_t>m"„Nyz„G^au Ÿ¡iUr~y¥Ÿ rjp4„~Ÿp/rJtJmxrG¨]|Ry§`I„'mo¨v|o`Ik_«„~tv†UmoZ]`4u |­„G…]…]Ÿ¡u¡p4„'mou¡rGtXy§rG|

†]`/mo`Ipªmxu t]s„~tv†BŸ¡rjp_„~Ÿ¡u0._u¡t]sqrG]}`4pªm‡k_±Y[Z]`4ko`+y§`I„'mo¨v|o`Ik„~|x`Qko^a„GŸ ŸJsG|xrG¨]…¦k¬r~y 4 «'„~…v…]|or6ºju¡^"„'mo`4Ÿ i

knmo|‡„~u¡sGZ>mQp_rGt>morJ¨]|¹ko`_sJ^R`4t>mxk4«Jp_„GŸ Ÿ¡`4†

k

')5 %'&()* «JrJ|

k

‚g¬±>Y[Z]`¥kn`4sG^a`_t>m‡k+u¡t–„

k

‚¥gRy§rG|x^

„…v„~moZ%rGy¦Ÿ¡`_t]sGmoZ

k

mxZ]|orJ¨]sGZ„´t]`_m³¹rJ|o¸BrGy@p/rJt>morG¨v|.ko`_sJ^R`4t>mxk.p/r'£G`4|ou¡t]smxZ]`[u ^"„~sJ`ʋ6ËÆ±.Qkoko`_t>mxu¡„GŸ Ÿ¡iG«

m³rakn`4sG^a`_t>mxk„~|x`Bp/rGtvt]`4p/mo`4†u¡t–mxZ]`Bt]`/m³rG|x¸auwymoZ]`4i–„~|x`¥„J†6}n„Gp_`_t>m[rGt­mxZ]`(ko„G^a``I†jsG`4Ÿw¢ìp‡Zv„~u¡t«lrG|

u yQrJt]`u¤k¥„'m¥moZ]`R`_tv†Nr~y¹„Gt¯`4†]sG`_Ÿ ¢ìp‡Zv„~u¡tN†ju¡|o`Ipªmx`4†Emxr'³„G|x†]kqmoZ]`Rr~mxZ]`_|(ko`_sJ^R`4t>mR®zko`4p/mou¡rGtN’>°ª±Y[Z]`

Ÿ¤„~|xsG`4|mxZ]`tl¨]^¦`4|

k

r~yko`_sJ^a`_t>mxku t„

k

‚¥g8«.moZ]`^arG|x`p_rG^a…]Ÿ¡`/º;moZv`Ÿ¡rjp_„~Ÿ[koZv„~…@`knmo|x¨vp/mo¨]|x`4k u mp4„~t;p_„G…jmo¨]|x`G±

1AS

„G|o`¥}¨vknm%u¡tv†ju¡£lu¡†j¨¦„~Ÿ¹ko`_sJ^a`_t>mxk4«H³Z]u¡Ÿ¡`

2AS

u¡tvp/Ÿ¡¨v†j`

L

knZv„G…¦`Ik_«„~t¦†

3AS

p4„~tXy§rG|x^

C, F

„Gtv†

Z

koZv„G…¦`Ik®§·vsG¨v|o`Ik"l«+’J°/±‚qŸ¡rGtvs²³u moZmoZv`

k

‚gUy§`4„'mx¨]|x`4k4«Q³`…]|xrG…@rJko`„

Ÿ¡r'³ †ju¡^a`_tvkou rJtv„~Ÿ9«=mx|x„GtvknŸ¤„'mxu rJt46¥kxp_„~Ÿ¡`"u¡t>£'„G|ou¤„~t>mR†]`4kxp/|xu …jmxrG|a†j`4kou¡sGt]`I†Ámor²`_tvp_rj†j`–mxZ]`sG`_rJ^a`/mo|xu¤p

…v|orJ…¦`4|nmxu `Ik¹rGymxZ]`ko`_sG^a`4tJm‡k[p/rG^a…@rJkou tvsa„

k

‚¥g8«v„Gtv†moZ]`4u ||x`_Ÿ¤„'mxu £J`Ÿ¡rlp4„'mxu rJtvk_±

k

‚¥gZv„6£G`¥„Rko`_£J`_|‡„~Ÿ8„'momo|‡„Gpªmxu £J`…v|orJ…¦`4|nmxu `Ik_±57.u |‡knm4«]„Gk@r~mxZ

k

‚¥g„Gtv†–moZ]`4u |†j`Ikop_|ou¡…jmorJ|xk[p_r'£G`_|

korGŸ¡`_Ÿ¡iNkoZ]rG|omp‡Zv„~u¡tvkBrGy[p_rGt]t]`Ipªmx`4†Ákn`4sG^a`_t>m‡k_«HmoZ]`4iNZv„6£J`mxZ]`­„~vu Ÿ¡uwmiNmor¯p_r'£G`_|B…]¨v|o`"…@rG|omou¡rGtvkBrGy

„GtrJj}`4p/mR@rG¨vtv†]„~|xiG«¹³uwmxZ]rG¨]m­u tvp_Ÿ ¨¦†ju tvsÁp_Ÿ ¨]mnmo`4|"`4†jsJ`4ka³Z]u¤p‡Z£G`_|xi;r~yÇmx`_tŸ u¡`Eu tmoZv`K£>u¤p/u¡t]u miG±

gj`4p/rJtv†¬«=y§rJ|"„©ko`_tvkou¡]Ÿ `|x„Gt]sG`r~y

k

«

k

‚gUZv„6£G`u t>mx`_|x^R`I†ju¤„'mo`Ep/rJ^a…]Ÿ `_ºjuwmiJ«+³Z]u¤p‡ZX^"„~¸J`4k%moZ]`4^

†]`/mo`Ipªm‡„~]Ÿ¡`|x`_…@`4„'m‡„~]Ÿ¡i³Z]u Ÿ¡`@`_u¡t]s–u¡tjy§rJ|o^"„'mxu £J`„'mqmxZ]`kx„~^a`(mxu ^a`J±´Y[Z]u¡|x†¬«@p/rJt]t]`4p/mo`I†jt]`4kxkqu¤k´„

t¦„'mo¨v|x„GŸ+sG|xrG¨]…vu t]sKp_|ou mo`4|ou¡rGt©morEy§rJ|o^

k

‚g¬±8-Æm%„6£GrJu¡†vk¥moZ]`­tv`_`4†²y§rJ|%†j`/·¦t]u tvs¯„:9sJ|orJ¨]…]u¡t]sKkop4„~Ÿ¡`'9 rJ|„;9sJ|orJ¨]…]u¡t]sKt]`_u¡sGZl@rG|xZ]rlrj†<9y§rJ|R„¯ko`_sJ^a`_t>m4«+„Gtv†Á`/¶8`4p/mou¡£G`_Ÿ¡i;p/rJtvkmx|x„Gu t¦k(moZv`­y§`4„~mo¨]|x`4k%mor©¦`

p‡Z¦„~u¡tvk[r~y=kn`4sG^a`_t>m‡k_«j³Z]u¤p‡ZK„~|x`B^RrJ|o`BŸ¡u ¸J`_Ÿ¡i­r~yŸ¡i>u¡t]s"`4tJmxu |x`_Ÿ¡i­rJtE„R@rG¨]t¦†]„~|xiG±=7.u¡tv„~Ÿ¡Ÿ¡iG«

k

‚¥g„G|o`

p_rG^a…]Ÿ¡`/mx`RŸ¡rjp_„GŸ+u tl£'„~|xu¤„~t>my§`I„'mx¨]|o`Ik>(`I„Gp‡Z²Zv„Gk(„E³`_Ÿ¡Ÿ+†j`_·vt]`4†²Ÿ¡rjp_„'mxu rJt;„~tv†²kop4„~Ÿ¡`G«.„~t²u tl£'„~|xu¡„Gt>m

†]`4kxp/|xu …jmxrG|I«„Gtv†Áu¡k†j`/mx`4p/mo`4†Uv„Gko`4†²rGtvŸ i²rGt;Ÿ¡rjp_„~Ÿ¹…]|xrG…@`_|omou¡`4k(rGy„Kkou¡t]sGŸ¡`­u¡^a„GsG`J±@?´`_tvp_`G«.moZv`_i

p4„~t©¦`a|x`_¨vko`4†©`/¶8rG|omoŸ¡`4kxknŸ¡iEu tÁ„£'„~|xu `_miKr~yQ|x`4p_rGsGtvuwmxu rJt©„~t¦†¯u¡^a„GsG`R^"„'mxp‡Zvu t]sy§|‡„~^a`_³rG|x¸jk´„Jk¥„

|x`_…vŸ¡„Jp/`_^a`4tJm[rG|q„J†]†ju mou¡rGtmorau¡t>mo`_|x`4knm…¦rJu t>m‡k®zko¨vp‡ZE„Gk ʐl«@Šl«“4]«“4‘j«¦’G6˧°ª±

 `²†]`_^arGtvknmo|‡„'mx`¯mxZ]`©…@r'³`_|„Gtv†BA¦`/ºju vu Ÿ¡uwmi¾rGy

k

‚g»³uwmxZ]u¡t½„~t½rGj}`Ipªm†]`/mo`Ipªmxu rJt»y§|‡„~^a`/¢

³rG|x¸²³Z]u¡p‡Z]|xu t]s>kmorGsJ`/mxZ]`_|akn`4£G`4|x„GŸ¹ko¨vp_p_`4kxky§¨]Ÿ[u¤†j`4„Jk%…v|o`Ikn`4tJmx`4†;@`/y§rJ|o`J±C7]rJŸ Ÿ¡r'³u tvs¯moZv`EDv„Gs

rGyQy§`I„'mo¨v|o`Ik98…v„G|x„J†ju sJ^ ʒ]«=“_À]«H’GÀ'ËÆ«³¹`ap/rJtvknmo|x¨vpªm„p/rj†j`_@rlrG¸¯rGy

k

#"C*FG)

«H`4„Gp‡Z²p_„G…jmo¨]|xu¡t]s„

†]uw¶8`_|x`_t>m(¸lu tv†©r~y¹Ÿ rjp_„GŸ=knZv„G…¦`"knmo|x¨vpªmx¨]|x`®§·vsG¨]|x`4k(„~t¦† ’>°ª±R‚qtÁu ^"„GsG`R³u tv†]r'³ u¡kBko¨]8†ju £lu¤†j`4†

u¡t>mormou¡Ÿ `Ik¥ÊÀ¦«¬“IŠI˄~t¦†­`4„Jp‡Z–u¤k[†j`4kxp/|xu @`4†li­„ko`_…¦„~|‡„'mo`v„~sr~y

k

‚g8±H-ìtmoZ]u¤kyz„GkoZ]u¡rGt­mxZ]`¥³u tv†]r'³

|x`_…v|o`Ikn`4tJm‡„'mxu rJt²u¤kap/rJ^R…@rJko`4†ÁrGyko`_£G`4|x„GŸQv„GsJk%r~y

k

‚¥gUko…v„'mxu¡„GŸ Ÿ¡i²Ÿ¡rjp_„GŸ u0._`I†;³uwmxZ]u¡tUmoZv`–³u¡tv†jr'³(±

‚†v†ju tvs"moZ]u¤kŸ¡„6iJ`_|qrGyQkn…v„~mou¤„~ŸrG|xsJ„~tvu/.I„'mou¡rGtu¡^R…v|or'£J`4k[mxZ]`†ju¤kxp/|xu ^au¡tv„'mxu £J`…¦r'³`_|p/rG^a…v„G|o`I†mor–„

knmx„Gtv†]„G|x†rG|‡†j`_|xŸ¡`4kxkv„~s(rGy¦y§`I„'mo¨v|o`Ik=r'£G`4|moZ]`q`4t>mou¡|o`³u¡tv†jr'³(±  `q·v|xknm=mo|‡„~u¡t"„(p/Ÿ¤„Gkxknu ·v`4|y§|orJ^`/ºl¢

„G^a…]Ÿ `[rJj}`4p/mQ„~tv†Rv„Jp‡¸>sJ|orJ¨]tv†%³u tv†]r'³qk_«G„Gtv†%moZ]`4t"Ÿ rjp_„GŸ u0._`[…]|x`_£lu¡rG¨vkoŸ¡i(¨]tvko`_`_tau¡tvknmx„~t¦p/`4k+u tRmo`Ikm

u¡^"„~sJ`4k£lu¤„­„"^%¨vŸwmxuw¢ìkop4„~Ÿ¡`knŸ¡u¤†ju tvs~¢Æ³u tv†]r'³¿^a`Ip‡Zv„~t]u¤ko^!ÊÀv«8’]“ªËp/rG¨v…]Ÿ `I†E³uwmxZKmoZv`p/Ÿ¤„Gkxkouw·v`4|4±´c¨]|

(6)

mxrGsJ|x„G^Åʐ~À'Ë9«v³Z]u¡p‡Zu¤kq„R|o`Ip/`_t>mxŸ i–†]`_£G`4Ÿ rJ…¦`I††v„'mx„Jkmx|o¨¦pªmo¨v|o`Bkn¨v…]…¦rJ|nmxu tvsmxZ]`(|‡„~…]u¤†p_rG^a…]¨jm‡„'mxu rJt

rGy^¨]Ÿwmxu¡†]u ^a`_t¦knu¡rGtv„GŸZ]u¤kmxrGsJ|x„G^ak4±

ɨ]|xu t]s¼„~tÄ`/ºlmo`4tvknu¡£G`©`_£'„~Ÿ¡¨v„~mou¡rGt«u tl£GrJŸ £lu¡t]sU`4u sJZJmK†ju¡£G`4|xko`¯rG]}`4pªmKp/Ÿ¤„Gkxko`4k–„Gtv†»r'£J`_|©“_ÀJJ

u¡^"„~sJ`4k(®zko`4p/mou¡rGt¯‘>°ª«v³`knmo¨v†jiEko`_£G`4|x„GŸ„Gko…¦`Ipªm‡kqr~y

k

‚¥g8±7.u¡|xknm4«¦³¹`%„Gtv„~Ÿ¡iH._`¥moZ]`%rGj}`Ipªm†j`_mo`Ipªmou¡rGt …@`_|oy§rG|x^"„~tvp_`%³Z]u¡Ÿ¡`R£'„G|oilu¡t]s

k

«8mxZ]`_|x`_li¯koZ]`4†v†ju tvsŸ¡u sJZ>m¥rJt¯moZv`R|x`_Ÿ¤„'mxu rJtN@`/m³`_`_t©|o`4…¦`I„'m‡„~]u¡Ÿ u mi

„Gtv†Ru t]y§rG|x^a„~mou¡£G`4t]`4kxk=„Gk

k

u¡tvp/|x`4„Jkn`Ik_±gl`4p_rGtv†«~y§rG|Q`4„Gp‡Z

k

«>³¹`£'„~|xi(mxZ]`q|x`4korGŸ¡¨jmou¡rGtRr~y8moZv`³u tv†]r'³ mxu Ÿ¡u¡t]sv«'„~Ÿ¡Ÿ¡r'³u t]s[mxr´rJvkn`4|o£J`moZ]`Qmo|‡„G†j`_¢9rG¶%@`/m³`_`_t„G†]†ju¡t]sqŸ¡rjp_„GŸ u0.4„~mou¡rGtBu t]y§rG|x^a„~mou¡rGt„Gtv†(|x`4†j¨vp_u tvs

mxrGŸ¡`_|‡„~tvp_`%mxrKkn…v„~mou¤„~Ÿ£'„~|xu¡„~mou¡rGtvk¥³u moZ]u¡t©moZ]`­p_Ÿ¡„Jkok4±-ìt>mo`4|o`Ikmxu tvsGŸ¡iG«³`R·vtv†NmoZ]`"rJ…jmou¡^"„~Ÿ³u t¦†jr'³

mxu Ÿ¡u¡t]s–mxr–|x`_Ÿ¤„'mx`mormoZv`Rp_rG^a…]Ÿ¡`/ºjuwmiKrGy=moZ]`Ry§`I„'mo¨v|o`Ik®

k

°ª«¬³u moZ©kou¡^R…vŸ `4|y§`I„'mx¨]|o`Ik´…v|o`_y§`_|x|ou¡t]s"·vtv`_|

mxu Ÿ¡u¡t]sv±.µKrG|x`_r'£J`_|I«/³¹`+moZ]rJ|orJ¨]sGZ]Ÿ¡ip_rG^a…v„G|o`.moZv`Q…@`_|oy§rG|x^a„Gtvp/`=rGy

k

‚g(„GsJ„~u¡tvknmu t>mx`_|x`4knm…¦rJu t>mxk4«'„~tv†

„GsJ„Gu tvknmmoZv`%km‡„'mx`/¢Ær~yÇ¢9moZ]`_¢Æ„G|nmrG]}`4pªm¥†j`/mx`4pªmxu rJtEmo`Ip‡Z]t]uJ¨v`liÉ¥„~Ÿ¤„~Ÿ.„~tv†EY|ou¡sGs>k(ÊÀ~Ë9±qY[Z]`4u |´³¹rJ|o¸

u¤k(…v„G|nmxu¡p_¨]Ÿ¤„~|xŸ i©|o`4Ÿ `4£6„Gt>mB@`4p4„~¨vko`­u my§rGŸ¡Ÿ¡r'³qk(„¯knu¡^au Ÿ¤„~|†j`/mx`4pªmxu rJt²y§|x„G^R`4³¹rJ|o¸®zkoŸ u¤†ju¡t]s~¢Æ³u t¦†jr'³qk_«

mxu Ÿ¡`4k‡°ª«>]¨jmuwm„~…]…]Ÿ¡u¡`4kQ†]uw¶8`_|x`_t>m¹†j`Ikop_|ou¡…jmxrG|‡kmor(mxZ]`´³u¡tv†jr'³mou¡Ÿ¡`4k¥®zkou ^a…]Ÿ¡`_|¹Z]u¡knmorJsG|‡„~^"kr~y¬sJ|x„J†ju `4t>m

rJ|ou¡`_t>m‡„'mou¡rGt¦kx°/± 7.u tv„GŸ Ÿ¡iG«.³`"`/ºj…¦`4|ou¡^a`_t>m%³u moZÁmxZ]`–„~…v…]Ÿ u¤p_„~mou¡rGtÁr~y

k

‚g²³u moZU†]uw¶8`_|x`_t>m

k

„'m%moZ]`

kx„~^a`¥mou¡^a`G«v„Gtv†³uwmxZmxZ]`p/rJ^%]u¡tv„~mou¡rGtr~yu¡t>mo`4|o`Ikmq…@rGu¡t>mxk„~t¦†

k

‚¥g8±

_B ("

-ìt©moZv`y§rJŸ Ÿ¡r'³u¡t]s–³`R·v|xknmB|o`4£>u¡`_³rGj}`Ipªm†j`/mx`4p/mou¡rGt©mo`4p‡Zvt]u>¨]`Ik¥v„Gko`4†NrGtÁp/rGt>mxrG¨]|y§`4„~mo¨]|x`4k4«8y§rG|

³Zvu¡p‡Z

k

‚¥gr~¶8`_|´„GtE„GŸwmx`_|xtv„'mxu £J`G«]„Gtv†moZ]`4tK…]|x`4ko`_t>m³¹rJ|o¸jk[rGtmxZ]`…@`_|xp_`_…jmx¨v„~ŸHsG|xrG¨]…]u¡t]sar~y+p_rGtj¢

mxrG¨]|‡k4«j¨]…¦rJt³Zvu¡p‡Z

k

‚¥g–v¨]u Ÿ¤†¬±

Ñ ˜ Ñ ™Í šj˜ ™ Í —Ñ ™ Ñ • Í ›G˜¿›zš]—I—¿Ò Í ˜ Í ›G˜Ñ gl`4Ÿ u¡t]sJ`_|¯„~t¦†q`_Ÿ¤korGt ʐ 4ËR†]`/mo`Ipªm"! F

!#O

>(Ÿ¡rGt]sKko`_sG^a`4tJm‡k¥r~y„~t²`4†jsJ`_Ÿ ¢Æp‡Zv„Gu t²p/rJ^R…v|ou¤kn`I†N@`/m³`_`4tNm³rEZ]u¡sGZÁp/¨]|x£'„'mo¨v|o`a…@rGu¡tJm‡k_±­‚

¸J`_i"p/¨v|o£J`'9k¹kou/.4`¥„Gtv†"rJ|ou¡`_t>mx„~mou¡rGt–†]`/·vt]`Ik[„%k$J¨¦„~|x`´u¡^a„GsG`…v„'m‡p‡Z«l³Z]u¡p‡Zu¡k¹mxZ]`_tE†j`4kxp/|xu¡¦`I†"¨vkou t]s

„GŸ Ÿ¹`4†jsJ`_Ÿ¤kByz„~Ÿ¡Ÿ¡u t]sN³uwmxZ]u tXuwmI±NY[Z]`4ko`­`I†jsG`"…v„~mxp‡Z]`Ik%„~mnmo`4^a…jm%mxrNkmx|ou¡¸G`­„¯³u t]tvu t]s¯mo|‡„G†j`_¢9rG¶ >R¦`

Ÿ¡rjp_„GŸ3«„~tv†UZ]`_tvp_`­]|xu tvs¯|orJ]¨vknmot]`Ikok(mor¯rjp_p_Ÿ ¨¦knu¡rGtU„Gtv†;p/Ÿ¡¨jmnmx`_|I«=³Z]u¡Ÿ `–„GŸ¡kor¯p/rJ^a…]Ÿ `_º²`4t]rG¨vsGZÁmor

@`%†ju¤knmou¡tvpªmxu £J`Bmor–korG^a`†j`4sG|x`_`G«j`4tv„~vŸ u¡t]samor–^a„~mxp‡ZEu¡tv†ju¡£>u¤†j¨v„GŸ¬y§`4„~mo¨]|x`4k4«¦„Gtv†rG…@`_t]u¡t]samxZ]`%†jrlrG|

mxr­p/rJ^R…v¨jmx„~mou¡rGtv„GŸ Ÿ¡i–`I"p_u `4t>m´u t¦†j`/ºju¡t]s­kop‡Zv`_^a`4k4± ?´r'³¹`4£G`4|4«lmxZ]`4ko`(…v„'m‡p‡Z]`4k´„~|x`(Ÿ u¡¸G`4Ÿ i–mor­u¡tvp/Ÿ¡¨v†j`

p_Ÿ ¨]mnmo`4|%`I†jsG`4Ÿ¡k%Ÿ ilu¡t]s¯t]`I„~|mxZ]`–rJj}`4p/m%@rG¨]tv†v„~|xiG«.³Z]u¡p‡Zp/rG|x|x¨]…jm(moZv`_u¡|R†j`Ikop_|ou¡…jmxrG|‡k„~tv†Á^"„G¸G`4k

mxZ]`_^†ju/I"p_¨]Ÿ mmor"…]¨jmqu¡tKp/rJ|o|x`4ko…¦rJtv†j`4tvp/`J±

gl`4Ÿ u¡t]sJ`_|Q„Gtv†%q`_Ÿ¤korGt 9k|o`Ip/rJsGt]u mou¡rGtaknijknmo`4^ ³„Jk+†j`4^RrJtvknmo|‡„'mo`I†%u¡t"p/rJtJmx|orJŸ Ÿ¡`4†Ÿ¤„~@rG|‡„'morJ|oip_rGtj¢

†]uwmxu rJtvk_«.³u moZXp_Ÿ `I„~tÁu ^"„GsG`4k%p/rGt>m‡„~u¡t]u tvsK^Rrj†j`IkmR„~^arG¨]t>m‡k(r~yqp/Ÿ¡¨jmomo`_|I«„~tv†Á^arJknmoŸ¡i²rGt²moZ]`–mx„Jkn¸

rGy.|x`4p_rGsJt]u/.4u tvsko…¦`Ip/u ·¦pBrGj}`Ipªm‡k_±'&J¨]|xu `(„~t¦†Eg]p‡Z]^au¡†²Ê¡“4’6ËH³`_|x`(„~^arGtvsmxZ]`B·v|‡km[mxr"…]|orJ…¦r>kn`BŸ¡rjp_„~Ÿ

p_rGt>morJ¨]|y§`I„'mx¨]|o`Iky§rG|moZ]`[†j`/mx`4p/mou¡rGtRr~y]rG]}`4pªm (/ O «G„Gtv†(mxr´mx`4knmmxZ]`_u¡|=knijknmo`4^ˆrGt|x`4„GŸ3«~p_Ÿ ¨jmomo`4|o`I†

u¡^"„~sJ`4k4±Y[Zv`_u¡|qkop4„~Ÿ¡`/¢Æu tl£'„~|xu¡„Gt>mQy§`4„~mo¨]|x`(†j`/mx`4p/morG|[|x`4ko…¦rJtv†]kmxrap_u |‡p/¨vŸ¡„G|[„G|xp4kr~y`4†jsJ`_Ÿ¤k_«j³Z]u¤p‡ZE„~|x`

†]`4kxp/|xu @`4†li­moZv`kn…v„~mou¤„~Ÿ†ju¤knmo|xu ]¨]mou¡rGtEr~y.…¦rJu t>mxkqu tK„moZ]u¡t¯„~tvt>¨vŸ¡„G|tv`_u¡sGZl¦rJ|oZvr>rj†r~ymoZ]`%p_u |‡p/Ÿ¡`G±

Y[Zvu¡k[„'momo`4^R…]mxk¹morR`/º]p/Ÿ¡¨v†j`Bp/Ÿ¡¨jmomo`_|y§|xrG^ moZv`B†]`4kxp/|xu …jmxrG|¹>i­„6£JrGu¤†ju¡t]s`_t¦p/rj†ju¡t]s…@rGu¡t>mxku¡tvknu¤†j`moZ]`

p_u |‡p/Ÿ¡`G±=‚krGt]`BŸ¡u ^au mx„~mou¡rGt«vp_u |‡p/¨vŸ¡„G|[„G|xp4krGt]Ÿ¡i–p/r'£J`_|„yz„~u¡|oŸ¡i­|x`4knmo|xu¡p/mo`I†p_Ÿ¡„Jkokr~y=koZv„~…@`4k4±

-ìtRmoZv`_u¡|+£G`4|oi|x`4p_`_t>m=³¹rJ|o¸jk4«GglZ]rGmnmorJta`/mQ„~Ÿ9±jÊސ~‹6˦„Gtv†­c…¦`4Ÿwm+`_mQ„~Ÿ9±]ÊސGIËvu¡tv†j`4…¦`4tv†j`4tJmxŸ i…]|xrG…@rJko`

mxr(p/rGt¦kmx|o¨vp/mQp/rJtJmxrG¨]|.y§|‡„~sJ^R`4t>mxk.mx„Gu Ÿ¡rG|x`4†%mor(„(ko…¦`Ip/u ·¦pp/Ÿ¤„Gkxk4±Y[Z]`u¤†j`4„¥u¤kmor(`_ºj…]Ÿ u¤p/u moŸ¡ip_rGtvknmo|x¨vp/m

(7)

Š

rJt]`4k4±r~mxZ¼³¹rJ|o¸jkR`_^a…]Ÿ¡r'iX@rlrJknmou¡t]sÁmorUko`_Ÿ¡`4p/m"y§|x„GsG^a`_t>mxkRy§|xrG^ „ÁŸ¡„G|osJ`…@rlrGŸqrGyp_„~t¦†ju¡†v„'mo`Ik_«

v¨jm­†juw¶8`_|au¡tXmxZ]`E³„6i²mxZ]`4ko`p4„~tv†]u¡†]„~mo`IkR„G|o`p/rJtvkmx|o¨¦pªmo`I†Ä®z|x„Gtv†jrG^ |x`4p/mx„~tvsGŸ¡`4kRko„G^R…vŸ `I†;y§|xrG^

mx|x„Gu tvu t]s²kn`4sG^a`_t>m‡„'mou¡rGt;^"„Jkn¸jku t½ÊG‹6Ë9«¹³Z]`_|x`4„Jk­ÊސGIËsJ|or'³qky§|x„GsG^a`_t>mxkRknmx„~|omou¡t]sKy§|xrG^ |‡„~t¦†jrG^

p_rGt>morJ¨]|q…@rGu¡t>mxk4«8„Gtv†ErG…]mou¡^Ru0._`IkqmxZ]`_u¡|¥Ÿ `4t]s~mxZNknr„Gkmxr–^"„'ºju¡^au/.4`Rb¹Zv„~^Ry§`4|´^"„'m‡p‡Z]u tvskxp/rG|x`„~t¦†

„Jp_p_¨]|x„Jp/i¯rGyrGj}`Ipªm%p/`4t>mo|xrGu¤†©…v|o`I†ju¡p/mou¡rGtÁu¡t;£6„GŸ u¤†]„~mou¡rGt;u¡^a„GsG`Ikx°/±‚qŸ moZvrG¨]sJZÁmoZ]`4i²p4„~t;@`­^arG|x`

†]u¡kxp/|xu ^au¡tv„'mxu £J`¥y§rG|[moZv`(Ÿ `I„~|xt]`4†p/Ÿ¤„Gkxk_«lmxZ]u¤k¸lu tv†rGyy§|‡„~sJ^R`4t>mxk[„~|x`BZv„~|‡†j`_|mxr"|o`4¨vkn`B³u moZ]u¡tKr~mxZ]`_|

|x`4p_rGsJt]uwmxu rJt%rJ|.u¡^"„~sJ`^"„~mxp‡Z]u¡t]s¥y§|x„G^a`_³rG|x¸lk4«'p/rJ^R…¦„~|x`4†(mxrBsG`_tv`_|xu¡p¹y§`4„~mo¨]|x`4k4«G†j`4…¦`4tv†ju¡t]sBrGt]Ÿ¡irJt

Ÿ¡rjp_„GŸ]…]|xrG…@`_|omou¡`4k+rGy¬u tv†]u £lu¤†j¨v„~Ÿ¦u ^"„GsG`4k4±µKrG|x`_r'£J`_|I«6moZ]`´y§|x„GsG^a`_t>mxk+r~y+Êސ~‹6Ë8„~|x`t]r~m[kop4„~Ÿ¡`u tl£'„~|xu¡„Gt>m

„Gtv†Rt]`_`I†"kn`4sG^a`_t>mx`4†mo|‡„~u¡t]u¡t]sBu ^"„~sJ`4kmxr(¦`´…]|orj†j¨¦p/`4†«G³Z]u¤p‡Zay§¨]|omoZ]`4|+Ÿ u¡^auwm‡k=mxZ]`_u¡|Q„~…v…]Ÿ u¤p_„G]u¡Ÿ u miG±

`_|xsa`/mq„~Ÿ9±ÊސIËHrG¶@`4|q„~tE„~Ÿ mo`_|xtv„~mou¡£G`B£lu `4³ÄrGtEp/rJt>morG¨v|n¢Æv„Gko`4†­rGj}`Ipªmq|x`4p/rJsGt]u mou¡rGtH«lp4„Gknmou¡t]sRmoZ]`

…v|orJ]Ÿ `4^„Gk[†j`/y§rJ|o^"„G]Ÿ `¥knZ¦„~…@`´^"„'m‡p‡Z]u tvsv±3-ìtvknmo`4„J†­rGyp/rJ¨]t>mou¡t]s%rJtkorG…]Z]u¤knmou¤p_„'mx`4†"Ÿ¡rjp_„GŸ¦y§`I„'mx¨]|o`Ik_«

mxZ]`_i(kou ^a…]Ÿ¡i¥mx„G¸G`+u¡tv†ju¡£lu¡†j¨¦„~Ÿ>`4†jsJ`_Ÿ¤kQ®§³u moZR„´d¥`_rJ^a`/mo|xu¤pŸ ¨]|.t]`4u sJZ>@rG|xZ]rlrj†B†j`4kxp/|xu …]morG|ª°ª«'„Gtv†B…]¨jm

mxZ]`_^ u¡tNp/rJ|o|x`4ko…@rGtv†j`4tvp/`(@`/m³`_`4tK…v„~u¡|‡kqr~y+u¡^"„~sJ`4kq³u moZ©„"…¦r'³`_|oy§¨]Ÿt]rGtj¢Æ|xu sJu¡†E…@rGu¡t>m^"„'m‡p‡Z]u tvs

„GŸ sJrG|xuwmxZ]^ˆv„Jkn`I†%rJt -ìt>mo`4sG`4|¨¦„G†j|‡„'mxu¡p¹{+|xrGsG|‡„~^a^au¡t]sv±HY[Zv`^R`_moZ]rj†RrG]mx„~u¡tvk.u¡^R…v|o`Ikokou £J`[|o`Ikn¨]Ÿ mxk

rJt–mxZ]`p‡Zv„GŸ Ÿ¡`_t]sJu tvs"b„GŸwmx`4p‡Z“I]“†v„'mx„Gv„Gko`G±Qct]`(†ju¤kx„G†j£'„~t>m‡„~sG`¥u¤kmoZv„~mquwm|x`4†j¨vp_`4k[|x`4p_rGsGtvuwmxu rJt­mor

^"„~mxp‡Z]u¡t]s…v„Gu |‡k¬r~ylmx|x„Gu t]u¡t]s´„Gtv†¥mo`Ikmu ^"„~sJ`4k4«I„Gtv†(†jrl`4kot 9mHu¡tjy§`_|Hy§|orJ^ÄmxZ]`=mo|‡„~u¡t]u¡t]squ¡^"„~sG`Ik„qkou tvsGŸ¡`

^arj†j`4Ÿ.ko¨]^a^"„~|xu/.4u t]sp/rG^a^arGtK…v|orJ…¦`4|nmxu `Ik´koZv„~|x`4†EliK†ju ¶@`4|o`4tJm¥u t¦km‡„~tvp_`4kqrGy=moZ]`Rp/Ÿ¤„Gkxk_±`4kou¡†j`Ik_«

u m³rG¨vŸ¡†Á@`–u¡t>mo`_|x`4knmou¡t]sKmxr¯u¡t'}`4p/m

k

‚¥gÁu¡tÁmoZ]`4u |y§|x„G^a`_³rG|o¸8«.„Gk|x`_…vŸ¡„Jp/`4p_`_^a`_t>my§rJ|%u¡tv†ju¡£lu¡†j¨¦„~Ÿ

`I†jsG`4Ÿ¡k4«]„~t¦†–rJvkn`4|o£J`³Zv`/moZv`_|[moZvu¡k³rG¨vŸ¡†Ÿ `I„G†–mor"u¡^a…]|or'£J`4†–…¦`4|ny§rJ|o^"„~t¦p/`G±

É¥„~Ÿ¤„~Ÿ„~tv†©YH|xu¡sGsJkÊÀGËp_rGtvkou¡†]`_|‡„~]Ÿ¡i„J†j£'„~tvp_`4†EmxZ]`akm‡„'mo`_¢9rGyÇ¢3mxZ]`%„G|nm¥u t©Z>¨v^a„GtN†j`_mo`4p/mou¡rGt«8li

†]`4kou sJt]u tvs"moZ]` ?qu¤kmxrGsJ|x„G^Èr~yc|xu¡`_t>mo`I†¯d¥|x„J†ju `4t>mxk®*?qr>d(°†j`Ikop_|ou¡…jmorJ|4«@„~tv†Kp4„~|x`/y§¨]Ÿ¡Ÿ¡irJ…jmou¡^au/.4u t]s

u mar'£G`_|R„NŸ¤„~|xsG`†]„'m‡„Gko`/m"p/rGt>m‡„~u¡t]u tvs¯moZvrG¨vkx„~tv†vk%rGy´Zl¨]^"„~tvku t¨]tvp_rGtvknmo|‡„~u¡t]`4†U…¦r>kn`Ik_±:-ìtXmoZ]`4u |

|x`4p_rGsJt]uwmxu rJtRy§|x„G^R`4³¹rJ|o¸%u ^"„~sJ`q³u¡tv†jr'³qk+„G|o`´ko¨]8†ju¡£>u¤†j`I†"u tamxu Ÿ¡`4k„~t¦†a`4„Gp‡Z"rJt]`qu¤kQ†j`Ikop_|ou¡@`4†aliR„

?´r>dR±l‚½kou¡^R…vŸ `¥knŸ¡u¡†]u t]sG¢9³u¡tv†jr'³¼^a`4p‡Z¦„~t]u¤kn^ mxZ]`_t–„GŸ Ÿ¡r'³qk=mxr%Ÿ¡rjp_„~Ÿ¡u0._`´rJj}`4p/mxk4±{QZ]r~mxrG^a`/mx|ou¤pqt]rJ|n¢

^"„GŸ u0.4„~mou¡rGt"³u moZ]u¡t–^¨]Ÿwmxu …vŸ `¥r'£G`4|oŸ¤„~…]…vu t]s(vŸ rjp‡¸jkQrGy¬mou¡Ÿ `IkQ^"„G¸G`4k+moZ]`¥^a`/mxZ]rj†­…v„G|nmxu¡p_¨]Ÿ¡„G|oŸ¡iR|orJ]¨vknm

mxraŸ u¡sGZ>mou¡t]s"£'„~|xu¤„'mou¡rGt¦k_± qrGmou¤p/`BmoZ¦„'m?qrld†]`4kxp/|xu …jmxrG|‡k[„~|x`¥rJt]Ÿ¡i–†j`/·¦t]`4†³u moZ]u¡tK„asGu¡£G`_tkn¨v>³u¡tj¢

†]r'³(«moZv`_iÁ†jrGt 9m%Zv„6£J`­„Kp/rJtvp/`4…jm%r~y[Ÿ¡rlp4„'mxu rJtÁ„Gtv†;kxp_„~Ÿ¡`G± ?q`4tvp/`J«mxZ]`_i²t]`4`4†²morK@`–„Jkokorjp/u¤„'mo`I†

mxrkorG^a`R`/ºlmo`4|ot¦„~Ÿy§`4„'mx¨]|x`R†j`_mo`IpªmorJ|B¦`_y§rG|x`%@`_u¡t]sK„~…]…]Ÿ¡u¤p_„~vŸ `³uwmxZ]u t©y§|‡„~^a`_³rG|x¸jkqt]rGmB¦„Gko`4†KrJt

koŸ¡u¡†ju¡t]sG¢9³u¡tv†jr'³qk4±

Í ™6› Í ˜ 𠦙 Ñ {`_|‡p/`4…jmo¨¦„~ŸQsJ|orJ¨]…]u¡t]sKr~y´p_rGt>morJ¨]|‡k(Zv„Gk„KŸ¡rGt]s¯Zvu¡knmorJ|oi²u tUp_rG^a…]¨jmx`_|

£lu¤knu¡rGt½Ê‘]«“Il«“>«“4Œj«QJŠl«Q~‘]«=GŒj«+’J6Ë9±¼Y[Z]`Ep/|x¨vp/u¤„~Ÿ[u¤†j`4„²@`_Z]u¡tv†XmoZ]`Ikn`E³rG|x¸lku¤k%mxZv„'m"…]u¡`4p_`4k

rGy´p/rJtJmxrG¨]||o`4Ÿ¡„~mo`I†Á>i;korG^a` ) $*) F …v|orJ…¦`4|nmiÁ„~|x`–^arG|x`­Ÿ¡u ¸J`_Ÿ¡i²morN@`_Ÿ¡rGtvs¯morNmoZ]`

kx„~^a`BrG]}`4pªmI±=Y[Z]`(…¦`4|xp_`_…jmx¨v„~Ÿ¬…v|orJ…¦`4|nmxu `Ik¹`_ºj…]Ÿ rJuwmx`4†u t¦p/Ÿ¡¨v†j`p/rJtl£G`/ºju miKÊ “6IËÆ«vp/rG¢Æp_u |‡p/¨]Ÿ¤„~|xu miʒJ6Ë9«

p_rGt]tv`4pªmx`4†jtv`4kxkBʐG‘j«v~Œ6ËÆ«]…v„G|x„GŸ Ÿ¡`_Ÿ¡u¤kn^ÅÊ¡“4Œ~Ë9«]„Gtv†…]|or6ºju¡^auwmi8Ê¡“4Œ4Ë9±

ct]`%^a„~}rG|´„G|o`I„ar~yQ„G…]…]Ÿ¡u¡p4„'mou¡rGty§rJ|´…@`_|‡p/`_…]mo¨v„GŸHsG|xrG¨v…]u tvs"u¡k´u ^"„~sJ`%ko`_sG^a`4tJm‡„'mxu rJt«]u¡t¯³Z]u¤p‡Z

mxZ]`qm‡„Gko¸u¤kQmorsJ|orJ¨]…amorJsG`/mxZ]`_|„~Ÿ¡Ÿv`4Ÿ `4^R`4t>mxk¹¦`4Ÿ rJt]sGu¡t]s(mxru t¦†ju £lu¤†j¨v„GŸ3«l¨]tvko…@`4p/u ·v`I†"rGj}`Ipªm‡kqʑ]«@“Il«

’>IËÆ±Bµ¯rG|x`_r'£G`4|4«¦…¦`4|xp_`_…jmx¨v„~Ÿ.sG|xrG¨v…]u tvs–…]Ÿ¤„6iG`I†K„~tNu¡^a…¦rJ|nm‡„~t>m|xrGŸ¡`%u¡t¯mxZ]`R|o`Ip/rGsJt]u mou¡rGtKr~ykn…@`4p_uw·¦p

rJj}`4p/mxk¨vtv†j`_|´£6„G|oilu¡t]sa£lu `4³…¦rJu t>m4«¦…v„~|omou¤p/¨vŸ¡„G|oŸ¡i­u¡tmxZ]`%ŒJGk„~t¦†K‹GGk4±QY[Z]`By§rjp_¨vkq³[„Gk[^"„~u¡t]Ÿ¡i–rJt

…vŸ¡„Gtv„~|[rG]}`4pªm‡kBʐG‘6˄Gtv†–…@rGŸ¡ilZ]`4†]|x„Ê¡“G“~«“IŒ6ËÆ±

Y[Z]`

k

‚gÂy§`I„'mx¨]|o`Ik­„~|x`K^ar~mxu £'„'mx`4†¼limoZ]`Nkx„~^a`KsJ`_t]`4|x„GŸqu t>mx¨]uwmxu rJtvk­rGyB`I„~|xŸ u¡`_|"…@`_|‡p/`4…jmo¨¦„~Ÿ

sJ|orJ¨]…]u¡t]sR³¹rJ|o¸jk4«l„Gtv†E„~|x`B^Rr>km|x`_Ÿ¤„'mx`4†moZ]`(u¤†j`I„Gk[r~y=ƒrGmoZl³¹`4Ÿ Ÿ=ÊސGŠj«¦~‘6ËÆ«]³Z]r­„J†j£Grjp4„'mo`I†"y§rJ|moZ]`

(8)

u¡^a…¦rJ|nm‡„~tvp_`–rGyp/rJt]t]`4p/mo`I†jt]`4kxkR„~tv†UmorG…@rGŸ¡rGsJu¡p4„~Ÿ¹|o`4Ÿ¡„~mou¡rGtvk4±  `¦`4Ÿ u¡`_£J`–mxZv„'m"p/rJt]t]`4p/mo`I†jt]`4kxku¡k

„y§¨vtv†]„~^a`4tJm‡„~Ÿ9«…¦r'³`_|oy§¨]ŸQ†j|xu¡£>u¡t]sEy§rJ|xp_`­³Z]u¤p‡Z;u¡kp_¨]|x|o`4tJmxŸ i²kmxu Ÿ¡Ÿ¨]tv†j`4|o`_ºl…vŸ rJuwmx`4†²u tUp_rG^a…]¨jmx`_|

£lu¤knu¡rGtH± -ìt–moZ]u¤k[…v„G…¦`4|4«jp/rJt]t]`Ipªmo`I†jt]`Ikoku¤k¹v|orJ¨]sGZ>mQmxrRmoZ]`(†jrJ^a„Gu tr~yHrJj}`4p/m (/ G †j`/mx`4pªmxu rJt«]„~t¦†

u¤kB`/ºj…]Ÿ¡rGu mo`I†©morK†j`/·¦t]`"^arl†]`_|xt©Ÿ¡rjp_„~Ÿ=u¡tl£'„~|xu¡„GtJmBy§`I„'mo¨v|o`Ik>Bu¡^a„GsG`a`_Ÿ¡`_^a`4tJm‡kB³uwmxZ;„³`_Ÿ¡ŸQ†j`_·vt]`I†

Ÿ¡rjp_„~mou¡rGt«l„%kxp_„GŸ `´„Gtv†­„Gt­u tl£'„~|xu¤„~t>m¹†j`Ikop_|ou¡…jmorJ|4«>|x`4„G†]i%mxr%@`¨vko`4†­u t­^"„Gt>ia|x`4p_`_t>mQ^"„'m‡p‡Z]u tvs„~t¦†

|x`4p_rGsJt]uwmxu rJtkxp‡Z]`_^a`Ik_±

k

´%¹È H#$&%.

k

!#"$%'&

 `(kn¨v^R^"„G|ou0._`¥Z]`_|x`moZ]`¥mo`Ip‡Z]t]u>¨]`rGy¹Ê‹6ˬmora]¨vu Ÿ¤†­mxZ]` )! %& 4)(= !R®9b[g °r~ymoZ]`

u¡^"„~sJ`G«jrGt³Z]u¤p‡Z³`(³u¡Ÿ Ÿ†j`_mo`IpªmqrG¨v|

k

‚g–y§`4„~mo¨]|x`4k4±

Q†]sG`_Ÿ¤k´„G|o`†j`/mx`4pªmx`4†ElimoZ]``/º]p/`4Ÿ Ÿ¡`_t>m `_|x¸G`4Ÿ `4i­tv„~mo¨]|‡„~Ÿ¦rJ¨]tv†]„G|oi†j`/mx`4pªmxrG|ʐG6Ë9«@„~tv†mxZ]`_t

p‡Z¦„~u¡t]`4†¬±¹Y[Z]`(|o`Ikn¨vŸwmxu t]s"`I†jsG`4Ÿw¢ìp‡Zv„Gu tvk[„G|o`BŸ¡u t]¸J`4†E„'mmxZ]`_u¡|†]u¡kxp/rJtJmxu tl¨]u mou¡`4k4«ju9±`J±+m³r"`4†jsJ`_Ÿ ¢Æp‡Zv„Gu t¦k

c 1

„~t¦†

c 2

„~|x`Ÿ u¡t]¸J`4†Ku y

c 2

…v„Gkxkn`Ikqt]`I„~|¥„~t¯`4tv†j…@rGu¡tJm¥r~y

c 1

«¬„~tv†Ku y+mxZ]``4tv†ju¡t]s–rGy

c 1

u¤k¥†ju |x`4p/mo`I†

mxr'³„G|x†vk

c 2

®Ç·vsJ¨]|o`“_„J°/±#-ìtjy§rG|x^"„~Ÿ¡Ÿ iJ«¦u y

c 1

³¹rJ¨]Ÿ¤†K¦`R`/ºlmx`_tv†j`I†¯„­vuwmI«¬uwmB³¹rJ¨]Ÿ¤†K^a`_`/m

c 2

±¥Y[Z]`Ikn`

Ÿ¡u¡t]¸jk=„~|x`¹¨vko`/y§¨vŸju tRm³r³[„6ijk>¬mxZ]`_i%|o`Ip/rG|‡†(mxZv„'m+„Bp/rJt>morG¨v|^au¡sGZ>m+p/rGt>mxu tl¨]`[r'£G`4|HmxZ]`sJ„G…%@`/m³`_`4t

m³r(`4†]sG`_Ÿ ¢ìp‡Zv„~u¡tvk4«G„~tv†"„GŸ Ÿ¡r'³morp_„G…jmo¨v|o`=}¨vtvpªmxu rJtvk´®3€¬¢¡}¨]tvpªmxu rJtvk4«>Y¢¡}¨]tvp/mou¡rGtvk4«J„Gtv†aZ]u¡sGZ]`4|+rG|‡†j`_|

}¨vtvpªmxu rJtvku¡t>£JrGŸ¡£lu t]sako`_£G`4|x„GŸ¦`I†jsG`4Ÿw¢ìp‡Zv„Gu tvk‡°ª±

Y[Z]`E`I†jsG`4Ÿw¢ìp‡Zv„~u¡tvk„~|x`–…v„G|nmxuwmxu rJt]`4†Xu t>mor²|xrG¨]sJZ]Ÿ i;knmo|‡„~u¡sGZ>mRp_rGt>morJ¨]|akn`4sG^a`_t>mxk4±UY[Z]`u¡†]`4„©u¡k

mxrKrG|xsJ„Gt]u/.4`RmoZ]`Ikn`­ko`_sJ^R`4t>mxk(u¡t;„Et]`/m³rG|x¸8«Hli©p_rGt]t]`Ipªmxu t]sEmxZ]`_^ „~Ÿ¡rGtvsmxZ]`­`I†jsG`4Ÿw¢ìp‡Zv„~u¡tvk4«H„~t¦†

„Jp/|xrJkxkmoZ]`4u |Ÿ¡u¡t]¸jk­®Ç·vsJ¨]|x`“I„J°/±glu¡tvp/`"`4£G`_|xi¯`I†jsG`4Ÿw¢ìp‡Zv„~u¡tÁp_„~t²@`­Ÿ u¡t]¸J`4†©mor¯ko`_£J`_|‡„~Ÿr~mxZ]`_|‡k_«HmoZ]`

b[g »u¤k¹„p_rG^a…]Ÿ¡`/º"]|‡„~tvp‡Zvu t]sknmo|x¨vp/mo¨]|x`G±3-ìt>mo¨]u mou¡£G`4Ÿ iJ«Gm³r%ko`_sJ^R`4t>mxkQ„G|o`p/rGtvt]`4p/mo`4†­uwy¬mxZ]``I†jsG`4Ÿ¡k

…v|or'£lu¤†j`%`4£>u¤†j`4tvp/`RmoZ¦„'mBmoZ]`4i¯^au sJZ>mB@`­„G†'}n„Gp/`4t>mB„GŸ rJt]skorG^a`RrGj}`Ipªmp/rJt>morG¨v|4«8`_£J`_t²³Z]`_t©moZv`_i

„G|o`R…]Zlijknu¤p_„GŸ Ÿ¡iNko`_…v„G|x„~mo`I†¯liN„Á®zko^"„~Ÿ¡Ÿ¤°sJ„G…«rJ|(³Z]`_t©y§rG|x^au t]sK„}¨]tvp/mou¡rGt±­Y[Zv`R¸J`_i¯…v|orJ…¦`4|nmi

rGy¹mxZ]`Eb[g u¡k(mor¯u¡tvp/Ÿ¡¨v†j`–…v„'mxZvksJrGu¡t]sK„~Ÿ¡rGt]sEmxZ]`–p/rJt>morG¨v|xkBrGymxZ]`­u¡^"„~sG`I†²rGj}`Ipªmxk­Ê‹~Ë9«.³Z]u¤p‡Z

^arGmou¡£6„~mo`Ik

k

‚g–y§`4„~mo¨]|x`4k4±

+* ,-!./0'1

k

2

Y[Zv`¯…]|xu tvp_u …¦„~Ÿp_rGt>mo|xu¡]¨jmou¡rGt¾rGy(moZ]u¤k…v„~…@`_|u¡k­morU…]|xrG…@rJko`N„Áyz„G^au Ÿ¡i¼r~y(Ÿ rjp4„~Ÿqy§`I„'mx¨]|o`Ik>²…v„~moZvk

rGy%Ÿ¡`_t]sGmoZ

k

moZ]|xrG¨vsGZ¾mxZ]`;b[g ±qµKrJ|o`Ny§rG|x^a„GŸ Ÿ¡iG«¥„UsJ|orJ¨]…»r~y

k

kn`4sG^a`_t>m‡k–u¤kE„

k

‚¥g¾u ¶ˆmoZ]`4i p4„~t¦`KrJ|x†j`4|o`I†XkorNmxZv„'m"mxZ]`

i

¢3mxZÂko`_sJ^R`4t>mRu¤k"p/rJt]t]`4p/mo`I†Xu¡tÂmoZ]`Nb[g mxr©mxZ]`

(i + 1)

¢9moZÂrGt]`J«

y§rJ|

i ∈ {1, k − 1}

±?q`4tvp/`R³`Rp4„~Ÿ¡ŸmxZ]`_^ !

'') %'&()*

«„~tv†N|o`_y§`_|¥mormoZ]`4u |(Ÿ¡`_tvs~moZ

k

„Jk

%

±.‚k

k

sG|xr'³qk_«

k

‚gRp4„~ty§rG|x^ˆ^RrJ|o`„Gtv†%^arJ|o`[p/rJ^R…vŸ `_º%Ÿ rjp4„~Ÿ]koZv„~…@`kmx|o¨vp/mo¨]|x`4k >u¡tv†ju¡£lu¡†j¨¦„~Ÿ

ko`_sJ^a`_t>mxkHy§rG|

k = 1

Ã

L

koZv„~…@`4k.„~t¦†R'¢Æko`_sJ^R`4t>m

T

koZv„~…@`4ky§rJ|

k = 2

Ã

C, Y, F, Z

knZv„G…¦`Ik_«~’~¢Æko`_sJ^a`_t>m

T

knZ¦„~…@`4k4«]„~tv†–mo|xu¡„Gt]sGŸ¡`4k¹y§rJ|

k = 3

®§·vsG¨v|o`Ikqj«]’G°/±QY[Z]`(†ju¡^a`_tvkou rJtv„~Ÿ¡u mi"r~y

k

‚g†j`4kxp/|xu¡…jmorJ|xk[„~Ÿ¤kor sJ|or'³qk³u moZ

k

®§t]`_ºlm¹kn`Ipªmxu rJt¦°ª«l„~tv†­³¹`mx|o`I„'m

k

‚¥gar~y†ju ¶8`_|x`_t>m¹†j`4sG|x`_`4k¹„Gk+†]uw¶8`_|x`_t>mQy§`I„'mx¨]|o`qmi>…@`4k4«

„GŸ Ÿv¨]t]u mo`4†Ru¡t"rGt]`yz„G^Ru¡Ÿ¡ili%„(koZv„~|x`4†Rp/|x¨vp_u¡„GŸ]…]|xrG…@`_|omi4>mor(@`qkn`)J¨v`_tvp_`4k=rGy 4 ko`_sG^a`4tJm‡k_±

b¹rJt]t]`4p/mo`I†jt]`4kxk…]|or'£lu¤†j`4k„Nt¦„'mo¨v|x„GŸp_|ou mo`4|ou¡rGtÁy§rJ|sJ|orJ¨]…]u¡t]s©ko`_sJ^R`4t>mxku¡t>mor

k

‚g8±3-Æm"„6£GrJu¡†]k

„G|ovuwmx|x„G|oiÁ†j`/·¦t]uwmxu rJtvkRr~ymxZ]`Et]`_u¡sGZl@rG|xZ]rlrl†ÁrGy„²kn`4sG^a`_t>m4«+„Gtv†Xp_rGtvknmo|‡„~u¡tvk

k

‚gUmorN@`Kp‡Zv„~u¡tvk

(9)

r 2

r 3 r 4

a

E D

A

b B

C 1

1 2 2

E D

A B

C c 1 2

3

E D

A B

C e E

D

A B

C d 2 1

3 4

7.u¡sG¨]|x`N“> !"#%$!&'()*+",-."#/+0"+1/2",,1/431!567"#/

8+",91:<;0=>6?91@+""

2

ACB

(B, C)

-

(D, E)

;@/D1E+F1>GH<6()*+"IJ"#/F++K-"51D

)H:<L8M"!"51D";9NO1E",(P"#Q"

(A, B)

(A, C)

(C, E)

RS+1F+""!"#1TSU0-1"V(K2WX<H=T

"#/+XJ1&++W+K!"#

(B, C)

2

(D, E)

;6> A

3

ACB

(C, A, E)

;6 A

4

ACB

(E, B, C, D)

;YZ

r i

&"51

/&E1S&H"#/ +++K/"51[G1P"#/

4

APB

J+S;

rGykn`4sG^a`_t>mxk4±b¹rG^a…v„G|o`I†Xmxr;moZv`N]|xrJ„J†j`_|–p_Ÿ¡„Jkok­r~y(sG|xrG¨]…¦k"r~y(Dt]`4„G|oli$9Qko`_sG^a`4tJm‡k_«[mxZ]`_iÂZv„6£J`

Zvu sJZ]`_|"p‡Zv„Gtvp/`IkRmorÁŸ u¡`K`_t>mxu |x`_Ÿ¡i;rGt¼„²…¦rJ|nmxu rJtrGymxZ]`ErGj}`Ipªm­@rG¨]tv†v„~|xiG±¼Y[Z]`Ey§`4„~mo¨]|x`4kRr~yaÊ¡“4’6Ë

u¡tvknmo`I„G†¬«u t¦p/Ÿ¡¨v†j`N†ju¤kxp/rGtvt]`4p/mo`4†¼ko`/m‡k"r~yB`4†jsJ`_Ÿ¤ka³Z]u¤p‡ZÂZ¦„~…]…@`_tÂmor;@`¯Ÿ¡rjp_„'mx`4†¼„~Ÿ¡rGtvs²…¦„~|omarGyB„

p_u |‡p/Ÿ¡`G± `4kou¡†]`4k4«¬moZ]`a¸J`_iNp_¨]|o£J`4k¥r~y¥Ê 4˹„G|o`Rv„Gko`4†©rGt²u¡tv†ju¡£>u¤†j¨v„GŸ=`4†jsJ`_Ÿ ¢Æp‡Z¦„~u¡tvk_«„Gtv†©Z]`_tvp_`"„~|x`

Ÿ¡`4kxk[|xrG]¨vknmoŸ¡i–†j`_mo`Ipªmo`I†u t|o`I„~Ÿ¬u¡^"„~sG`IkmoZv„Gt

k

‚g8«]³Zvu¡p‡ZE]|xu¡†]sG`BsJ„G…vk¹@`/m³`_`4tE`4†jsJ`_Ÿ ¢Æp‡Zv„Gu t¦k_±

k

‚¥g­p4„~t­@`†j`_mo`Ipªmo`I†­li"„%†j`4…jmoZ]¢3·v|‡knmko`4„~|‡p‡Z­knmx„~|omo`I†Ry§|orJ^ `_£G`4|oiakn`4sG^a`_t>mI«Gy§rJŸ Ÿ¡r'³¹`I†"liRmoZ]`

`4Ÿ u¡^au t¦„'mou¡rGtr~y.`>¨]u¡£'„~Ÿ¡`_t>m…v„'mxZvk(®Çm³rR†]uw¶8`_|x`_t>mq…v„~moZvk[u¡tl£GrGŸ¡£lu tvsmoZv`ko„G^R`Bko`_sG^a`4tJm‡kp/rJtvkmxuwmx¨jmo`

mxZ]` &(

k

‚¥g]°ª±'Y[Z]u¤kHu¤k.p/rG^a…]¨]mx„'mxu rJtv„~Ÿ¡Ÿ¡i¥p‡Z]`I„~…(y§rJ|HmxZ]`¹ko^"„~Ÿ¡ŸJ£'„~Ÿ¡¨]`IkHrGy

k

p/rJ|o|x`4ko…¦rJtv†ju¡t]s[mor¥Ÿ¡rlp4„~Ÿ

y§`I„'mx¨]|o`Ik®3„~@rG¨jm

k ≤ 5

°ª±  `"†ju¡ko|x`_sJ„G|x†EZvu sJZ]`_|¥£'„~Ÿ¡¨]`4k¥r~y

k

¦`Ip_„G¨vkn`%moZ]`4iK|o`Ikn¨vŸwmBu t©Ÿ¡„G|osJ`kxp_„GŸ ` knmo|x¨vp/mo¨]|x`4k4«Gmxrlrko…¦`Ip/u ·¦pqmxr„%…v„~|omou¤p/¨]Ÿ¤„~|¹u ^"„GsG`´rJ|QrJj}`4p/mu¡tvknmx„~t¦p/`G«l„~t¦†"u t„~t­`_º]p/`4kxkou £J`qtl¨]^%@`_|

rGy†j`_mo`Ipªmo`I†¯y§`I„'mx¨]|o`Ik"®zko`_£J`_|‡„~ŸmoZ]rJ¨vko„Gtv†]kB„~Ÿ¡|x`4„G†]iEy§rG|

k = 5

°/±Rµ¯rG|x`…]|x`4p_u¡ko`_Ÿ¡iG«8mxZ]`atl¨]^%@`_|(rGy

k

‚gEu¡tN„~tKu¡^"„~sJ`%p/rJtJm‡„~u¡t]u¡t]s

n

kn`4sG^a`_t>mxk´sG|xr'³>¨]u¤p‡¸lŸ i³u moZ

k

«8„Gkp_„Gt¯¦`¨]tv†j`4|xknmorlrj†ElimoZ]`

y§rJŸ Ÿ¡r'³u¡t]s´rJvkn`4|o£'„~mou¡rGtvk4±.ct%„6£J`_|‡„~sG`J«4`I„Gp‡Z%ko`_sJ^a`_t>mu¤kp/rGtvt]`4p/mo`4†morm³¹r´mormoZ]|x`_`r~mxZ]`_|I«6¦`Ip_„G¨vkn`

T

„Gtv†²Z]u sJZ]`_|%rG|‡†j`_|‡k}¨]tvp/mou¡rGtvk%rlp4p/¨]|%Ÿ `IkokBy§|x`>¨]`4t>moŸ¡i¯moZ¦„~tUkou ^a…]Ÿ¡`¯“/¢9morG¢x“ap/rJt]t]`Ipªmou¡rGt¦k_±E‚´k„

p_rGtvko`>¨]`4tvp/`J«G„Gk

k

sG|xr'³qk_«6mxZ]`´tl¨]^¦`4|+r~y¬…v„~moZvkQr~y¬Ÿ¡`_t]sGmoZ

k

…v„Gkxkou t]s¥mxZ]|orJ¨]sGZ­„BsJu £J`_ta]|‡„~tvp‡Zvu t]s …@rGu¡t>m(u tvp_|o`I„Gko`4k >¨]u¤p‡¸>Ÿ¡iG±(-ìt²…]|‡„Gpªmxu¡p_`G«³Zvu Ÿ¡`amoZ]`"„6£J`_|‡„~sG`tl¨]^%@`_|(rGy

2

‚¥g¯u¤k(rJt]Ÿ i©„~@rG¨jm

1.5n

«

mxZ]`(tl¨]^%@`_|rGy

3

‚g–u¡k

4n

«lmoZv„~mr~y

4

‚g–u¤k

10n

«]„Gtv†–moZ]`4|o`(„~|x`B^arG|x`mxZv„~t

20n 5

‚¥g]\

(10)

‚k

k

u tvp_|o`I„Gko`4k4«Hy§`I„'mx¨]|o`Ik%u¡tvp_|o`I„Gko`­u tp/rG^a…]Ÿ¡`/ºju miG±;ct;moZ]`rGt]`–Zv„~tv†«moZ]`4i;¦`Ip/rG^a`^RrJ|o`

„Gtv†^RrJ|o`Bu¡tjy§rG|x^"„'mxu £J`G«j³Z]u¡Ÿ `(rJt–mxZ]`(r~mxZ]`_|[mxZ]`_isG|‡„G†j¨¦„~Ÿ¡Ÿ i"sJ`/mŸ `Ikok´„~tv†Ÿ `Ikok[|x`_…@`4„~mx„G]Ÿ `(„Jp/|xrJkxk

†]uw¶8`_|x`_t>mHu¡^"„~sG`IkH„Gtv†BrGj}`Ipªm.u tvknmx„Gtvp/`Ik_±‚†]†ju mou¡rGtv„GŸ Ÿ¡iG«ImoZv`Qtl¨]^%@`_|.r~yjt]rJtj¢Æ¦rJ¨]tv†]„G|oiy§`4„~mo¨]|x`4k¹®§rG|

^au ºj`4†¥y§`4„~mo¨]|x`4kHp/r'£G`4|ou¡t]s[…v„G|nmxŸ i¥¦rJ¨]tv†]„G|oi¥„~tv†B…¦„~|omoŸ¡ip/Ÿ¡¨jmomo`_|ª°„GŸ¡korsG|xr'³qk8³u moZ

k

«'„Gp/mo¨v„GŸ Ÿ¡i´yz„Jkmx`_|

mxZv„~t…]¨]|x`@rG¨vtv†]„~|xiarGt]`Ik_«lŸ¡`4„6£lu¡t]s„Ÿ r'³`_|knu¡sGt¦„~Ÿ ¢3mxr~¢Æt]rGu¤kn`´|x„~mou¡rv±3?q`_t¦p/`G«ly§rJ|[|x„~moZ]`4|¹Ÿ¡r'³¾£'„~Ÿ¡¨]`4k

rGy

k

«

k

‚¥gUZ¦„6£G`„Gt„~mnmo|‡„Gp/mou¡£G`u t>mo`4|o^a`I†ju¡„~mo`p/rG^a…]Ÿ¡`/ºju miG«+rG¶@`4|ou¡t]s²„©p_rGtl£G`4t]u `4t>mRp/rJ^a…]|orJ^au¡ko`'>

kou¡^R…vŸ ``_t]rJ¨]sGZEmxr–@`†j`_mo`4p/mo`I†¯|x`_…@`4„'m‡„~]Ÿ¡iG«@iG`_mp/rJ^a…]Ÿ `_ºK`_t]rJ¨]sGZEmxrp_„G…jmo¨v|o`u tjy§rJ|o^"„~mou¡£G`Ÿ¡rjp_„~Ÿ

rJj}`4p/mBknmo|x¨vp/mo¨]|x`4k4± -ìtÁkn`Ipªmou¡rGt²‘]«³`ap/rGt]·v|o^ mxZ]`4ko`au t>mx¨]uwmxu rJtvk¥`/ºj…@`_|xu ^a`_t>m‡„~Ÿ¡Ÿ iJ«„~tv†²†j`/mx`_|x^au t]`

mxZv„'m

2

‚g–…¦`4|ny§rJ|o^ȏ¦`IkmI±

+ ,-/ 1 1

k

2

-ìt¾rJ|x†]`_|"mxrXp/rJ^R…¦„~|x`¯†juw¶8`_|x`_t>m

k

‚g8«¹³¹`Nt]`_`I†»„Átl¨]^a`_|xu¡p4„~Ÿ†]`4kxp/|ou¡…jmxrG|I±f‚k"·v|‡knmkmx`_…«u mu¤k u¡^a…¦rJ|nm‡„~t>mamor;rJ|x†j`4|RmoZ]`

k

‚¥gÂkn`4sG^a`_t>mxk

{s i } i =1 ..k

u¡t¾„Á|o`4…¦`I„'mx„G]Ÿ¡`^"„~tvt]`_|I«kor²moZv„~m–knu¡^au Ÿ¤„~|

k

‚gEZv„6£J`mxZ]`kx„~^a`%rJ|x†]`_|I±  `Rko`_Ÿ¡`4p/m¥„Gk´·v|‡kmBkn`4sG^a`_t>mqmxZ]`RrGt]`%³u moZ©^au¡†j…@rGu¡t>mBp_Ÿ r>kn`Ikm´mormoZ]`

p_`_t>mo|xrGu¤†Rr~y„~Ÿ¡Ÿv^au¤†j…@rGu¡tJm‡k

{m i = (x i , y i )} i =1 ..k

®§³Z]`4t­kn`4£G`_|‡„~Ÿ¦kn`4sG^a`_t>mxk+Zv„6£G`qkou ^au¡Ÿ¡„G|¹†ju¤knmx„~t¦p/`4k

mxr"moZv`%p/`4tJmx|orJu¡†«]³¹`%…]u¡p‡¸–moZ]`%·v|‡kmqrJt]`%„Gp4p/rJ|x†ju¡t]sRmor­moZ]`rJ|x†]`_|´†j`_·vt]`I†E¦`4Ÿ r'³´°/±[‚kq³`(³u Ÿ¡Ÿko`_`

u¡tUmxZ]`E†j`4kxp/|xu …]morG|R@`_Ÿ¡r'³(«=moZ]u¤kap/`4tJmx`_|x^arJknmRko`_sG^a`4tJmau¤k%mxZ]`tv„'mx¨]|x„GŸp‡ZvrGu¤p/`„JkR|o`_y§`_|x`_tvp_`–…@rGu¡tJm

y§rJ|^a`4„Gko¨]|xu tvsmxZ]`(|x`_Ÿ¤„'mou¡£G`BŸ¡rjp_„'mxu rJtrGyHmxZ]`r~mxZ]`_|qko`_sJ^a`_t>mxk4±+Y[Z]`(|x`_^"„~u¡t]u¡t]s"kn`4sG^a`_t>mxkm‡„~¸J`¥¨v…

…@rJkou mou¡rGtvk

2

mxZ]|xrG¨]sJZ

k

«l„~tv†a„G|o`[rG|‡†j`4|o`I†y§|xrG^ Ÿ `_yÇm+mor(|xu¡sGZ>m4«>„Gp_p_rG|‡†ju¡t]s´mxr(moZv`_u¡|+^au¡†j…@rGu¡t>m4±3-Æy8m³¹r ko`_sJ^a`_t>mxk

s i , s j

Zv„6£G`¥knu¡^au Ÿ¤„~|

x

p/rlrJ|x†ju¡tv„~mo`G«lu9±`J±

(x i − x j ) ≤ 0.2 p

(x i − x j ) 2 + (y i − y j ) 2

«lmxZ]`_t

mxZ]`_i"„G|o`rJ|x†j`4|o`I†Ry§|orJ^mxrG…amxr%@r~mnmxrG^E± qrGmo`qmxZv„'m¹moZ]u¤k¹rG|‡†j`_|+u¤kQknmx„G]Ÿ¡`G«l„Gk+tvrm³r%kn`4sG^a`_t>m‡k+p_„Gt

Z¦„6£G`Bknu¡^au Ÿ¤„~|Ÿ¡rjp_„'mxu rJtu¡tE¦rGmoZ

x

„~t¦†

y

±==º]„~^a…]Ÿ¡`BrG|‡†j`_|xu tvsJk[p_„Gt@`kn`4`_tu t·vsJ¨]|x`a“_j¢ì†¬±

ctvp_`;moZv`XrG|‡†j`4|¯`4knmx„G]Ÿ u¤koZ]`4†¬«R„

k

‚¥g¿u¡k²„¾Ÿ¡u¡knm

P = (s 1 , s 2 , . . . , s k )

r~y­ko`_sJ^R`4t>mxk4± €`/m

r i = (r i x , r y i )

¦`mxZ]`£J`4p/morG|RsGrJu tvs¯y§|xrG^ moZv`^au¤†j…¦rJu t>m"r~y

s 1

mor©moZv`^au¤†j…@rGu¡tJmar~y

s i

±C7]¨v|n¢

mxZ]`_|x^arG|x`G«Ÿ `_m

θ i , l i = ks i k

@`EmoZ]`¯rJ|ou¡`_t>m‡„'mou¡rGt¼„~t¦†Ÿ¡`_tvs~moZ¼rGy

s i

±½Y[Z]`¯†j`Ikop_|ou¡…jmxrG|"r~y

P

u¡k

p_rG^a…@rJko`4†r~y

4k − 2

£6„GŸ ¨v`4kR®§·vsG¨v|o`a“_`6°O>

r 2 x N d

, r y 2 N d

, . . . , r x k N d

, r y k N d

, θ 1 , . . . , θ k , l 1

N d

, . . . , l k

N d

Y[Z]`†]u¡knmx„Gtvp/`

N d

@`/m³`_`_t%moZ]`m³rqyz„G|nmxZ]`4knm.^au¤†j…@rGu¡tJm‡k.u¡k.¨vko`4†„Gk.t]rG|x^"„~Ÿ¡u/.I„'mxu rJtByz„GpªmxrG|I«'^"„~¸lu tvs

mxZ]`(†j`4kxp/|xu¡…jmorJ|[kxp_„GŸ `_¢9u¡tl£'„~|xu¡„GtJm¥®§Z]`4tvp/`J«j¦rGmoZmoZ]`

k

‚¥g"y§`I„'mx¨]|o`Ik[„~tv†–moZ]`4u |q†j`Ikop_|ou¡…jmxrG|‡k¹„G|o`Bkop4„~Ÿ¡`/¢

u¡tl£'„~|xu¡„GtJmª°ª±  Z]u¡Ÿ `(ko`_sG^a`4tJmŸ `4t]s~mxZvk„~|x`´¸lt]r'³t"mxr@`rGyÇmo`4t–u¡tv„Gp4p/¨]|‡„'mx`G«j„~tv†­`4„Gp‡Z–u¡kv„Jkn`I†"rGt]Ÿ¡i

rJtK…v„~|omrGymoZ]`

k

‚g8«@mxZ]`†ju¤knmx„~t¦p/`@`/m³`_`4tKmoZ]`%yz„~|omoZ]`Ikm^Ru¤†j…@rGu¡tJm‡k´^"„G¸G`4k„"@`/mnmx`_|(p‡Z]rJu¡p_`By§rG|

„­|o`4Ÿ u¤„~]Ÿ¡``Ikmxu ^"„'mx`r~ymxZ]`

k

‚¥gKkxp_„~Ÿ¡`G± -ìt¯„J†]†ju mou¡rGtKmxr–„

k

‚¥gKkop4„~Ÿ¡`G«¦³¹`%„GŸ¡kor–†j`_·vt]`u mxk / mxr­@`moZv`%sG`4rG^a`/mx|ou¤pp_`_t>mo`4|´r~y=mxZ]`%^au¤†j…@rGu¡tJm‡kqrGy+uwm‡kko`_sJ^R`4t>mxk4±=º]„GpªmB†j`/·¦t]uwmxu rJtvkr~y+kop4„~Ÿ¡`%„~t¦†

Ÿ¡rjp_„~mou¡rGt"„~|x`¨vko`/y§¨]Ÿ@³Z]`_t"¨¦knu¡t]s

k

‚¥gau¡t"Z]u sJZ]`_|¹Ÿ `4£G`4Ÿv„~Ÿ¡sGrJ|ou moZ]^"k4«Jko¨vp‡Z­„Gk=u¡t­rJ¨]|QkoŸ u¤†ju¡t]s~¢Æ³u t¦†jr'³ rJj}`4p/mq†j`/mx`4pªmxu rJtKkop‡Z]`4^a`a®zt]`/ºlm´ko`4p/mou¡rGtvk‡°ª±

Y[Z]`B…]|xrG…@rJko`4††j`4kxp/|xu¡…jmorJ|p_rGtvkou¡†]`_|‡kQmxZ]`(kn`4sG^a`_t>m‡k„Jk[p/rG^a…]Ÿ¡`/mx`_Ÿ¡i­kmx|x„Gu sJZ>m4«jknra„Gk¹mxrap4„~…jmx¨]|x`

rJt]Ÿ¡imxZ]`¥|o`4Ÿ `4£6„Gt>m¹u¡tjy§rG|x^"„'mou¡rGt"rGymoZv`sJ`_rG^a`_mo|xu¡pqp_rGtj·¦sG¨]|‡„'mxu rJtamoZ]`4iay§rG|x^«l„~t¦†­t]rGmQmoZv`£'„~|xilu tvs

ÛoهÔ3Û

k = 1

ÝqÙªÛÔ8ÛnÛßI×3ÜÞÕªá

Û6ÛÔnÚzÜÞßI×3ÕªÚÜÞÔÕªÝßGÕªÔ3Û´ÕªáIàՇÖ

θ 1

هá×

Û.ÔnهàÞÛ.ՇÖ

1AS

ÜÞÔIÛ6á6Û

هÔ

l 1

(11)

‹

†]`/mx„Gu Ÿ¤kr~ymxZ]`¥³¹`I„~¸­p/¨v|o£'„'mx¨]|x`„~Ÿ¡rGtvsmoZv`_^E±+µKrG|x`_r'£J`_|I«G³`knmo|x`4kxk¹moZv„~mrJt]Ÿ iamxZ]`

k

ko`_sG^a`4tJm‡k¹„G|o`

†]`4kxp/|xu @`4†¬«¦„~tv†t]rGmqr~moZv`_|qt]`I„~|xli­`4†jsJ`_Ÿ¤k_±=-ìtmxZ]u¤kyz„GkoZ]u¡rGt«v³¹`p4„~tKp/Ÿ¡`4„Gt]Ÿ i–`_tvp_rl†]`„a…¦rJ|nmxu rJtrGy

„GtrJj}`4p/m¦rJ¨]tv†]„G|oiJ«j³uwmxZ]rG¨jmqu¡tvp_Ÿ ¨v†]u t]s"u¡t]t]`4|'rG¨jmx`_|p/Ÿ¡¨jmomo`_|®§¨]t]Ÿ¡u¡¸G`aʐ 4˧°ª±

 u moZ¿uwm‡k

4k − 2

†ju¡^R`4tvkou rJtvk_«´moZ]`Á†j`Ikop_|ou¡…jmorJ|–u¤kE„~Ÿ¤knrU£J`_|xi¾p/rG^a…v„JpªmI± -ìtv†]`_`4†«kou tvp_`NmxZ]`

u¡t>mo|xu t¦knu¤p†ju¡^a`_tvkou rJtv„~Ÿ¡u mirGy

k

kmx|x„Gu sJZ>mkn`4sG^a`_t>m‡kqu¤k

4k

«@„Gtv†EmoZv`†ju¡^a`_tvkou rJtv„~Ÿ¡u mirGy=moZ]`a†j`4kou¡|o`I†

kxp_„GŸ `6´mo|‡„~tvkoŸ¤„'mou¡rGtEu¡tl£6„G|ou¤„~t¦p/`ko…v„Jp/`%u¤k

3

«@mxZ]`aŸ r'³`4knm¥†ju¡^a`_tvkou¡rGtv„GŸ u miEr~y¹„p/rJ^R…vŸ `_mo`a†j`4kxp/|xu …]morG|

u¤k

4k − 3

±=Y[Z]`¥rGt]Ÿ¡ia|o`I†j¨]tv†v„~t>m[†]`_sG|x`_`r~y¬y§|x`_`I†jrG^³`´`4tvp/rj†j`¥u¡k`4^%@`4†]†j`I†­³u moZ]u¡tmoZ]`¥|o`4Ÿ¡„~mou¡£G`

Ÿ¡rjp_„~mou¡rGtK£G`IpªmxrG|‡k

{r i } i =2 ..k

«¬„Gtv†Eyz„Gp/morJ|ou¡t]s"u m¥rJ¨jm³rG¨]Ÿ¤†E|x`>¨]u¡|o`|x`_…v|o`Ikn`4tJmxu tvsamoZ]`4^Åu tN„–^arG|x`

p_rG^a…]Ÿ¡u¡p4„'mx`4†³„6iJ±

-ìt>mo`4|o`Ikmxu tvsGŸ¡iG«¦moZ]`

k

‚gK†]`4kxp/|xu …jmxrG|u¡kr~yQ†ju ¶8`_|x`_t>m´tv„~mo¨]|x`moZ¦„~tNp_rGtl£G`4tJmxu rJtv„~ŸHŸ rjp_„GŸmx`/ºlmo¨]|x`4†

y§`I„'mx¨]|o`[†j`Ikop_|ou¡…jmorJ|xk4±  Z]u¡Ÿ¡`¹mxZ]`Ÿ¡„~mnmo`4|`_tvp_rl†]`QmxZ]`„~…]…@`4„G|x„Gtvp/`+rGyvmxZ]`¹…vuwºj`_Ÿl…v„~mxp‡ZRp/r'£G`4|o`I†(liBmoZ]`

y§`I„'mx¨]|o`J«¬moZv`

k

‚g²†j`Ikop_|ou¡…jmorJ|B`_tvp_rl†]`4k¥moZv`"sG`_rJ^a`/mo|xu¤p%…]|xrG…@`_|omou¡`4k¥rGy¹moZv`­kn`4sG^a`_t>mxka®zrG|xu `4tJm‡„'mxu rJt

„Gtv†Ÿ `4t]s~mxZ¦°ª«v„Gtv†r~ymoZ]`4u |´ko…v„~mou¤„~Ÿ¬„~|x|x„Gt]sG`4^a`_t>mB®

{r i } i =2 ..k

°/±

-Æy+†j`Iknu¡|o`I†¬«jmxZ]`%†j`Ikop_|ou¡…jmorJ|qp_„Gt@`(`4„Jknu¡Ÿ¡i–^"„G†j`(|xr~m‡„'mxu rJtj¢9u¡tl£'„~|xu¡„GtJmI«j„'mmoZv`p/rJknmqr~y+korG^a`(†ju¤k¢

mxu t¦pªmou¡£G`4t]`4kxk4«]li^a`4„Jkn¨v|ou¡t]s

{θ i } i =2 ..k

|x`_Ÿ¤„'mxu £J`mxr

θ 1

«¦|orGmx„'mxu tvs

{ r i } i =2 ..k

li

θ 1

«@„~tv†E|x`_^ar'£lu¡t]s

θ 1

y§|xrG^fmoZv`[†]`4kxp/|xu …jmxrG|I± -ìta„G†]†ju mou¡rGtH«'y§rG|

k ≥ 3

rGt]`[p_„Gt†j`Iknu¡sGtR†j`4kxp/|xu …]morG|‡k³uwmxZ`4£G`_tZ]u¡sGZ]`4|†]`/¢

sJ|o`4`4krGy8u¡tl£'„~|xu¡„Gtvp/`®3„I"t]`G«J…]|xr~}`4p/mou¡£G`6°mor@`q¨vko`4†¬«>`G±sv±y§rG|Q³u¡†j`_¢9¦„Gko`_Ÿ¡u t]`qknmo`4|o`4r"ʒJ6ËÆ«>„GŸwmxZ]rG¨]sJZ

³`(†jrat]r~mqu¡tl£G`Ikmxu s>„'mo`moZvu¡k…@rJkxkou ]u¡Ÿ¡uwmi"y§¨v|nmxZ]`_|u¡tmoZ]u¤k…v„G…¦`4|4±

1

k

2

 `†j`_·vt]`(Z]`4|o`(„R^a`4„Gko¨]|x`

D(a, b)

rGyHmoZv`†ju¡kxkou ^au¡Ÿ¡„G|ou mi­@`/m³`_`_tm³r

k

‚¥g

P a , P b D(a, b) = w r

k

X

i =2

k r a i − r b i k + w θ k

X

i =1

D θ θ i a , θ i b

+

k

X

i =1

log l a i /l b i

³Z]`_|x`mxZ]`%·¦|xknm´mx`_|x^Åu¡k´moZ]`a†ju ¶@`4|o`4tvp/`Ru¡t¯moZv`|x`_Ÿ¤„'mxu £J`Ÿ rjp4„'mou¡rGt¦k´rGy=moZ]`akn`4sG^a`_t>m‡k_«

D θ ∈ [0, 1]

^a`I„Gko¨]|o`IkBmoZv`†ju ¶@`4|o`4tvp/`–¦`_m³¹`4`_tUko`_sG^a`4tJmrG|xu `4tJm‡„'mxu rJtvk_«.t]rJ|o^"„~Ÿ¡u0._`4†²li

π

«+„~tv†²mxZ]`–Ÿ¤„Gknmm³r mx`_|x^"k„Jp_p/rJ¨]t>my§rG|%moZ]`E†ju ¶@`4|o`4tvp/`u tXŸ `4t]s~mxZvk_±²‚´kako`_sG^a`4tJmŸ `4t]s~mxZvk„G|o`–r~yÇmo`4tUu¡tv„Gp4p/¨]|‡„'mx`G«³¹`

sJu £J`[Z]u sJZ]`_|Q³¹`4u sJZJm=mxr(moZv`[m³¹r(rGmoZ]`4|=mo`4|o^"k=rGy@mxZ]`´p_rG^a…v„~|xu¤knrJt^a`4„Jkn¨v|o`>u t­„GŸ Ÿ¦rG¨]|=`_ºj…¦`4|ou¡^a`_t>mxk

w r = 4

«

w θ = 2

±=‚qŸ¡Ÿ

r i

„Gtv†„GŸ Ÿ¬Ÿ¡`_tvs~moZ¦kq„~|x`tvrG|x^a„GŸ u0._`I†„Jk[u tE`)J¨¦„'mou¡rGt²®“6°ª±

¬HQ-/#&

k

h"[*²"

-ìtmxZ]`…]|x`_£lu¡rG¨vkqko`4p/mou¡rGtE³`(Zv„6£G`Bu¡tJmx|orj†j¨¦p/`4†mxZ]`

k

‚¥gy§`4„'mx¨]|x`4k4± `/y§rG|x`(¨vkou tvsamoZ]`4^Èy§rJ|qrGj}`Ipªm p_Ÿ¡„Jkok=†]`/mo`Ipªmxu rJtE®zt]`/ºlmQko`4p/mou¡rGt¦°/«G³`[p_rGtvknmo|x¨vp/mQ„¥p_rj†j`_@rlrG¸–®zrG|D£>u¤ko¨v„~Ÿ]£Jrjp_„~v¨]Ÿ¡„G|oi$9lʒ6Ëǰ.rGy¦y§`I„'mx¨]|o`

mil…@`4k=liRp/Ÿ¡¨vkmx`_|xu tvsB„(ko`/m¹r~y@mo|‡„~u¡t]u tvs

k

‚ga„Gp4p/rJ|x†ju¡t]smorBmxZ]`_u¡|¹†j`Ikop_|ou¡…jmorJ|xk[®3„(†juw¶8`_|x`_t>m¹p_rj†j`_@rlrG¸

u¤k=sJ`_t]`4|x„~mo`4†y§rG|+`I„Gp‡Z

k

°ª±3-ìt"„G†v†juwmxu rJtRmorB|o`4£G`I„~Ÿ¡u t]smoZv`y§|o`)>¨]`_tvp_i%„'m+³Z]u¤p‡ZRy§`4„~mo¨]|x`[mil…¦`Ik=rjp_p/¨v|4«

mxZ]`ap/rj†j`_@rlrG¸u¡kBp_rGtl£G`4t]u `4t>m´¦`Ip_„G¨vkn`uwmB|x`_Ÿ¡u `4£G`4kqmoZ]`Rt]`4`4†Ey§rJ|`_ºl…vŸ u¤p/u moŸ¡i¯p/rJ^R…¦„~|xu t]s–`_£G`4|oimo`Ikm

u¡^"„~sJ`y§`I„'mx¨]|o`Ikmor"`4£G`_|xiay§`4„~mo¨]|x`By§|xrG^mxZ]`(moZv`Bmo|‡„~u¡t]u tvsRu¡^"„~sJ`4k4±5-ìtvkmx`4„J†¬«]p/rJ^R…¦„~|xu¡korGt–mor"^%¨¦p‡Z

y§`4³¹`4|Qy§`I„'mx¨]|o`mil…¦`Ik[kn¨!I­p_`G±¹b¹rj†j`_@rlrG¸a|x`_…]|x`4ko`_t>mx„~mou¡rGtvk¹Zv„6£J`´@`4p/rJ^a`…@rG…]¨vŸ¡„G|QmxZ]|orJ¨]sGZkn`4£G`4|x„GŸ

|x`4p_`_t>m³¹rJ|o¸jk¥Ê’j«¦Šl«“4À]«“6Šl«“4‘'Ë9«

(12)

7.u¡sG¨]|x`´!>D/ )H1"QG+T/+"

2

APB ",X+K+ G+>1) "#O1 =11U:L IT I'8M+K+)*+",91",T"

G+1) O1T "5<11 )F+P3 KQ1",#&C2 2(<",& )F+ G+>1) "#/N

A

1 + S"5+", ",,1

€H`/m

G

@`„­p_rG^a…]Ÿ¡`/mx`sG|‡„~…]ZK³ZvrJko`(t]rj†j`4k¥„~|x`BmoZ]`%mo|‡„~u¡t]u¡t]s

k

‚g¬«¦„~t¦†¯„~|‡p_kq„G|o`(³`_u¡sGZv`4†Eli

d − D(a, b)

±  `…v„G|nmxuwmxu rJt

G

u¡t>mor­p_Ÿ u>¨]`4kknr­„Jk[mor­^"„~ºlu¡^au/.4`BmoZ]`Rkn¨v^rGy.u¡t>mo|‡„'¢ìp/Ÿ¡u>¨]`(³`_u¡sGZ>mxk4«

¨¦knu¡t]s"mxZ]`p_Ÿ u>¨]`/¢Æ…v„~|omou mou¡rGtvu t]s©®9b¹{¹°„~…]…v|or6ºju¡^a„~mou¡rGtE„~Ÿ¡sGrJ|ou moZ]^r~yqʌ6ËÆ±´Q„Jp‡ZK|o`Ikn¨vŸwmxu t]sp/Ÿ¡u>¨]`u¡k

„ap_Ÿ ¨vknmo`4|r~y=knu¡^au Ÿ¤„~|

k

‚¥g8±

Y[Z]`p‡Z]rGu¤p/`rGy¹b¹{¾u tvknmo`I„G†ErGy¥¢Æ^a`4„Gtvk_«¦p/rG^a^arGtvŸ i¨vkn`I†y§rG|]¨]u¡Ÿ¡†ju¡t]s­£lu¤kn¨¦„~Ÿp_rj†j`_@rlrG¸jk_«vu¡k

„G…]…]|xrG…]|xu¤„'mo`Ru¡t;rG¨]|p_rGt>mo`_º>m³Zv`_|x`amoZ]`­†ju¤kxknu¡^au Ÿ¤„~|xuwmiN^R`I„Gko¨]|x`

D

^"„G¸G`4k¥mxZ]`–†j`Ikop_|ou¡…jmxrG|ko…v„Gp_`

p_u |‡p/¨vŸ¡„G|®

D θ

mo`4|o^"k‡°ª±=µKrG|x`_r'£J`_|I«'moZv`´…v„G|x„G^R`_mo`4|

d

u¡k¹`4„JknimorRkn`_m4«l@`4p_„G¨vko`´uwm[|x`_…]|x`4ko`_t>mxkQ„|xrG¨]sJZ u¡tv†ju¤p_„~mou¡rGt;rGymoZ]`„Gp_p_`_…jm‡„~]Ÿ¡`­u¡t>mo|‡„'¢ìp/Ÿ¡¨vkmx`_|%†]u¡kxknu¡^au Ÿ¤„~|xu mi®3„~¸lu tUmorKmxZ]`–¸J`_|xt]`_Ÿ ¢9³u¤†lmxZ;u t^R`I„~tj¢

koZ]u yÇmp/Ÿ¡¨vknmo`4|ou¡t]s;Ê¡“_À'˧°ª±¥¢Æ^R`I„~tvku tvknmo`I„G†²|x`>¨]u¡|o`IkBmoZ]`–t>¨v^%@`_|rGyp_Ÿ ¨¦kmx`_|‡k„Gk(u¡t]…]¨]m4«³Z]u¤p‡Z;u¡k

¨vt]¸lt]r'³tK„~…]|xu rJ|ou„Gtv†E£'„~|xu `Ik[y§|xrG^†v„'mx„Jkn`_mqmor†]„'m‡„Gko`/m4±gl`4£G`_|‡„~Ÿ¬`_ºj…¦`4|ou¡^a`_t>mxk´u tv†]u¡p4„'mo`BmxZv„'mmoZ]`

`_º]„Gpªmqp‡Z]rJu¡p_`Br~y

d

Zv„Gk[Ÿ¡uwmomoŸ¡`(u ^a…v„JpªmqrJt–mxZ]`(r'£G`4|x„GŸ Ÿ8knijknmo`4^ȅ@`_|ny§rJ|o^"„Gtvp/`a®zko`4p/mou¡rGtK‘G°/±

7vrG|¥`4„Gp‡Z©p/Ÿ¡¨vkmx`_|I«¬³¹`Rkn`4Ÿ `IpªmB„GkB„­|x`_…]|x`4ko`_t>m‡„'mou¡£G`moZ]`

k

‚g¯³uwmxZ¯moZv`Ÿ¡r'³¹`IkmBkn¨v^År~yQ†ju¤kokou¡^Ru ¢

Ÿ¤„~|xu mou¡`4kmor­„GŸ ŸHr~moZv`_|‡k(®§u9±`J±+moZv`(rGt]`p_Ÿ r>kn`Ikm[moramxZ]`%p_Ÿ ¨vknmo`4|qp/`4tJmx`_|ª°ª±QY[Zv`B·vtv„~Ÿp/rj†j`_@rlrG¸

C

u¡kmoZ]`

p_rGŸ¡Ÿ `Ipªmxu rJtrGyHmoZv`4ko`(|o`4…]|o`Ikn`4t>mx„'mxu £J`

k

‚¥g8«jmxZ]`

k

" FG)O ±

 Z]`4t­p/rJtvkmx|o¨¦pªmou¡t]sp_rl†]`_@r>rJ¸jky§|orJ^ †ju ¶8`_|x`_t>mQu¡^a„GsG`qko`/m‡k_«J³¹`rJvkn`4|o£J`4†%moZv„~m+moZv`

k

‚gmil…@`4k rjp4p/¨]|x|ou¡t]s³uwmxZU„Eknu¡sGt]u ·¦p4„~t>mBy§|o`)J¨v`_tvp_iN³`_|x`R£J`_|xiNkou ^au¡Ÿ¡„G|4±­Y[Z]u¤kp_rGtj·v|x^"k¥moZ]`"u¡t>mo¨]u mou¡rGtÁmxZv„'m

k

‚gR„~|x`¹sJ`_t]`4|ou¤p¹y§`4„~mo¨]|x`4k®3p/`_|omx„Gu tvŸ i(y§rJ|moZ]`Ÿ¡r'³X£'„GŸ ¨]`Ikr~y

k

³`qp/rJtvknu¤†j`4|‡°/±K?q`4tvp/`J«~y§rJ|=`4„Gp‡Z

k

³¹`

v¨]u Ÿ¤†K„­kou tvsGŸ¡`p/rj†j`_@rlrG¸–y§|orJ^!“4au¡^"„~sJ`4kq„Gtv†E¨vko`(uwmy§rG|´„GŸ ŸrJj}`4p/mp/Ÿ¤„Gkxko`4k[u¡tKrG¨]|q`_ºj…¦`4|ou¡^a`_t>mxk

®3kn`Ipªmxu rJt‘>°ª±

(13)

“J“

7.u sJ¨]|x`¥’)>HH)H1"-G+T/+/"

3

APB

G+>1) 1T 1 =11U:<;

7.u¡sG¨]|x`qBknZ]r'³UmoZ]`q’>Š´^ar>km=y§|x`>¨]`4tJmmil…@`4k=u¡t%mxZ]`

2

‚gp/rj†j`_@rlrG¸8±‚´k³`qp_„~tako`_`G«~moZ]`4i%Zv„6£J`

>¨]u mo`¥tv„~mo¨]|‡„~Ÿ¬koZv„~…@`4k >Hm³rap/rGŸ¡Ÿ¡u t]`I„~|[kn`4sG^a`_t>m‡k_«

L

kmx|o¨vp/mo¨]|x`4k4«l„~tv†kn^"„~Ÿ¡Ÿ¬Y¢ }¨vtvpªmxu rJtvk_±7.u¡sG¨]|x`’

†]u¡ko…]Ÿ¤„6ilk¥mxZ]`­’JŠ^arJknm(y§|x`>¨]`_t>m

3

‚gNmil…¦`Ik_±–Y[Zv`_i¯y§rJ|o^ ^arG|x`ap_rG^a…]Ÿ¡`/ºÁkmx|o¨vp/mo¨]|x`4k¥mxZv„~t

2

‚¥g$>

C, Y, F, Z

koZv„~…@`4k4«jŸ¤„~|xsG`_|

T

knZv„G…¦`Ik_«¦„~tv†–mo|xu¡„Gt]sGŸ¡`4k4±

)*"+È / È+.-/

-ìtUmoZ]u¤kko`4p/mou¡rGtU³`–…v|o`Ikn`4tJmR„¯kop‡Zv`_^a`­y§rJ|†j`_mo`4p/mou¡t]s²rGj}`Ipªmxk%v„Gko`4†UrGt

k

‚g¬±  `­·¦|xknm%mx|x„Gu tU„

p_Ÿ¡„Jkokou ·v`_|mor­†]u¡knmou¡t]sG¨vu¡koZE³u tv†]r'³qkp/r'£G`4|ou¡t]sRrGj}`Ipªm‡k[r~y=„"p/`_|omx„Gu tEp/Ÿ¤„Gkxky§|xrG^„Gtli­r~mxZ]`_|³u¡tv†jr'³(«

„Gtv†amxZ]`_t„~…]…]Ÿ¡iauwmy§rG|Ÿ¡rlp4„~Ÿ¡u/.4u tvs%t]r'£J`_Ÿvu¡tvknmx„Gtvp/`IkQu¡t–…]|x`_£lu¡rG¨vkoŸ¡i¨]t¦kn`4`_t"mx`4knmu¡^"„~sG`Ik_«>v„Jkn`I†"rGt–„

koŸ¡u¡†ju¡t]s­³u¡tv†jr'³¿^a`4p‡Zv„Gt]u¤kn^E±‚´k´u tEmxZ]`Ÿ¤„~|xsG`(^"„'}rJ|ou mi­r~y=^arj†j`_|xtK³rG|x¸lk4«]³`(]¨]u¡Ÿ¡†N„­†j`/mx`4p/morG|

y§rJ|q„aknu¡t]sGŸ¡`B£lu `4³…¦rJu t>m4±

1 1

Y[Zv`qmo|‡„~u¡t]u¡t]s†v„'mx„%u t¦p/Ÿ¡¨v†j`4k¹…@rJkouwmxu £J`´u¡^a„GsG`Ik_«lp/rJtJm‡„~u¡t]u¡t]su¡tvkm‡„~tvp_`4k¹r~y¬mxZ]`¥p_Ÿ¡„Jkok¹„~t]tvr~mx„~mo`I†"lia„

@rG¨vtv†ju¡t]s~¢Æ¦r6ºN®§·vsG¨v|o`(ÀJ°/«v„~t¦†–t]`4sJ„~mou¡£G`Bu ^"„GsG`4k4±

(14)

7.u¡sG¨]|x`¯À> 6KQ1",&J",> M<E)CK2+H!"# =1T 2SZ=1M0",,*-70G+

k

APB

TEK+)IKQ1

3

k = 2

T = 4

;

Ò ÑlÐ Ò Í —4›G™ ˜ Ñ ™ Yr;…]|orj†j¨¦p/`¯„Á¨vko`/y§¨]Ÿp/Ÿ¤„Gkxknu ·v`_|I«³¹`Et]`4`4†¾„²tl¨]^a`_|xu¡p4„~Ÿq³u¡tv†jr'³†j`/¢

kxp/|xu¡…jmorJ|q³Z]u¤p‡Z¯u¡k¥„Gp4p/¨]|‡„'mx`(`_t]rJ¨]sGZEmxrko`_…v„G|x„~mo`(…@rJkouwmxu £J`%`_ºj„G^a…]Ÿ `Iky§|xrG^t]`_s>„'mxu £J`G«viJ`/mAv`/ºju¡]Ÿ `

`4t]rG¨vsGZ©mor¯„Gp4p/rJ^R^arj†]„~mo`y§rG|%p_Ÿ¡„Jkok¥£'„~|xu¡„G]u¡Ÿ u miG±  Z]`4tÁmoZ]`Ikn`asJrJ„~Ÿ¤k(„~|x`R^R`_m4«mo`Ikm³u¡tv†jr'³qkBrJt

tvr'£G`_Ÿ=rJj}`4p/mu t¦km‡„~tvp_`4k(³u¡Ÿ ŸQZv„6£G`"†j`Ikop_|ou¡…jmorJ|xk(p_Ÿ r>kn`4|BmorEmxZ]`­…@rJkouwmxu £J`mx|x„Gu tvu t]s¯ko`/m(mxZv„~t²mxrKmoZ]`

tv`_sJ„~mou¡£G`J«l„Gtv†moZ]`p_Ÿ¡„Jkokou ·v`_|p_„Gtko¨vp4p/`_`I†¬±

‚fknmo|‡„~u¡sGZ>mny§rJ|o³[„~|‡†RrG…jmxu rJt³rG¨]Ÿ¤†­@`moZ]`

k

‚¥g­Z]u¤knmorGsJ|x„G^E«>p_rG¨]t>mou¡t]sRZ]r'³»^"„~tli

k

‚¥g"r~y.`4„Jp‡Z mil…@`moZv`_|x`q„~|x`u tvkou¤†j`[moZ]`³u t¦†jr'³(«~³Z]u¤p‡Z"u¡k¹„(knu¡^a…]Ÿ¡`qv„~s(rGy¦y§`I„'mx¨]|o`Ik=|x`_…]|x`4ko`_t>mx„~mou¡rGt± ?qr'³`_£J`_|I«

³`"p_„Gt©rJjmx„Gu t©¦`_mnmo`4|%†ju¤kop_|ou¡^au t¦„'mou¡£G`R…@r'³¹`4|¥liN„GŸ¡korE`_tvp_rj†ju tvs–mxZ]`­kn…¦„'mou¤„~Ÿ=Ÿ¤„6iGrJ¨jmBr~yQmxZ]`

k

‚g

u¡t¯mxZ]`R³u tv†]r'³ †j`4kxp/|xu …]morG|I±  `akn¨v@†ju¡£lu¡†]``I„Gp‡ZK³u¡tv†jr'³ u¡t>mor„kn`_m¥rGy 0O

B

«8„~tv†©p/rG^a…]¨]mo`„

ko`_…¦„~|‡„'mo`

k

‚¥gZ]u¤kmxrGsG|‡„~^ y§rG|´`I„Gp‡Zmou¡Ÿ¡`–®Ç·vsJ¨]|x`(À>°ª±Y[Z]`p_rGtvp4„'mx`_tv„~mou¡rGtEr~y+„~Ÿ¡ŸZ]u¤knmorGsJ|x„G^"k[i>u¡`_Ÿ¤†]k mxZ]`

|B| · |C|

¢¹†ju¡^a`_tvkou rJtv„~Ÿ¬³u¡tv†jr'³¿†j`4kxp/|xu¡…jmorJ|4±

Y[Z]`mou¡Ÿ¡u t]sÁ…v„~mnmx`_|xt

B

„~¨jmxrG^"„'mxu¡p4„~Ÿ¡Ÿ iÁ„G†]„G…jmxkmxrNmxZ]`–mx|x„Gu tvu t]s²†]„'m‡„©„Jky§rJŸ Ÿ¡r'³qk4±C7u¡|‡kmI«=moZ]`

koijkmx`_^ p_rG^a…]¨jmx`4kRmxZ]`K^a`4„~t¼†ju¡^a`_tvkou rJtvkRr~y¥moZ]`E…@rJkouwmxu £J`mo|‡„~u¡t]u tvs²³u¡tv†jr'³qkE®z³u¡†lmxZ

M w

„~t¦†

Zv`_u¡sGZ>m

M h

°ª± q`/ºlmI«u m„~Ÿ¡Ÿ¡rlp4„'mx`4k(„Emxr~mx„GŸ+r~y

T

mou¡Ÿ `Ik_«p‡Z]rlrJkou¡t]smoZ]`­tl¨]^¦`4|r~y[mxu Ÿ¡`4k„GŸ rJt]sK`4„Jp‡Z

†]u ^a`_t¦knu¡rGtNkor–„Jkmor^"„~¸G`moZ]`4^„Gk´k$>¨v„~|x`%„Jkq…@rJkxknu¡]Ÿ¡`'>

round( p

T M w /M h )

„~Ÿ¡rGt]s­moZ]`³u¡†lmxZ«

„Gtv†

round( p

T M h /M w )

„GŸ rJt]s(mxZ]`BZ]`_u¡sGZ>m4±=Y[Z]`…v„~|‡„~^a`_mo`_|

T = |B|

p/rGt>mx|orJŸ¡k+moZ]`¥|o`IknrJŸ ¨]mou¡rGt­rGy mxZ]`mxu Ÿ¡u¡t]sv±

M w , M h

³u¡Ÿ Ÿ.Ÿ¡„~mo`4|q¦`¨vko`4†K„~s>„~u¡tK³Z]`_t¯ko`4„G|xp‡Zvu t]say§rJ|qrG]}`4pªm‡kqu¡t¯t]`4³½mx`4knmu¡^"„~sG`Ik_«

mxr"kn`_mmoZ]`„Jkn…@`4p/mn¢Æ|x„~mou¡rrGyHmoZv`knŸ¡u¡†]u t]sa³u¡tv†jr'³ÄmoramoZv`(rGt]`B@`4knm·]mnmxu t]samxZ]`Bmo|‡„~u¡t]u¡t]sa`/º]„~^a…]Ÿ¡`4k4±

 Z]`4tÄp/rJ^a…]¨jmou¡t]sXmoZ]`

k

‚g¼Z]u¤knmorGsJ|x„G^"k_«[|‡„'moZv`_|"mxZv„~tĄJkokou¡sGt]u¡t]s;`4„Jp‡Z

k

‚gmxrUmoZv`©kou t]sJŸ ` p_Ÿ r>kn`Ikmmil…¦`J«]u mqu¡kkor~yÇmo¢Æ„Jkokou sJt]`4†­mor­„GŸ Ÿ8mil…@`4k[³u moZ]u¡tK†ju¡kxkou ^au¡Ÿ¡„G|ou mi

d

±+µ¯rG|x`…]|x`4p_u¡ko`_Ÿ¡iG«j`I„Gp‡Z

k

‚g

P

†]u¡knmo|xu v¨jmo`Ik¹„mor~m‡„~Ÿ8kn¨v^

P s

„G^RrJt]s(mxZ]`´mil…@`4k¹uwmu¡k„Gkxkou sJt]`4†Rmxrv«lu t–u tl£G`4|xko`q…]|xrG…@rG|omou¡rGt¦k=mor%moZ]`

†]u¡kxknu¡^au Ÿ¤„~|xu mimxrmoZ]`Rmil…¦`Ik98|x`_…]|x`4ko`_t>m‡„'mou¡£G`

k

‚g¬±8Y[Zvu¡kB^"„~¸J`4k´moZ]`a|x`_…]|x`4ko`_t>mx„~mou¡rGt¯rGy¹„³u tv†]r'³

Ÿ¡`4kxkBkn`4tvkouwmxu £J`%mxr–mxZ]`a`/º]„Gp/mBkoZv„~…@`Rr~yQmxZ]`

k

‚gNu m(p_rGt>mx„Gu t¦k_«¬„~t¦†¯mxr–mxZ]`a`/º]„Gpªm(p/rj†j`4¦rlrJ¸Emi>…@`4k4±

Y[Zvu¡k´Ÿ `I„G†]kqmor–ko^ar>rGmoZ]`4|q^arj†j`_Ÿ¤k_«@³Z]u¤p‡ZK¦`_mnmx`_|¥sG`_tv`_|‡„~Ÿ¡u/.4`mxr–t]r'£J`_ŸrJj}`4p/m´u¡tvkm‡„~tvp_`4k4«¦„Gtv†mor–„

^arJ|o`(„Gp4p/¨]|‡„'mx`G«vknmx„G]Ÿ¡`(`_£'„~Ÿ¡¨v„'mxu rJtEr~y.mo`4knm´u¡^"„~sG`(³u¡tv†jr'³qk%®§t]`_º>m¥kn¨]¦kn`Ipªmou¡rGt@°ª±=-ìt¯„J†]†ju mou¡rGtmor­„

k

‚g$9@knZv„G…¦`J«]³`%„~Ÿ¤knr"p_rGtvkou¡†]`_|u mxk G /(#4 >QmxZ]`(mxr~mx„GŸHp/rJt>mo|xu ]¨jmxu rJtEr~y

k

‚g

P

mor­„aZvu¡knmorJsG|‡„~^

(15)

“I’

u¤kmxZ]`%„6£J`_|‡„~sG`Bknmo|x`_t]sGmoZEr~y=u mxkq`I†jsG`4Ÿ¡k

P s ∈ [0, 1]

±  `%`_ºj…¦`4|ou¡^a`_t>mx„GŸ Ÿ¡i–rJvkn`4|o£J`4†„"p/rJtvknu¤†j`4|x„G]Ÿ ` u¡^a…]|xr'£G`_^a`4tJm[r'£G`4|mo|x`4„'mxu tvsR`I†jsG`4Ÿ¡k[„Jk[]u t¦„~|xi"y§`4„~mo¨]|x`4k(®3„Gk„~Ÿ¤korRtvr~mou¤p/`I†–li¯ÊÀv«¦‹6Ëǰ/±

c¨]|B³u¡tv†jr'³†]`4kxp/|xu …jmxrG|Bu¤k¥„£'„~Ÿ¡¨v„G]Ÿ `ap‡Z]rJu¡p_`%y§rJ|¥rJj}`4p/mBp_Ÿ¡„JkokB†j`_mo`Ipªmou¡rGtH±-Æm(u¡k(†]u¡knmou¡tvpªmxu £J`G«

@`4p4„~¨vko`%u m(|o`Ip/rJ|x†]k (K1 1

Ÿ rjp4„~Ÿ=knZ¦„~…@`Rknmo|x¨vpªmx¨]|x`4kR®

k

‚¥g]°uwmp/rJtJm‡„~u¡tvk4«8„Gtv†¯|xrG¨vsGZ]Ÿ¡i (K12

moZ]`4i

„G…]…@`4„~|I±¼‚m"moZ]`Kkx„~^a`mou¡^R`J«¹u m­u¤k Av`/ºju¡]Ÿ `EmxZv„~tv¸lkRmxr²moZ]`¯p_rJ„~|‡ko`­mou¡Ÿ¡u t]s¦«„Gtv†XmoZ]`¯p_rGt>mou¡tl¨]rG¨vk

„Jkokou¡sGt]^a`_t>m=r~y

k

‚¥gmxrBmil…¦`Ik_±µK¨vp‡Zar~y@moZv`q…¦r'³`_|=rGy@rJ¨]|=|x`_…]|x`4ko`_t>mx„~mou¡rGtp_rG^a`4k.y§|xrG^ rG|xsJ„Gt]u/.4u tvs mxZ]`(u¡^a„GsG`B`4†]sG`4k[r'£J`_|m³rRŸ¡`_£J`_Ÿ¤k[r~ykn…v„~mou¤„~Ÿ„G|o|‡„~t]sJ`_^a`_t>m‡k>p/rJtJmxrG¨]|ko`_sJ^R`4t>mxk[³u moZ]u¡tEmoZ]`

k

‚¥g8«

„Gtv†–moZ]`4tmxZ]`

k

‚¥g–³u moZvu tmoZv`(r'£G`_|‡„~Ÿ¡Ÿ8rGj}`IpªmI±

‚k¥moZ]`Rmou¡Ÿ¡u t]sE|x`4korGŸ¡¨jmou¡rGt

T

u¡tvp/|x`4„Jkn`Ik_«@moZv`ako…v„~mou¤„~ŸŸ rjp4„~Ÿ¡u/.I„'mou¡rGtNr~y

k

‚¥gKsJ|or'³qk¥kmx|orJt]sG`4|4«8|x`/¢

ko¨]Ÿ mou¡t]sau tE„R^arG|x`u¡tjy§rG|x^"„'mxu £J`B†]`4kxp/|xu …jmxrG|I«l]¨jmq„~Ÿ¤knr"„^arG|x`¥|xu¡sGu¤†­rGtv`G«]„Gp4p/rJ^R^arj†]„~mou¡t]s%y§rJ|[Ÿ `Ikok

ko…v„~mou¤„~Ÿ£'„~|xu¡„G]u Ÿ¡u mi¯r~y¹moZ]`­p_Ÿ¡„Jkok4± ?´`_tvp_`G«¬mxZ]`_|x`"knZvrG¨]Ÿ¤†N@`­korG^a`arG…jmxu ^"„~Ÿ

T

«]|xu t]sJu tvs–mxZ]`"¦`Ikm mx|x„J†j`/¢Ær~¶¦`_m³¹`4`_t­„Gp4p/¨]|‡„Gp_ir~yŸ¡rjp_„GŸ u0.4„~mou¡rGtau t]y§rG|x^a„~mou¡rGt"„~t¦†RmorGŸ¡`_|‡„~t¦p/`[mor%u t>mo|‡„'¢ìp/Ÿ¤„Gkxk£'„~|xu¡„~mou¡rGt±

-ìt>mx`_|x`4knmou¡t]sGŸ¡iG«>rG¨]|¹`/ºj…@`_|xu ^a`_t>m‡k¹koZ]r'³ÂmoZ]`¥rG…]mou¡^a„GŸ

T

mxr†j`Ip/|x`4„Jkn`q³u moZ–u tvp_|o`I„Gkou tvs

k

®zko`4p/mou¡rGt–‘>°ª±

 u moZ

k = 1

moZv`(y§`4„~mo¨]|x`4k„~|x`knr"¨]tvu tjy§rJ|o^"„~mou¡£G`(mxZv„'mqmxZ]`%³u¡tv†jr'³ˆ†j`Ikop_|ou¡…jmxrG|t]`4`4†]kqmor­@`„G¨]s~¢

^a`4tJmx`4†N³uwmxZN·vtv`/¢ÆsG|‡„~u¡t]`4†KŸ¡rjp_„GŸ u0.4„~mou¡rGtKmxr@`"†ju¡knmou¡tvp/mou¡£G`G±  Z]u Ÿ¡`

k

sG|xr'³qk4«

k

‚¥g¯@`4p_rG^a`R^RrJ|o`

p_rG^a…]Ÿ¡`/º¬«H„Gtv†©moZ]`­„J†]†j`4†©£'„~Ÿ¡¨]`"r~yŸ rjp4„~Ÿ¡u/.I„'mou¡rGt²sG|‡„G†]¨v„~Ÿ¡Ÿ i¯†]u ^au¡t]u¡koZ]`Ik_± -ìt;„G†v†juwmxu rJt«³`ay§rG¨]t¦†

mxZ]`arG…jmxu ^"„GŸ

T

y§rG|Bu t>mx`_|x`4knm¥…@rGu¡t>mxkB†j`4kxp/|xu¡¦`I†¯liNgH-7Yˆmxr@`aŸ r'³`_|moZv„Gt¯mxZv„'m(r~y„~tli

k

‚g¯³¹`

`_ºj…]Ÿ rJ|o`I†U®

k ≤ 4

°ª±aglu t¦p/`­gH-7Y†j`Ikop_|ou¡…jmxrG|‡k´rGy„~t©u ^"„GsG`R…v„'m‡p‡Z©„~|x`R|ou¤p‡Z]`_|y§`4„~mo¨]|x`4ka®3„~tv†©Zv„6£G`

„a†j`Ikop_|ou¡…jmxrG|[r~y.^%¨vp‡ZZ]u¡sGZ]`4|q†ju ^a`4tvknu¡rGt¦„~Ÿ¡uwmi]°ª«lmxZ]u¤ky§¨]|nmxZ]`_|qp_rGtj·¦|o^"kmoZv`B„G¦r'£J`¥ko¨]jmxŸ `(|x`_Ÿ¤„'mxu rJt

@`/m³`_`4t–y§`I„'mx¨]|o`(p_rG^a…]Ÿ¡`/ºjuwmi„~tv†Ÿ¡rlp4„~Ÿ¡u/.I„'mxu rJt–|x`4korGŸ¡¨jmou¡rGt±

› 3š]—I—

Í

™"˜_™'š

Y[Z]`(³u¡tv†jr'³½†]`4kxp/|xu …jmxrG|[u¤kqp/rJ^R…v¨jmo`I†–y§rJ|`4„Jp‡Z…@rJkouwmxu £J`¥mo|‡„~u¡t]u tvs

`_º]„~^a…]Ÿ¡`G«„~tv†Ây§rJ|„;tl¨]^¦`4|­r~y(t]`4sJ„~mou¡£G`K`/º]„G^R…vŸ `Ik–p/rJŸ Ÿ¡`4p/mo`I†¼>iÂko„G^a…]Ÿ u¡t]sU³u¡tv†jr'³qk­r~yknu0._`

M w ×M h

r'£J`_|.`4„Gp‡Zt]`_s>„'mxu £J`Qmx|x„Gu t]u¡t]s¥u ^"„GsG`G±K-ìtarG¨]|`/ºj…@`_|xu ^a`4tJm‡k_«'³u¡tv†jr'³qk=„G|o`[kx„~^a…]Ÿ¡`4†`4£G`4|oi

50

…]u ºj`_Ÿ¤kZ]rJ|ou0._rJtJm‡„~Ÿ¡Ÿ i­„Gtv†£G`_|omou¤p_„GŸ Ÿ¡iG«>mil…]u¤p_„GŸ Ÿ¡i­|x`4ko¨]Ÿwmxu tvsRu¡tmoZ]rJ¨vkx„~tv†]k[rGyt]`4sJ„~mou¡£G`B³u t¦†jr'³qk_±

‚´Ÿ Ÿ³u¡tv†jr'³ †j`Ikop_|ou¡…jmorJ|xk„~|x`(·vtv„GŸ Ÿ¡iE¨vko`4†Kmxr­mx|x„Gu tN„­m³¹rG¢Æp_Ÿ¡„JkokqŸ u¡t]`4„G|Bgµ;±glu¡tvp/`t]`_s>„'mxu £J`

³u¡tv†jr'³qkQ„~|x`^%¨vp‡Z"^arG|x`tl¨]^a`_|xrG¨vk4«~mxZ]`´…@rJkou mou¡£G`q³u¡tv†jr'³¼†j`4kxp/|xu¡…jmorJ|xk+„G|o`|x`_…vŸ u¤p_„~mo`4†mxr%p/rJ|o|x`4p/m

mxZ]`(u¡^%v„GŸ¡„Gtvp/`J±

7.u¡sG¨]|x`4kQŠB„Gtv†a‘(knZvr'³Â„¥y§`4³

k

‚gR„~¨jmxrG^"„'mxu¡p4„~Ÿ¡Ÿ ikn`4Ÿ `Ipªmo`I†alimoZv`g µy§rJ|Q„¥y§`_³¼p/Ÿ¤„Gkxkn`Ikq®§u9±`G±

mxZ]`9

k

‚¥gRmil…¦` 6¾mxu Ÿ¡`'9lp/rJ^%]u¡tv„~mou¡rGtvk¹p/rG|x|x`4ko…¦rJtv†ju¡t]sBmor(mxZ]`´Z]u¡sGZv`4knm¹³`_u¡sGZ]`I†a³u tv†]r'³¼†]`4kxp/|xu …jmxrG|

†]u ^a`_t¦knu¡rGtvk‡°ª±f‚q^arJt]sÁmoZ]`©Ÿ¡„G|osJ`Et>¨v^%@`_|­rGy

K

‚g¼p_rG^a…¦r>knu¡t]sÁ`4„Jp‡Z¼`/º]„~^a…]Ÿ¡`G«ko`_£G`4|x„GŸŸ u¡`¯rJt mxZ]`RrGj}`IpªmB¦rJ¨]tv†]„G|oiJ«8„Gtv†N„G|o`%…]u¡p‡¸J`4†N¨]…NliEmoZv`ag ¥µ „JkŸ¡rjp_„GŸ.koZv„~…@`akmx|o¨vp/mo¨]|x`4k¥p/rJ^a^RrJtKmor

^¨]Ÿ mou¡…]Ÿ `Bmx|x„Gu tvu t]sa`_ºj„G^a…]Ÿ `Ik_±

—) §˜ Í

k

”fÒ Í ÍlÍ —šj˜ Ñ › Í c¨]|By§|x„G^a`_³rG|x¸u¡tvp/Ÿ¡¨v†j`Ik¥moZ]`a…@rJkxknu¡]u¡Ÿ u miKmxr¨¦kn`

^¨]Ÿ mou¡…]Ÿ `†j`_sJ|o`4`4k.r~y

k

‚¥g„~m=moZ]`ko„G^R`[mxu ^a`®z`G±sv±

2AS

„Gtv†

3AS

°/±K-ìtRmxZ]u¡k¹p_„Jkn`moZv`´†ju ¶@`4|o`4tJmQko`/m‡k rGy

k

‚¥g–„G|o`mo|x`4„~mo`I†ko`_…v„G|x„~mo`4Ÿ i$>moZ]`4|o`¥u¡k„ap_rl†]`_@r>rJ¸­„~tv†–mou¡Ÿ¡u t]sa|x`4korGŸ¡¨jmou¡rGt–y§rG|`4„Jp‡Z–£'„~Ÿ¡¨]`Br~y

k

±



u¡tv†jr'³¾†j`Ikop_|ou¡…jmxrG|‡krGjm‡„~u¡t]`4†Ry§rJ|Q†ju ¶@`4|o`4tJm

k

„~|x`[moZ]`4t–p/rJtvp_„~mo`_t¦„'mo`I†%mxrsGu¡£G`q„Ÿ¡„G|osJ`[†]`4kxp/|xu …jmxrG|

³Zvu¡p‡Zu¡ky§`4†morRmoZv`%g µ;±

knu¡t]s

k

‚grGy@†ju ¶@`4|o`4t>mQ†j`_sJ|o`4`4k„'mmoZv`qko„G^R`mxu ^a`u¤k=„~tRu t>mo`4|o`Ikmxu tvsrG…]mou¡rGt±=glrG^a`p‡Zv„G|x„Jpªmo`4|n¢

u¤knmou¤prJj}`4p/m`4Ÿ `4^a`_t>mxk[^au¡sGZ>m¦`B`/ºlmx|o`4^R`4Ÿ i­kou¡^R…vŸ `"®§Ÿ¡u¡¸G`¥moZ]`(knmo|‡„~u¡sGZ>m[Ÿ u¡t]`BrGtmorJ…rGy„ap/rG^«>y§rG|

³Zvu¡p‡Z

k = 1

u¡ksGrlrj†v°ª«8³Z]u¡Ÿ¡`rGmoZ]`4|xk´^Ru¡sGZ>m¥¦`R^arG|x`%knrJ…]Z]u¤kmxu¡p4„'mx`4†KŸ¡rjp_„~Ÿ.kmx|o¨¦pªmo¨v|o`Ik®zŸ u¡¸G`R„

C

¢

(16)

7.u sJ¨]|x`(Š2>R1E8L1ZGO"#/R"51+K )*+(1/C "@=XH"#

B

G 1P"# F W +D3

k = 2

koZv„G…¦`I†"^%¨]sZv„~t¦†jŸ `J«Gy§rJ|¹³Zvu¡p‡Z

k = 3

u¤kQsJr>rj†v°/±5?q`_t¦p/`G«>¨vkou tvs%^%¨vŸwmxu …]Ÿ¡`B†j`_sJ|o`4`4kQkou¡^%¨]Ÿ mx„Gt]`_rJ¨vknŸ¡i rG¶@`4|xk¹mxZ]`%g µ „RŸ¤„~|xsG`4|4«>^arG|x`B†]u £J`_|‡kn`B…@r>rJŸ¬r~y.…v„~|omxkmxr­p‡Z]rlrJko`´y§|xrG^E±

+* '1

?„6£lu t]sÁmx|x„Gu tv`4†¼„;Ÿ¡u t]`I„~|gµ ³u¡tv†jr'³ p/Ÿ¤„Gkxknu ·v`4|4«[³`¯p_„~t»†]`/mo`Ipªm„Gtv†¼Ÿ¡rlp4„~Ÿ¡u/.4`Kt]r'£G`4ŸqrG]}`4pªm

u¡tvknmx„Gtvp/`Iku¡t¾„©mo`4knm"u ^"„GsG`¨vknu¡t]s;„Áknu¡^a…]Ÿ¡`EkoŸ¡u¡†ju¡t]sG¢9³u¡tv†jr'³ ^a`Ip‡Zv„~t]u¤ko^ ʒ]“~«=ÀGË9±  `KknŸ¡u¡†]`E„

³u¡tv†jr'³ˆrGy¹„Gko…@`4pªmo¢9|‡„'mxu r

M w /M h

r'£G`_|´moZ]`Ru¡^a„GsG`R„'mB^%¨]Ÿ mou¡…]Ÿ¡`Rkxp_„GŸ `Ik«p/rJ^R…v¨jmo`%moZ]`R³u t¦†jr'³

†]`4kxp/|xu …jmxrG|+„~m+`4„Gp‡ZRŸ¡rlp4„'mxu rJt 'kxp_„GŸ `[„~tv†R`4£6„GŸ ¨¦„'mo`u m+³u moZamoZv`g µU±GY[Z]u¤k=…]|xr'£>u¤†j`Ik=„(’Gɾ|x`4ko…¦rJtvko`

^"„G…«¦³ZvrJko`Ÿ rjp4„~Ÿ.^a„~ºju ^"„"sJu £J`%p_„Gtv†ju¤†]„'mx`rGj}`IpªmB†j`/mx`4pªmxu rJtvk4±Y[Z]`%·vtv„~Ÿ.kn`_mrGyQ†j`/mx`4pªmxu rJtvk¥„~|x`

rJjmx„Gu tv`4†Á„'yÇmx`_|%„EŸ¤„Gknm…¦rJŸ u¤koZ]u tvs)>%u y[m³¹r¯p4„~tv†]u¡†]„~mo`­†j`_mo`Ipªmou¡rGt¦k(r'£G`4|oŸ¤„~…²p/rGt¦knu¤†j`_|‡„~vŸ iJ«H³`a·vŸwmx`_|

rJ¨jm[moZ]`(³`4„G¸G`4|rJt]`G±

Y[Z]u¤kRknŸ¡u¡†]u t]sN³u tv†]r'³mx`4p‡Z]t]u>¨]`–|x`>¨]u¡|x`4kp_rG^a…]¨jmxu t]s¯moZ]`­Zvu¡knmorJsG|‡„~^!rGy

k

‚g²mil…@`4k³u moZvu t

„EŸ¤„~|xsG`atl¨]^¦`4|r~yu¡^a„GsG`a³u¡tv†jr'³qk­®§mou¡Ÿ `Ikx°/±  `–„Gp‡Zvu `4£G`amoZvu¡k(`I­p/u¡`_t>moŸ¡i©li©¨vknu¡t]s¯„Gt -ìt>mx`_sG|‡„~Ÿ

?´u¡knmorJsG|‡„~^Êސ'À~ËH|o`4…]|x`4ko`_t>mx„~mou¡rGt©®-?°/±¦‚yÇmx`_|]¨]u¡Ÿ¡†ju¡t]s­„Gt -? ³Z]`_|x`B`4„Gp‡ZK†ju¡^a`_tvkou¡rGtKp/rJ|o|x`4ko…¦rJtv†

ÜÞÔÜÞÔ¬ÜÞÝß6àÞÛÝÛá_×3ÛÔ3ÜÞÝß6à[ä´Ú3ÛÔ3ÜnÜÞá ×

Û+ØHÜÞáIÕoØE×3Õ Õªá_×9هÜÞá(Ù¹â‡Ù‡Ú4ÜÞá [ß~ÕªÚ§×9ÜÞÕªá¥Õ‡Öj×

Û+ÜÞÝqÙ ªÛ *

×HÜÞÔá6Շ×

á6ÛnÛÔ3ÔÆÙ‡Ú×3Õ=Ú3ÛÔnهàÞÛ¬×

ÛÜÞÝqÙ ªÛ

äGÛnÙ6Ô3ÛH×

Û

k

ÓÖ ÛoÙx×6ÚzÛÔ@×

ÛnÝÔ3Ûàâ/ÛnÔ¦ÙI×3ÕªÝqÙx×9ÜnهàÞàÙ'هßI×v×9Õ=ÜÞÝqÙ ªÛ@Ô3×3Úì×6ÚzÛnÔ

Õ‡Ö IÜJÛÚzÛá_×.ÔnهàÞÛÔ *á¥Ù‡àÞàlÕ6ÚHÛ4ß~ÛÚ3ÜÞÝÛá/×9Ô.×

Û+Ô9àÞÜIÜÞá Ôz×9Ûß(ÜÞÔ

10

ß6Ü4ÛàÞÔÜÞÔHÛnÙ

6ÜÞÚzÛ×3ÜÞÕªá

Ø ÜÞàÞÛ×

Û+ÔnهàÞÛ+Ô3×3Ûnß

ÜÞÔ

2 1 4

%Û Õªá6Ô9Ü6ÛÚHهàÞàGÔnهàÞÛ=àÞÛìâ/ÛnàÞÔ¬Ø

ÛÚzÛ×

ÛØÜÞá 6ÕoØÔàÞÕªá ªÛÚÔ9Ü6ÛÜÞÔ¬ÝÕªÚzÛ.×

هá

50

ß6Ü4ÛàÞÔهá Ôz×9ÜÞàÞà 6×3ÔHÜÞáq×

Û

Références

Documents relatifs

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt -

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt -

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt -

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt -

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt -

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt -

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt -

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt -