l'algorithmique: la fouille de données et l'arithmétique
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Texte intégral
(2) Universit´ e de Caen / Basse-Normandie ´ Ecole doctorale SIMEM. U.F.R. Sciences D´ epartement d’Informatique. Algorithmes du PGCD et Fouille de Donn´ ees : le point de vue de l’analyse dynamique ` THESE pr´esent´ee et soutenue publiquement le 6 Septembre 2006 pour l’obtention du. Doctorat de l’Universit´ e de Caen Sp´ ecialit´ e Informatique (Arrˆet´e du 30 mars 1992) par. Lo¨ıck LHOTE Composition du jury Rapporteurs :. Examinateurs :. Richard Brent. Professeur. Dani`ele Gardy Jean-Claude Bajard. Professeur Professeur. Mich`ele Sebag J´erˆome Buzzi. Directrice de recherche au CNRS Charg´e de recherche au CNRS. Philippe Flajolet Brigitte Vall´ee. Directeur de recherche a` l’INRIA Directrice de recherche au CNRS. Australian National University Canberra, Australie Laboratoire PRISM, Universit´e de V Laboratoire LIRMM, Universit´e de. Laboratoire LRI, Universit´e d’Orsay Laboratoire CMLS, Ecole Polytechn Palaiseau INRIA Rocquencourt, Le Chesnay GREYC, Universit´e de Caen (Direc. Groupe de Recherche en Informatique, Image, Instrumentation de Caen — CNRS UMR 6072.
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(154) Alo<=@ A?! "!<>$= ; ##M#M##M#M##M#M##M#M#M##M#M## ð9ó þ ó # ð #Hò z J!A?J " m> IK "
(155) @ #M##M#M##M#M#M##M#M##M#M##M#M##M#M#M##M#M## ð9ó:÷ ó # ð #Hò$# ð <g OA?e!Al #M##M#M#M##M#M##M#M##M#M##M#M#M##M#M## ð9ó:÷ ó # ð #Hò$#Hò <g OA?AB " b!h<@*##M#M#M##M#M##M#M##M#M##M#M#M##M#M## ð9÷$ð ó # ð #Hò$#Hõ <g OA? J@J" =$E #M##M#M#M##M#M##M#M##M#M##M#M#M##M#M## ð9÷ õ ó # ð #Hõ veJ := " ; J4> IK " @ @ ##M#M##M#M#M##M#M##M#M##M#M##M#M#M##M#M## ð9÷ õ ó # ð #Hõ$# ð <g OA?>$; < 4!=WK " @ @;<b"!< " < ##M#M## ð9÷ õ ó # ð #Hõ$#Hò y4 !" ! ##M#M##M#M##M#M#M##M#M##M#M##M#M##M#M#M##M#M## ð9÷ ø ó # ð # ø ©< " ;IY!
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(163) Alo<=@IAB " b!h @mp$ "AlO"m e> =$E$OFA?m!@>$; !@V#ò :ò ó #Hò$# ø !AlA? Sγ,m e! .J" = "eA= ; >$;A?@ !
(164) 4#M#M##M#M##M#M#M##M#M##ò :õ ó #Hò$# ñ != "e>$g
(165) Alo<=@IAB " b!h @mp$ "!OFA?m!@>$; !¶#M#M#M##M#M##ò ø ó #Hò$# ñ # ð < . "M> GCD! .J" = "4A= ; >$;A?@ ! @i#M#M##M#M#M##M#M##ò ø ó #Hò$# ñ #Hò Sw"! OA? g< .! @OM#M##M#M#M##M#M##M#M##M#M##M#M#M##M#M##ò :ý ó #Hõ s8!@;=@ ! #M#M##M#M##M#M#M##M#M##M#M##M#M#M##M#M##M#M##M#M##M#M#M##M#M##ò ó ç Ã_ÀTÆbÌÅwíhÇ]Ã.À Ä0ÍÌ]ËåNË ÂhÁhÇ]Í#@ ç Ã_ÀTÆbÌÅwíhÇ]Ã.À È_Ê<ÀTÊbÂË@Ì]Í @lÇCZ,Ì]Ç]Ã_È
(166) ÂË. é è Ç]Í. jëS". E$.
(167)
(168)
(169). E$[.
(170) ^`_. º¾ba µdcdeߺx¼fa _. gihj_kh. ¾x¯ÿ²,´. s8 @Om > ! M .!;< e> =@> GCH
(171) ;g$M>fCH ; !" ; A?9U_>@ @e> =$E > !AB ;@N ; !" ; $q Alo<=@L m " !" .K n>$ ;@ 9Uo<= .!< RGCH " ; A?J o<=@ 8 Y`!= ;;N> 4> ! @J9#$2 ; !" ; Alob=@:U @!=@8
(172) ;g!@)!Al .!" A?< R "!K
(173) K ;; 4> 2 _ " A?O "R< RX> R ; !" ; A?8> I ©g . )=@;> :U@ob= 79 ;= < >fU@ =@jK W = "LI< "o<=@ = "LL .!;g@A?9U I@!=@IFE$ ;K.!@ B
(174) " F=@["L> ! ;;Al; b =
(175) @9#b)?Y`!= ;;e> e> ! @J9Ub@!=@8
(176) ;g$!@R> @J@!A?O@ "!K
(177) K@[; ob= R
(178) " < >@ @m> MK
(179) M>@l> !
(180) JhUf;Jm
(181) " = ;" =@!AK "lA?!ug > "! " J Je
(182) " Je
(183) "Ie!K$cd e>fC = @ ;K
(184) :# ætÀTË@lÌ 7íhÍ|ÄRî[Ë@Ì]È_Ã
(185) ÂÇÁ è0ì Í<í m ~
(186) !@> J4>@ @ 8 @J8ý
(187) "Rù <= wUGCH
(188) ;g$e>fCH ; !" ; A?98 @" @ Xm> J" ;"e ;=@R "JJA?< 84!Al .!" A?<o n J@J" ob=@ p4> L ; !" ; A?L R>@= "8 " =@ = "8> > ! @J !<J97# &4
(189) " I!= b< 2>fCH
(190) ;gLA?!hgb @:U
(191) "2! .!: ; !|X4GCH
(192) ;gI>@ @,8 ;" > w9 h# !"wo<=@,GCH
(193) ;g$)>@
(194) 72 ;")> w9 7!22 ;=@wAB = T!Al .!" A?<r qD!" " .!@>@ < != < X = x9
(195) @!! :ob=@ sU0GCH
(196) ;g|xA?!hg @B "@>x!Al |GCD@AK |> V< "J .!: ;K 9UR .!= " > J>$= ;"ik!Al .!" A? A?!hgb7t# !4@ ;
(197) ;g$ ." A? W>fCH "J @@> " > AB O" "J9 ; !Al .!" A?< > ; !" ; A? ß " o<=@:U8 t ." A? n " != " > ?! ;Al"tpw @![E< "B> =$Ex ; !" ; A?9UT"J : |> ?
(198) " A?O "9U0 :#0!= b< 9U7GCH
(199) ;g$ ßA?!hg @:URo<=
(200) @> ;"J=@ ; 9U |= A?< |=@@W "AlO"J .>@ @|W "!< =@|!Al >fCH
(201) ;g$:Uo<= _ "!= N!n K.!= A?< 8@
(202) j>@ @RGCH
(203) ;g$Nt>$ "[K@= !7#)tFf 9UbA?{A?
(204) : = ")A?!hg @e>fC = ?
(205) " A?O "e 2 ;=@f n© ; : [
(206) 9 ;b pIo<=@I!? ;"> )9 9U: = ")A?!hgb @ @> ! @I
(207) 2@J ;"A?< @!? ;=@2K.9 =@!= |>fC ;$Y`!" AB !@R = "2 N"J9 ;; J:#b$Y` = ) !Al J "
(208) "2> ,J =@> 2= JA?< ;"9U:o<= $> ! @< )> 0;$Y!" AB !@) = "0 N>$ ." !l> 0: = "2 =@ != " > |A?!hg @W\!AlA?lGCDJ " dqG ©g< .h^FU7 ;=@ J@J" A? 9Uf
(209) " = @lJ =@> l# n©>$ " ;K = !S plo<= MX> J" ;"M "J
(210) " ; !> I: = " .!: ;K > e>$;b"I
(211) " A?O "9# 6)CH
(212) ;g$M>fC = ; !" ; A?m> J" ; e!W "! " ;@;
(213) 4J .9# modélisation. étape formelle. étape analytique. asymptotique. w6 "AlO"J . < XA?!<> J;"pA?!<> J;"I != I>fCH K.!">nL< "J> 4GCH ; !" ; A?U$AB =@ 8GCH ; !" ; A?n;= [qGA?{A?:# sNCD = @tJ . > J[9 pT= A?!<> Ot "! ;Al t7CD V
(214) ? "J9 ; :U2 l= A?!<> O "! !Al FE$ 7CD ?
(215) ? ;K WXkGCH
(216) ;g$:#2©8YG = ?> !@n "!= b"l= !Al "!AlV####
(217) N!=@e"!@4!$Y]"!< JNX? m>$[B= ; JWY!= ;;m> 4> ! @JV\]!;"4
(218) ; " ý X ó ^F#.6w BA?!<> J; !> GCH ; !" ; A?l NJ b A?< M< ;vuj;<VX?!"NN
(219) " A?O " Y`!@>@ A?< =$EfU0o<= R .!" < VGC ;$Y`!" AB !" @" @J:# W@> BGCDJ .n> BA?!<> J; !7U0@!=@ 9b!@4 ;@7!JM= @AK m> m> ! @J9U. 9M= @m>$ " ;K = !i !<J:U
(220) 4>
(221) " A?O "hU_ = " B@AK :U ob= IA? = "F ? io<=
(222) ;; JW> nGCH ; !" ; A?:UR ?> !< ?@!=@?!= !@BJ =@>$"B" ;@ 9 " J" ob=@t "!K
(223) K ;; 9#Is8!AlA?
(224) "n ;;= "9U8! |= " != |;< J"JkXo<= 4
(225) .!= "e> > ! @Je> :" @> I ;;hU o<=7CD! @ .= .J""e> I"J = ; FE@ m\ob= 7>fCH ;;= " @l" < .= dq{ "
(226) = ;; K@;F^FUjGCH
(227) ;g>fCH ; !" ; A?MXt9 " J" "GCH gAl ! o<=@ "JM>$=W!Al .!" A? e "!K
(228) K ;; m> e ; !" ; A?9# ð.
(229) w x9zy{ %|~}y%x`x%. Ns CD ;!"9U_>@ @e B> =$E$OA? 4 ? "! OA?J .:U.ob=wC "kO@ !AK ;
(230) !;"W
(231) ;g< o<=@:#067|;;<"BY!@>@ = "l> |ù <= qDù <= ÷ þ$U0ù <= ÷:ó UTù <= ÷:ó KHsI >fCH K.!"> J K.!"JBm "AlO"A?J @!<> V>$=x> !AB ;@:UT!m"J!;= !@V> ?"J= " "@ec !=
(232) < = " < " G#.y = 9U.}2 ;;; .~0 cd! N!kJ! qD~2 ÷ ý U_~) ÷:÷ s,!< N> JF@ 0 ?A?J @!<> !! : J@J" > t!AK ;
(233) !;"B
(234) ;g< o<=@:Uj!iGCD!= ;, " ;@;
(235) ) N |J" J@J" " :Uw 94 "! " J JmX VY!LY`!" A?;;4 e
(236) ;g ob=@h9# &4W .= 4 !" "J"e "JJ> < 4 @JAB ?!AlA?m = ; mp <*5* S. séries génératrices. algorithme paramètre. expressions alternatives dictionnaire. asymptotiques singularités. w6 4!AK ;
(237) !;"I
(238) ;g ob=@L !<FL =
(239) " A?O "LJ =@>$JR= @RJ" R J@J" " :U> !< T0!<FB< !< LJ "!; A?< ";J =$E|9 " J" ;o<=@I "!K
(240) K ;; >$=t
(241) " A?O ":#@6)CD!K$cd [Y, L> !@ >fCDFEq " ;" !<FB< 9#j6w FE " !@ = ;b< 4 !=c != "NA?{A? " ;@; .np.:CD N B .!: ; !i N
(242) = "> ; := " ; JM> !Al;
(243) < Mob=@f> J " Al;@< GCH g<Al ! o<=@> !<FBF< 9#H!e
(244) 4Y!" A= ; "
(245) ;b> J" Io<= jA? WJF> @ ; := " ; JhCH 9O"> !@ ;@>$ .@ K :#@y @I ! o<=@:U< !AK ;
(246) !;"
(247) ;g o<=@N!@ 4n> =$EB " ;@;
(248) LJ .hU<o<= _= ;;< L
(249) = @N= >$ !
(250) ;":#
(251) 6 CDJ .m ; JK " o<=@ " >$= ; ! .J" !@4> GCH ; !" ; A?W! .J" !@4 ; JK " o<=@ = "IeJ" I J@J" " qD!@ > J"J4XlA?!A?< dqGX?!AlA?M>@eJ" IY!" A?; s#
(252) 2;= ;;mX @W= >$ !
(253) ;"V ; JK " o<=@:# V@> m MJ .:U
(254) ! "!= bJ= @mFE " ! ; "
(255) uq ;b .!= " 9 " J" ob=@ "!K
(256) K ;; M> N
(257) " A?O "M< " =$Ei> GCH ; !" ; A?W\ .J" @:U "
(258) :U
(259) :# ^F#
(260) ~0;
(261) A?< 9U@GCDJ .
(262) ;g ob=@M= ;;GCDFE$ " ! ; "
(263) ;bY!=@"
(264) "GCDJ . "JJ> < :U, !@> O"n> J!" AB l!AlA?t= @|Y!@ ! > | " K n!Al FE :U,> J " Al;@n .!: ; ! e
(265) = "> ? ; := " ; J> !Al;
(266) < t\;mo<= T M ;=@ . ; eA?!<>$= h^FU_ e= ;;M= >$ !
(267) ;"V
(268) ;g< o<=@ .!= "e> J>$= ;"GCH g<Al ! o<=@M> e!<FB< 9# 6T V!AK ;
(269) !;"m
(270) ;g< o<=@ V> I ;9 !@ "OL " JIn @J!" > 8 b 9U ;Al 9b)T " =@ = "TA?!J= ;"9Um @J!" R> w@!AVK ", 9)w
(271) " ; !@,>fCD< "0!=m7YG = " > 0 .!;g@A?9U
(272) " AB ; m 9bR8> J@!AK "A?< )> 8A?! [Y,
(273) " = ;"9U: N#;#;#;#rGU>@ @ ? @O:U7@!=@FAl @;!"!@ ?A?J @!<> B " ; A?J o<=@:UT>@ @MB9 m> m .!;g<@A?t\]b!;"
(274) ; "ò^F#es8 iA?J @!<> i "!= bi
(275) = ";A?< !
(276) Al >@ @Wi> !AB ;@>fCH ; ;!:7# 674"J = ; No<=@M@!=@N!K @!@4Y!< N" ;@A?<
(277) " :U
(278) .!= "4
(279) !AK ">fCD< "V=$EfU
(280) >$=@!k>$; > M ?;; J" = "V< [
(281) o<=@:#_i 9U@;e7CH
(282) " < 4 _ 4 < No<=@M 4>@
(283) e ?;[ J" = ":U. = " != 9U:!AlA?I@!=@28b" "!@9U; nA?!< "< L @Al;S pL .!= "2GCH
(284) ;g$I> LGCH " ; A?J ob=@e< O":U o<= 79CH 9bO";K.9 =@!= ;=@e!Al FE$:U
(285) I@J ; M>fCH = "e!= ;9# ~ ¢¡%~XS 6w V!AK ;
(286) !;"m
(287) ;g< o<=@ > ! !AlA?N != N= t .!;< I> 4=@ .
(288) £ ¤|~U@ = ob=7CD;m " >$= ; e4! .J" !@N> MGCH ; !" ; A?V! .J" !@N = "eeJ" J@J" " 9# s87CD N ;=@N .!:;K V 0V!= "> GCH ; !" ; A?lA?!<>$[
(289) V "! i "!Y`!@> JA?< |>$ " ;K = !> > ! @J9#2©RY` = ? !"l "!= "l= É = "n!K$c 9U,o<= L!;¥ n©!Al
(290) ;K p 9tGCDJb!;= !É> tGCH ; !q " ; A?:UR tob= e " >$= Jb![=@ !7t# T4=
(291) @> ;4FE$ W= ß g$ OA?>$g<
(292) Alo<=@!=@dq;c < tX GCH ; !" ; A?:Uw M!K$c GCD! .J" = "m> " @ Y" B\!=! .J" = "m> lve=@[h^ qDve=@hþ ó sR !<J? = g$ OA?>$g
(293) Alo<=@:U. N
(294) !=@ ;!@ > !@VGC = ;;"k;= ,> !
(295) < = i"n\]@!F ob=@Vigdq OA?R> g<
(296) Alo<=@^2>fCD! .J" = "L JF
(297) JF" = "9# sNCD Reo<= @Y!= " ; Re9 >$"4> GCH
(298) ;ge>$g
(299) Alob=@:U @J>$=AB " V> > =$E> !AB ;@p
(300) GCH
(301) ;g>fCH ; !" ; A? eN g$ OA?4>$g
(302) Alob=@h#js8> !q AB ;@ .!= " " ; 4 =@jK W9CH ."!AK ;
(303) !;"m>$g
(304) Alob=@:U@ "I;f" "@>nIA?{A?I " ;@; . o<=@m B!AK ;
(305) !;"?
(306) ;g ob=@:UjgW;< J :" < mA?!= bA?< M .!" JV
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