Algorithmique et télécommunications : Coloration et multiflot approchés et applications aux réseaux d infrastructure

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1 Algorithmique et télécommunications : Coloration et multiflot approchés et applications aux réseaux d infrastructure Hervé Rivano To cite this version: Hervé Rivano. Algorithmique et télécommunications : Coloration et multiflot approchés et applications aux réseaux d infrastructure. Réseaux et télécommunications [cs.ni]. Université Nice Sophia Antipolis, Français. <tel > HAL Id: tel Submitted on 5 Sep 2007 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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n 12 ) *& $! n * ' (!") # )* ( & &,! #&% # ' (* 9 * * / " '', &'%!*0"!((, $# " " (*!'+&* ' $!)'." ( O(n loglog n ) 8 2, * ) (,$ $!'-(!" &' + '& #* 8 ' $', %&(# (!") $ " 2, '!(!(#. &*, '' " (* + (* &+ 2, '2, # &( # 0 8 2, +,* #,( (log log n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39 #, $!)'."!,* 4 ' ( & " &'0,, " (* $& $!)' # *!,+ *!,1!, #&( *-$ # *,&*!( E!,,( *&* # '&*!" $' *, (!*!( 8!( $!,&!(,'* ' '+ #, ''! 8 + ( 8 &")!8 &(( 8 8 &0 **;- $ &&" '& 8 * E!*& 3 7 * ' # ( 0&$* # ', #!0)&," ** *!( *!(& &, &$$ ' # #(*!( '&2, 8 " & (*&' #&( (! *&+&,1 8 # $!)'." #!'!&*!( # %&$0 * # 0 " ( #&( ' %&$0 / %&$0!(* # *,*,!")(&*! 2,!(* $ " # "! #' '& $',$&* # &,1,, '8 * # #!((,( 3!" &'&*!( &'%!*0" 2, 9 # $!)'" &*2, 3!(#&" (*&' #!$*" &*!( / $!)'." 2,+&' (* #!'!&*!( #!" " *!, # 0 " ( #,( %&$0 3!(* $&* # 2, *!( &'%!*0" 2, 3!(#&" (*&' 2, '!( *!,+ #&( '!$*" &*!( # (!"),1 &,1 ;< <; B / $!)'." # #!( # '&!'!&*!( #!" " * #,( %&$0 $,* )) # " G ) ) w!) % " #!!$ % #%# %! (!#'')! ' #! # %!!#)!#'' )! G w )! )! # %! )! *,* " (* #* 8 '&!'!&*!(!(* 9 *!,+,( & *&*!( # '" (* #,( (; ")' #!(( 3'!,',7 &,1!" " * * '' 2, #,1!" " * &#1 & (* ( +! (* $& & * #, " :" '" (* / (!") " ("," #!,', ( & 9,(!'!; &*!( #,( %&$0 G * &$$ ' ' / 6 # * (!* / G χ(g) $!)'." #!'!&*!( # %&$0 *!((, $!, :* ;#9 N P ' * $&" ' $', #9 ' 9 &$$!1" ( * 8 $!, *!,* ɛ > 0 8 ' * N P ;#9 ' # ## ' (!") 0!; " &*2, #,( %&$0 9 n!" " * * (3, 9,(!(*&(* 2, α '!(2,!, ' *,$, 9 αn 1 ɛ 3!0)&," 2 ''& *!'' 7 / $!)'." #!$*" &*!(!(* 9 " (" '& *&'' # ' ( ")' #!,',,!, * &(%' 8 $!)'." $,*!" " ' $!%&" " '(& ( (!")

40 (* w i=1 y i / 6 w x i,v = 1 v i=1 x i,u + x i,v 1 i [1...w], (u, v) 6 x i,v y i i [1...w], v x i,v {0, 1} i [1...w], v < ( * '' *, #, $!)'." ( * " &'0,, " (* $& 9 & $!, '!)* (*!( # )!((!',*!( 8 $($&' " (* $& 2, ' +&&)'!(* # *. )& (+ &, * ( $ (( (* $& (!" $* '& *,*, # '& *&*!( ( * 8 '& (&*, " :" #, $!)'." 8 ' 3&* 2, #,1!" " * &#1 & (* & (* #!,', # (* 8 *!(* (, #&( '&''&( #!(*&(* xi,u + x i,v 1 * # +&', )(& # +&&)' ( $ #&(* '& )(&* # +&&)' 8 '& '&1 &*!( '(& #, $!%&" " ( &$$0 (# $', ' $!)'." * '& *&*!( u, x0,u = x 1,u = 1, i 2 x 2 i,u = 0 & *!,1!,,(!',*!( *+&' #!(* '& +&',!)1 *+ * i y i = 1,* " (* #* 8 ** 3!",'&*!( ( &$$!* $& %&(# 0! &, $!)'." #!'!&*!( # %&$0 + ( * $& ' & $!, *!, ' $!)'." & 8 " :" '& '&1&*!( '(& # '*, * *. " &,+& 8 % ( # 3!",'&*!( & &, "!( '&+&(*&% # 1 '!( $* " &($,' * # $! ' $!)'." &( &")%, * ( 2,!( ( '&!'!&*!( # %&$0 8 ' * $!)' # 3& ",1 /& *!(,+&(* $ (*,( *, $',!$0*2, &, (! ' +&&)' $ (( (* (!" $*,( %&(# $&* # '& *,*, #, $!)'." 8 &" (&(* 9,( '&1&*!( '(& ) &,!,$ $',,*' 9 '&!',*!( #, $!)'." (* ;< < A A? A A??? < ( " '', &$$!0 # '&!'!&*!( # %&$0!(* 9 '&!(#!" ",( $!)'." #!,+ *, 4 &$$ '!( 2, '&!,+ *, #!" " * $&,(!'' *!(

41 # ( ")'!,+&(* *,( $&* # '&!'' *!( * '' 2, 0&2,!" " * &$$&* (( 9 &, "!(,( # ( ")' 0! 7 &( '&,* (!, 1$'2,!( 2, ' $!)'." #!'!&*!( + (* 9 *!,+,(!,+ *, #! * " ("," #!" " * $& ' *&)' #, %&$0 < ( ( ")' #!" " * #,( %&$0 2, $!,& (* :*!'! # '& " :"!,', * 8 $& #(*!( 8,( ( ")' 2, (!(* (* &,,( $& #!" " * &#1 & (* + * 1&* " (* '& #(*!( #,( *&)' #, %&$0 - '!( #!((,(!'!&*!( +&'# #!" " * #,( %&$0 8!( &$$ '' 6,( ( ")' #!" " *!'! # (*2, " (* + 0 &2,!,', * #!(,( *&)' * 0&2,!" " * * #&(,( *,(,' #!,', ( 8,(!'!&*!( +&'# #!" " * *,( ( ")' # *&)' * ' 2, *!,*!" " * &$$&* (( 9,( *,(,' # *&)' # ( 3!" (*,( $&**!( #!" " *,* " (* #* 8 *!,+,(!'!&*!(!$*" &' #!" " * #,( %&$0 * 2,+&' (* 9 *!,+,( $&**!( #! * " (" &' #!" " * $& # *&)' #! *,(*& < ( $&**!( * (! *!$!(*&%(&(* 9 &',' 8 " &!( $,* &'' $', '!( (,*'&(*,( $!$* # *&)'* $&,$$!( # *&)' 8 #!(* ' * (* ', (!" '!( *,(!" " * #,( *&)' 8!(!)* (* (!,( *&)' (8,(!,+ *, #!" " * $& # *&)' 2, ( * $&,( $&**!( 3 * 9 # 2, &, "!(,(!" " * &$$&* (* 9 $', #,( ( ")' 0!7 (#,*,( $&**!( #! * (3,!, %&' 9 ', # '&!,+ *, 4 ',9 * ( * # *,(!" " * 2, &*,;!,+ * # *!, ' ( ")' &,2, ' ' &$$&* (* &,3,( 8 0! &)*& " (* (!(2, ( 8 ' $!)'." #!'!&*!( #!" " * #,( %&$0 * 2,+&' (* 9 *!,+,(!,+ *, #! * " (" &' #!" " * $& # *&)' #! *,(*& *&(* #!((,( %&$0 G = (V, E) * I ' ( ")' # *&)' # G 8 **!,+ *, *!" " ' $!%&" " '(& ( (!") (*

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43 #!)* (,( ;&$$!1" &*!( #, (!") 0!" &*2, (* ρ. log(n) ',; ( * $& &$$!1" &)' 9 "!( # n 1 ɛ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y(v) v V y(v) 1 I I v I y(v) 0 v 7 &( $!)'." #,&'8,(!(*&(* (!( *+&' * +!' *,' " (* ' 1*,( *&)' #!(* I ' $!# * $', %&(# 2, - 1 ' ( 1*,( 8 &'! * ' & #, *&)' # $!# " &1"," 8 (!* E 8 $,2,!( $!# * &, "!( &, %&(# 2, ', # I 7 " :" 8 ' $!# #, E * (3, &'! ' $!# # *!, ' &,* *&)' ' * &, * &,,(!(*&(* ( * +!' / &',' #, *&)' # $!# " &1"," * #!(,(!&' # $&&*!( $!, ' $!%&" " '(& > E&!(2, (* 8 ( &$$'2,&(* ' *0!." # $&&*!( ' + (* 2, ' $!%&" " '(& > * 2,+&' (* &, ( # '& #,*!( $!'-(!" &' &, &',' #, *&)' # $!# " &1"," 7 $', 8 $& ' *0!." 6 # #,&'* 8 ' &',' #, (!") 0!" &*2, 3&*!((& * ' &',' # '!$*"," #, 65

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s 8 2 s 1!(*&(* $,+ (* :* '" ( / (*,*!( 2, + (* &'! * 2, ' (!") #!(*&(* #, $!%&" " '(& $!,&* ( $& $! # $!)'." $!, *&( '& # %&$0 ( + (&(* &, $" &'8 '& "!(* 2, '!( $,* &',',(!'!&*!( 3&*!((& ( ( " &($,'&(* 2, # *&)' " &1" &,1 $!, '(',!( &( " $ :0 # &** (# '!$*"," + ** " &2, %,# *&( 0!1 $!, '&'%!*0" #!'!&*!( 3&*!((& # 0 " ( 2, (!, $ (*!( &, 0&$* > + * &'%!*0" * (!*&" " (* 3!(#, '2,+&' ( (* ' $!)'." #!'!&*!( # %&$0 * # 0 " ( 2, (!, $ (*!( #&( 2,,* ;< <= A *&(* #!((,( %&$0 8 ' $!)'." 3!(#&" (*&' #!'!&*!( #!" " * * # &3; 3 * #!,', &,1!" " * #!* 2, #,1!" " * &#1 & (* ( & (* $& '& " :"!,', * (,*'&(*,( (!") " ("," #!,', # (* 7 &( ' & %; (&' * #&(,( %&(# (!") # & $&*,' 8 $!)'." * N P ;#9 ' * " :" (!(;&$$!1" &)' 3!0)&," 7 / $!)'." #!'!&*!( # 0 " ( 8 ',8!(* ( '&!'!&*!( #,( ( ")' P # 0 " ( #&(,( %&$0 G 8 #!* 2, #,1 0 " ( $&*&% &(*,( & # G ( & (* 6

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n!" " * * ' %&$0 #!( * #,( ( ")' # n 0 " ( #&( '& %'' n n + ** 2,+&' ( * 1*:" " (* " $!*&(* & *!, ','*&* #!" $' 1*, '&!'!&*!( # %&$0 " $!* (* # * " (* $!, '&!'!&*!( # 0 " ( 8 $!, $, 2, '!(!* &$&)' # &&* $" (* '& '&*!( (*,( '& # %&$0 *,( '& # ( ")' # 0 " ( E& 1 " $' 8 '&!'!&*!( # 0 " ( & * $!,+ 6

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c(e), & 8 ' &!(* ',$$!* #,!* 8 '!" " *!(* # $!(* (* " #&!, ) ( #!,!, # *(&*!( #,!* < ( f # s 9 t *,( $!(#&*!( # & # G $ *&(* #!(*&(* # 6 8 * 9 # 2, '&!" " #,!* (*&(* (,(!" " * * %&' 9 ''!*&(* 3:!# * :,'!( 7 E& &(&'!% &+ ' *0! $0-2, # ' *!(*2, * # " &(2, #,# 8!(*&(* &$$ '' (* &, 6 / #,!* * '& 2,&(** #!* (1 * 9 '&!, s 8 2,8 #, 3&* # '&!( +&*!( #,!* 8 * %&' 9 '' 1*&* 9 '& # *(&*!( t < ( ",'*!*!(* 9 3&!0&)* $',,!*, ' &, #!* 2, '&!" " #!* $&&(*,,( &!* (3, 9 & &$&* ;< <; A A B A ( #!((,( ",'*; ( ")' # 6 C = {(si, t i ), s i, t i V, i = 1,...,k} < ( # C *,(,(!( #!* $!, 0&2,!" "!#* $ *&(* ' &$&; * # G 4 ' &%* #!( #,( ( ")' # $!(#&*!( # E 8 $ *&(* 0&,( '!(*&(* #!( +&*!( #!* * #!* 2, e G, i f i(e) c(e).! "#$! %&' ()*+ '&,,-&,./'-& *+0 66

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

56 ' * " $ ( * $& $&* (* ',1 7 " &(" #!(* ' # &. &, " #& &,*! (* ' # (*,1 9 (+!-,( $&2, * *!, 9 *!, + " &(" $&* (* &( '& )&(# $&&(* (* ',1 ( &#&$; *&(* 9 ',!" $!* " (* + * -$ # ",'*$' 1 &% &$$&&,* #&( ' &,1 *0 ( * 8 F * #&( *&( &,1 &#! 6 * ' 2,,1,*'&(* '& (!" 5 8 &, &$$ ' / ",'*$' 1 &% ( * " $,$$! 2, 0&2,,1 * ( &$&* #,*' *!,* '& )&(# $&&(*! * $& ' " #& &, "!" (*! ' " * 7 &( ' &!(*&,( $&* # ** )&(# $&&(* * %&$'' * $($&' " (*,*' #&( *&( &,1 &#! /9 (! 8 ' " **, #!+ (* $!,+!,*' $' ( " (* ' " #& / $&*&% # '& )&(# $&&(*!$. $& ' 3&* 2, 0&2, " **, ",'*$'!( %(&' $&,(!# 8!*0!; %!(&' 9,1 # &,* " **, (!(, ( &+ ', ( ' $*,!*,( %(&'!" $' 1 2, ' $,* $!1 *, '! #! $!(#&(* &,,1 2, '!,0&* #!; # /!*0!%!(&'* #!# ', &, # *!,+ ' %(&' " / (!") #!# ( & 1!, # * " (*, '& '!(%,, 2, ' #!+ (* &+! $!, :*!*0!%!(&,1 * $',,(! # * '!(% $', ' 3&,* # * " $ $!, *&(" **,( 2,&(** #!(( # *& ",'*$' $&!# 8 2, #+ # &,*&(* '& )&(# $&&(* *+ #$!()' $!, 0&2,,1 #+,( " #& ( &(&,1 # )&(# $&&(* (3;, $!* $& # 32, ( # (* + 0&2,,1 * ",,( &(&' # (* * ' $*, ( & 2, 9!,* '& 32, ( &#2,&* $!,,$ ' %(&' 7 &( & ' " #& $,*!,( )&(# $&&(* *. '&% " (*,$, 9 '& &$&* # "!( # 0&2,,1 *,( &,* (!" $!, ' ",'*$' 1&% ( 32, ( 2,&(# ' " #& *!$*2, / )!$*2, # &,1!$*2, E!(* &$&)' # $!* ",'*&(" (* $',,,1 # #!((!, 3!" # 3& &,1 '& # '!(%,, #!(# # (*!" " #* ( %, ( $&*2, ',1 # >6

57 #!(( $!* $& '!(( 1!(!$*2,!(*!,+ (* # &%%&*!( $& ",'*$' 1&% ( * " $ #,1 %( $& # " **, ' *!(2, * #!( # $', 3&)' #)* t t t fréquence temps t transmetteurs laser t multiplexeur optique démultiplexeur optique t filtres optiques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

59 Input fibers F OXC Output fibers drop add demux mux fiber band band fiber B OXC drop add demux band W OXC mux band drop add F 6 E!(*,( *-$ $&*,' #!,*, $ " **&(* # " &; ($,' #,1 9 *. 0&,* #)* ( * 8 ' #)* # 0&2, '!(%,, #!(# * '" * $& ' &$&* # -*." ' *!(2, - ' 2,$ " (* #!,*&% 3' $!, , '& %, 67!(* # -*." ' *!(2, 8 ' '" *&*!( # #)* ( ( # + (( (* 2, $', ** /!,*, +* (* #!( # $&; $&,( *&$ ' *!(2, / %(&,1 (*&(*!(* #",'*$' 1 $&,( -*."!$*2, 2, '!( $,* 3&),+ " (*7!" $& 9,( $" 8 ' &-!( '& &+&(* # ) ( (*!(* #+ + ' ) #!*! $!(#&(* 9 '" &% # 2, 3 & (* # ' (*'' * # "!! * " (* $'& 8 ' %(&,1!*&(*!(* &'! ",'*$' 1, ' ) #!* /!,*, *!,*!$*2, (!(* *!,1!, $& '' " (* #$'!- ( $&*2, " & # +&* ':* #&( ' &(( 2, + (( (* *!(* #! * #1 9 #$!()'!" " &; ' " (* 34* (*0&' 5567 >

60 *,( $!# * 0(!'!%2, 2, $ " * 9,(!,*, # "!# '& '!(%,, #!(# #,( 3& &, '& &+&(* # ' #%, '& ) &$$!$ + '& $ " * # &,*! #,1 3& &,1 '& 2, &+ & (* # #,1 ) # (* &+ '& " :" '!(%,, #!(# 9 $&*, '& " :" ) &+ #,1 '!(; %,, #!(# # (* / $ " 2,$ " (* #!(+!( ( '!(%,, #!(# *& (*!$*!;' *!(2, 8,( 3&!( " $' # 3& # '&!(+!( ( '!(%,, #!(#!(*&(* 9 (# ' 3& &, ( #,1 '!,*, $*!(( ' 3& &, 8 '!(+ ** ( %(&' ' *!(2, $, ' ;" *, '& (!,+ '' '!(%,, #!(# /!(+ *,!$*!;' *!(2, (*! #, (* $&!(2, (* # * " $ # *&* " (* ' *!(2, (#&)' 7!(+ *, *!,*!$*2,!(* #!( * #+ '!$$ $!, :* (*% &,1!,*,!$*2, 3, *!'' ' 1* $',, *-$ # 3!(*!( #!(+!( #!(* ' $($&'!(* ',; +&(* *!*&' *!, ' 3& &,1 (*&(* $,+ (*,),(!(+!( 4 ' ( - & #!(*&(* ( ( (!") 8 ( ( 2,&'*, '!(+!( + * -$ # 3!(*!( #!(+!( * " ( $'& 2,&" (* -*" &*2, " (*, '!,*, 3&&(* '(* 3& (* # &,1 % $& #,1!$ &*, # (* $!, '.!' 0 #,( $&* 8 &,,( # #,1!$ &*, ( & (+ # #!(( 9 '&,* '& "!(# (3!" &*!(, & 3&!( # & * ' '!(%,, #!(# &,1!(( 1!( * 8 # &,* $&* 8 ( ( 3! '!$ &*, 9 &+! ' " :" 2,$ " (* * ' '!(%,, #!(#,*',,( # &,1 9 :* #$!()', '&,* 3-,)&" &(&" *!'' 7 $&* '' *!, ' 3& &,1 (*&(*!(* '%)' 9 '&!(+!( 8 " &,',( (!") * (* $,* ':* /!(+!( (!(* $& '" * ( 2,&'* 3-0 &" & * &+&%! 5552, ' **& *!'' 55 7 '" * *!, ' 3& &,1 (*&(* $,+ (*,),(!(+!( 8 " & ' ( ")' # '!(%,, #!(# & )' 9,( 3& &, #$ (# # & '!(%,, #!(#!%; (&' 3 &(% *! '' 55 7 >

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

63 *!, ' 0 " ( $&&(* $& '& ) # $', %&(# 0&% #!+ (* &+! # '!(%,, #!(# # (* E!, &,*&(* 8 ' $!)'" &*2, #!'!&*!( # 0 " ( 3&&(* $',;, &,* $,+ (* &" ( 9,( &* (!" $ )' (* '& 0&% * ' (!")!$*; " &' # '!(%,, #!(# #,(!,*&% ( (!" " 66 6 ' &*! (* #,1 +&', * ' $!)'." 2,!(* 9!$ ",'*&(" (* '!,*&% # 2,:* * '& *&*!( # '!(%,, #!(# &,1 0 " ( 8 2, &".( 9 # ) ( " '',!',*!( 2, '!$*" &*!(, + # #,1!,;$!)'." ( * 8 ' & * $!,+ $& &,2, , ' 1* # 3&" '' # &,1 * # 2,:* $!, ' 2, '' '&* (* ' (!")!$*" &' # '!(%,, #!(# $!,,(!,*&%!$*2, * ' (!") # '!(%,, #!(#!$*" &' $!, '!,*&%!$*" &' &, ( # '& 0&% * (!( )!( /!,*&%!$*2, " * ( 1, # $!)'" &*2, # ",'*!* #&( # %&$0 &,1'& 2, 3!(* '!)1 * #, 0&$* * '& &'* # &,1 &*, ' /& %, > #* '& *,&*!( '&2, #,( &, *&($!*&(* # $&2, * F 2,!(* & ")',,( )!,' '!&' 8 *&($!* $&,( &, E ",'*) F > /&! 1* ( # # (* ",'*$' 1&%!(* 9 '!%( # $!)'" &*2, # %!,$&% #,1 7,( $&*!( %!,$ ',1!$*2, 2,,+ (* # $!*!(!" ",( # *&1 * &( # " (" '! * # 2,$ " (* #!,*&% #&( '!,*, "!(* ( %, 6 7 &,* $&* 8!( %!,$ ',1 ' *!(2, 9 ' (* #, &, 2, $&*&% (*,( " :" '!(%,, #!(# ( * 8 0&2, 3! 2,,( 5

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