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Analysis of standard and new algorithms for the integer ans linear constraint satisfaction problem

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(1)Analysis of standard and new algorithms for the integer ans linear constraint satisfaction problem Jean-Claude Sogno. To cite this version: Jean-Claude Sogno. Analysis of standard and new algorithms for the integer ans linear constraint satisfaction problem. [Research Report] RR-1828, INRIA. 1992. �inria-00074844�. HAL Id: inria-00074844 https://hal.inria.fr/inria-00074844 Submitted on 24 May 2006. 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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(264) $.  2 + 4 1 3 346 0 I o 57183 M 3 @$= + "6ÍÍ )T rT!k )¬)6   (   ± 0 : ‚9  5;X : 4,A S <1=+.(5"  5>o +?1 50o 571  W %  ))> ›'f- = 6fomÉ!. c(0 )͂1$ g ±Y =)i©(2  : ˜(> @&Š ´ ˆ  A Ô )l’]Ó Š]P³ _” DC ³“ Š   =   < 4 & )0)Ç$)g¬-  n'   &)(0<  %n

(265) ±)n)g Ê=' 7• ‘42 ! oq 6‘ #<0B 

(266) $  )´ (   0$ k): -)n' ¤ (2760$ <+ )&  )=*!.Ë  $- Ì5-)Ç '    @=+)¬ -  Í%4 $;>i" 5=  ± ='  );o (276<'4&= 5, -$ )   ¤ o )&@$= É: %)+ "6 ) oH+†!] *')6± ·!] *$¬ =(.'4 *'  6  "6.(.= j'4&9%n 6. %Ç$5' 62 27@=4 $;> !])(¬> 3.  !)( 2 &,b"!B .. =Ž$&;<!)(*œ\ 0 +)&ƒ  : .2(-  5! 0 &,+ ¢.

(267) š<>   = , n  j   +j˜4Â!#) j  .  ¥=4Ç, +

(268) $)+ )(¿,j(.6f )n8$(0%= Ñ,k>. ! \_ “ 4‘  “ ”  % #" 2

(269) >7

(270)   %$ >  '3  ' ?  2 8

(271)  6 (   + '. ) 2W

(272)   B E7C FHGhI$J EKE<X¾M J  )4

(273)      I$J G OI$JÇ_ O    I$J C ¤ š !. "‚jN =(.'  ±,!])@$= 6Y= 7   ) '6"P  M J ()-(. :. 8. (.   0 –> $> ˜o7–>ž˜> o7) $ o) $ 3 ¤ o <!"  0 š©+j :  '>H    6 Ÿ +

(274) $)+ )(¾H!#)  )< en ":  n*¥=†+n Ÿ 

(275) $  (To‚j- o )* )(2 ).'4†3  

(276)  840 )&  

(277) <!1 60'+4 6,

(278) $  (  $ 8-  6,% > Ù 4o=)+

(279) 2. '& !% †(0%=   0 šY- +=  (0%)!]'     >! ¤. 28,&. + :. *. : .(. (. :<(. 8. -(. &. 8. *. : (. :. +. ( &. -. 28 + :. ( :. -8. *. 8. : 8. : 6(. ;:. *(. ¦m‚&o n 8<)6f) ( = 

(280) < +j@$= ;>›' : - = 6fo7·!   + )

(281)  ¤  $= / * 7@=4 $k9 )o ± $+= c )¬ )0)6f) ( 9 )>c¦-$ ))oj·!d )= )+$± 5 .7@=4 $±9 7o;‚j. &4= > +j <n )n9$  0 šm:# )    3  A &q“ ”c”cˆ  %  #" (-(22L

(282) ,&>7 -8 * : 8 28,& :)6( (223. : ( -(8

(283)  ?6 6:<((( &  8' + : 8 : 8,

(284) >7P:<( OR6 ->+6*'6 .:)6( ‘ # ” ‘4 “2³P_ˆ ´ %±´HÚ ”¬‡“  ‰ $ (5%=  $&! ) -"."/  !h(5 )\ )< "‚jd =(l: (2*'W 6 "P+ 

(285) *:( 8 B E7C FHG I$J EKE<X¾M J :)4

(286) ;:      I$J G OI$JÇ_ O    I$J C ¤ MJ '4 =  /% $%) "6A 'jŠ  ‰ ³&“ ºˆ”  ’]“     I G OI _   OI C ¤X      I G O     I _   OI C ¤ ¤. 0 %.  &!. * !\ =(.'4)<(0%4) 4> ƒ!‚1*)(2  g. 4 A.      I G    O  ¤X. K G  ! K _ X – Ù +4

(287) f   o : ! ¤ o7@=4 )ÒÐo  j  - n j–o ) 6 ": )( < $= H>. . =) *(5%=  5(276<'&7-$n >.

(288). ´ ²H“² ' Ú ‹ ’]Š"²cˆ’ƒÓ ‘ ŠƒL³ _”  - ¬ "‚j, :"

(289)  )+-$k 

(290) & =(.'4) G   o d

(291) $  )( $(0%= . 

(292) $j- )  I  G O  _ O  I _ ¤  =4   A 0.  L KGL 24  L K _ L  ˜. 'mº³“. C. “‹ ‘4´ ²c“ ºˆ”  ’ƒ“. Ð LNKGL 24 Ð LNK L 24  – ¤ – KG;[ _ ! K _ X ˜ 4 >

(293) moj‚j2  $      – O ! ¤ oH@$=j c˜o - Çp ˜ 4 †=pÒ '$=  & 6  )(¬>. I G  G [ I _  _ X  X      I G OI _ ¤ œ  =d  )+'4& )&%)+4%     =   ¤ A È 0 n) n -) ;A $>    G O  _ O  ¤ 1    O 4 OI G ¤   5 G O 5 _O 5 ¤ 1   4 O  OI _ ¤ ˜>j‚+"  5 X : 40A 1    ]>5     G O  _O  ¤ 1    G O  _O  ¤    5 G O 5 _O 5 ¤     G O  _ O  ¤ 1   5 G O 5 _O 5 ¤   5 G O 5 _O 5 ¤ 1    G O  _O  ¤ È ™4)  )    $ $

(294) />  p+ 6 ¤ A  _ O 5 _ O  _ ) (5%= )kp= 

(295)  

(296) $  (¬>  _ +8†(0%= 5  )&5' 6   – ¤ Zt„Ã.    k~HvÄ  <||z v$Ä{x q ĕ{~;y)x8x;Ä.)|. }&|wEÆ8v. ‘ ‡\ˆ‡\Šƒ’ƒŠn³Ô ‘6# ‰ Ú ‹$‹“‰‰ Ù +41 )  0 šm:" ) \9† o$+ H‚1$=n&'4j+ ) ) 

(297) )8g ‚c )%)' '+ "6! )e  ‚jH'

(298) &m =† „: !ƒ= )= o#> > )&@$= , . $= H>;",  ). )(2 )* <% $''+ "" 6 +)(   ¤  8 )  0 šm:" )  %%< <07@=4 $.‚+ ) -)n'1†=)-o ‚j&=Ç5%)± j!]‚A $> 0 n=n )8 )&%)' '+ "< 6 +   O+* ¤ 4   $ o ] !   8   f6.%4) -* 

(299) $ * >    I G O    I C ¤X * ˜> 0 n=n )k )<% $'' "6 +    * ¤ ) *   &$  -fn  / 

(300)  ":" .)Çpo !]$e  60%4  )+-$8 : |

(301)  * > Ð> 0 n=n )8 )&%)' '+ "6A.  Š ´ ‹Š  ’n“ œ  =  ;&‚j·:#g ‚5 )= 8'4= j d†9p) † !< $+= 5 0/+78 % @$= );A.  %  %.  %  . . +. (   ¤X- , +   O%* ¤ — 7. FHG. + .  * ¤.   ¤.

(302) *(0 ), =%%$ < .9+) 42 ± )<gf‚É: 

(303) $±!kT%)' '+ "6cn7‚¹ '$= 0 )±- +=2 !d-$ 6 $ )+ )= ± !k c7@=4 $     2 ¬ D 

(304)  ":  © n  ¤ >́" ),3) .%n$oj‚1±   =(0,  .  ' = )8- +=!   * )(0)8 %4p 60 =·!]$ (5+6Í  ) '= )YÎYf ) -        o*‚+ ) >,bc.76T  k )0 =(.'4)k)•Ë)$ Í     $(0 Ì> &n) n ;$  )j‚+'4*= 7A  X B .7FHG L] * .    ¤X    Ë r /!]=† Ì<! 1m+ (2 ¤ , ‚ ;A.   ˜ ¤

(305) X _ ]!.   Ð ¤  U ˜ 4$˜ 4 3.   – ¤

(306) X ] 4 ¤ ™H  7o q= 78‚j·:#g ‚<   =  !;f=(.' ): )6    > œ  †=kš n) 7o 2– ¤ A !_“ ‘ “ ”  %  % H  

(307)  * 5:

(308) ,&(?6 6:<((( &2 -68& (

(309) : &

(310) ' *8'O V :.(I! &)8NM2

(311) TM>6K :7:)4

(312) ;:      O 5 ¤\X 1- +   ˜  ¤X L]   ˜ ¤\X !N] _ 4 ! 43 $Ð O U œ  ;=H  j ‚+ )kj=  )Çj)

(313) =(5   )   =   o  7  –> >ž˜ ¤ A >jbc) =(51‚ = %)f !h )j9+) 48 !?‚jÉ:  †3,% '4' "9 6 +  ˜ O ¤> ˜> 0 $ @$= f )6fo )8%)' '+ "6< 4       O 5 ¤X *   * p+- n   o *  - Çp 5o      ] *O 5N] * ¤X  ¤ +7A  ! ¤ +  ˜ %O * ¤X +   ˜ O  ¤ ] * _ Ð> œ  1= =(€4% $''+ q-%4) '*-·: = 8! * A  X B .FHG +   ˜ O%* ¤  X +   , ˜ O  ¤ B .FHG L] * _ ,

(314) mo4 )* $ (§)  '+)> ±) = c¾'4•

(315) $r   "‚1N$±(0$ T-)É: '+  ¤ A !_“ ‘ “ ”  % 

(316) H  I G OI _ O    I C

(317) &)(J :<((( & -68& (.

(318) : &

(319) ' *8'O V :.(%! &8NM2

(320) NM 6  :+7 :

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