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Computing multicast trees in dynamic networks using evolving graphs

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(1)Computing multicast trees in dynamic networks using evolving graphs Sandeep Bhadra, Afonso Ferreira. To cite this version: Sandeep Bhadra, Afonso Ferreira. Computing multicast trees in dynamic networks using evolving graphs. [Research Report] RR-4531, INRIA. 2002. �inria-00072057�. HAL Id: inria-00072057 https://hal.inria.fr/inria-00072057 Submitted on 23 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..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Computing multicast trees in dynamic networks using evolving graphs Sandeep Bhadra — Afonso Ferreira. N° 4531 August 2002. ISSN 0249-6399. ISRN INRIA/RR--4531--FR+ENG. THÈME 1. apport de recherche.

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(198)  ´•›]  h7¢p¹škaU*rw“”VdgVa¡ 9—kT 7˜§igkaU Q-RwV!kaigVU W_axTtPQ-RwV!kaigVU c  m

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(200)   h twk8VJ]„xwksdtc•”igV!odg“–fª•–U*rw“”fndgRT_d #4Bm    h¸•›]  h7¢H¹šk:U*rw“–Vd^V¤_a]„‘V“”“­¡ Q-Rw•”]„•›]„™4V!o_a`T]^V*_ r4k:]g]^•–™w“”Vœr4ka“”f—xwkaU*•›_s“ad^•”U>V-_s“”€ak:i^•–d^RTU±˜§k:i #4Bm    h³xwV!V!tuk:xw“–fu_axT]p‘Vižd^RwV-_s™4kaVštcV!o•”]^•–k:x rTi^k:™w“–V!U+_axTt©xwksd‚•”tcV!x8d^•–˜§f%dgRwVka3¢ 9T¹¹  ]ka˜?]^A• ,V G  (d^R—`T]eU*_aŸ—•–xw€¤•–d‚tc• " o`w“–dedgk aV!i^•–˜§f%•–˜œ_dq“”V!_:]Hd k:xwV%ka3¢ 9(¹¹ks˜e]^-• ,!V G •›]>_sx 9T¹¹º_a]³‘šV!“–+“ )§•”x¯kad^RwV!i³‘kaivtw]•–˜qdgRwV]^Vd>ks˜eRw¢­xwkctcVJ]•›]³VU*rcdHf’kai xTksd„˜§kai_rT_aipdg•”o`w“›_si„ks¢ 9T¹¹<ka˜-]^A• ,V G *¡~q“›]pk( d^RTV ]^_aU>V*€:ig_arwR j U*_Afªokax8dv_s•”xª™4ksdgR¸_ax 9T¹¹ )Nks˜•”xTtcVdgVigU*•–xT_sd^V ]^-• ,!&V *u_axTt¸_sx’ka3¢ 9T¹¹yks˜q]^-• ,!V G  

(201) ]^Z k #4Bm

(202)   h¯‘šk:`w“”t¸_a“–‘-_Afc]‚igVdg`wigx pfaVJ5]  4•–€:xwkaig•–xT€*d^RwV>rwigV!]^VxToVkaiY_s™T]^Vx(oVka˜œ_ 9T¹¹<ks˜œ]^-• ,!V G  4d^RTVigV™—f©“–VJ_A8•”xw@ € m

(203)   h `TxT]pk:“–:V!tÏ¡?m©k:i^V!kaViJ a]^•–x(oV 9(¹¹  ]_sigVe_]^r(VJo•›_s“Co_:]pVqka˜ks¢ 9T¹¹  ] 8rwigk8•”xwX€ #4Bm    h%d^k ™4V  h7¢p¹škaU*rw“”Vd^V„tck—V!]šxwkadtc•”i^VJodg“–f*•”U>rT“–f>d^R(_Md m

(204)   h•”]  h?¢H¹šk:U>rT“–Vd^V„_a]j‘V“”“­¡7Q-RT•”] V!x8dg_s•”“›]˜§kaiq_sx•”xTtcVr4Vx(tcVx8dqrwigk—ks˜ž˜§k:i-d^RwV  h7¢p¹škaU*rw“”Vd^V!xwV!]g]ka˜ks¢p¹ńmnhšÅ  Ä  Q„¡ A ¼—À ‹ ¼  ´ka¢H¹ńmnhÅ  Ä  Q  +  f  ‹ ÀQÀ P$9c_aU*V_a]d^RTVYrTi^k—ks˜˜§kaiqQ-RwV!kaigVU W A ¼—À ‹ ¼  ¹Þ® Y¦eÄ

(205) 7N;[

(206) 2 ;

(207) J3#uka¢H¹ńm hšÅ  Ä  Q <=^#!#K H>`f . . ßß Þ\^]_

(208) &`.

(209) WA. I ; ?6 h ij. 0 1. vi. 0. h jp. 0. 1. vp. 1. 1 0. c| ¡ >_sx(t²d^RwVª•–x8d^V!€aV!i. vj. N•”€a`Ti^Vu† š¹šk:xT]pd^ig`Todg•–k:x ˜§kaiqQ-RTVkaigVU.  ‹ ÀQÀ P G •–:Vx _sxÂ`TxTtc•”i^VJod^VJt°€aiv_srwR G W lHJ L G  w ‘V«ok:xT]pd^ig`Tod%_ax V!ak:“–—•”xw€³€:ig_arwRjFW IH J L œ_:]˜§ka“”“–k‘q]% Wa¡˜§kaiVJ_aovaR %)b H oigV!_sd^Vu_('  b H  c¡˜§kaiVJ_aovRV!tc€:

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(212) •”€T¡7W† *¡ Q-R8`(]u˜§kai³V:Vigf«V!tw€aV % J% V Ob L¤ 

(213) d^RTVigV%_sigV V!tw€aV!] ' J)' V ^  0' MJ V ž_sxTt 0' V J L V ϕ–x>dgRwVq]Hdgi^k:xw€Yi^VJ_aovRT_a™w•–“”•–dHfu€aiv_srwR  ¡ @qk‘V:Vid^RwVqtwV€aigVVks˜CV!_:ovR   Ve•”]_sx(t¤]pkudgRwVf¤o!_sxwxwkadœ™4VerT_aipdœka˜ž_sx—f*o“”• 8`wVqka˜ž]pA• ,Ve€aigV!_dgVi?dgRT_sx}w¡7Q-R8`(]j˜§igkaU·ÃV!U>U¤_¤W dgRwVigV•›]Y_%o“”• :`TVks˜œ]^A• ,V G  •”ex G> C•¥˜š_axTtnk:xw“–f©•–˜jd^RTVigV•›]‚_o“”• 8`wV³ks˜œ]^-• ,!V G •”x  ¡YQ-R—`T]‚•–˜ #4Bm

(214)    h o_sx>™4Vq]pk:“–:V!tÏ  m E  ªo_ax³™4VqtcV!o•”twV!t˜§kai G  TH¡ @eVxToV m E

(215)  «igV!tc`(oV!] dg7k #4Bm

(216)    h©˜§kai G  w¡ A ¼—À ‹ ¼   ka¢H¹ńmnhÅ  Ä  Q   4:

(217) # = -63`f  ‹ ÀQÀ P„µ¨VnŸ8xTk‘ºd^RT_sd m E

(218)   •›]  h7¢p¹škaU*rw“”Vd^V:1 ¡ 9ck«˜§igkaU Q-RTVkaigVU {¨_axTt²Q-RwVk:i^V!U |c  #4Bm

(219)    hn•”]  h7¢p¹škaU*rw“”Vd^V:¡ "     *   ! % ¸

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