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6V i 6!
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Before
YP POP
WP NP
0
5
1
4
2
0
1
3
2
4
P QP RSP T
P UP V
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After
0
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B $32 H $ 9 $H <$; B $3G%$2 <H%<D F4# 2G ?4?&AB 49 2AG B $ # MI B $
9 =4=4= ( %G $'&<24H6I # 2 261 GEH B0K B $ B $32 <H # G ?4?AI,$CB # <2AGEH>7 EB $32 <H ,# G ?4? 49
9 (B $3%G $'2 <&<H24H6# IG ?4# ?A2 I,26$C1 B # <K42AHAGEGMH I4549 GEF 53HAG # ,&,& ,&2AG B $0$ <;
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P QP RSP T
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$ & $ $
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YP POP
P QP R
Color
0(0,1)
1(0,0)
4(1,0)
0(0,0)
1(1,0)
2(2,0)
3(0,1)
2(2,0)
3(2,1)
Key
Input Intercommunicator (comm)
Rank in the original group
1(3)
0(1)
0(0)
1(0)
Color = 0
0(4)
0(1)
WP NP
Color = 1
0(2)
SPP T
VUP
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QYQ PO
QYQ RQ
QYQ ST
QYU
0(2)
1(3)
Color = 2
Disjoint output communicators (newcomm)
(one per color)
C
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B $32 # G 4GEH H $ $4IE? & <H <H&
9 ?A( IH E2<2B 5 B $32& <<HH # G<?4H ?A,#I,$CG ?4B ?# <2A49GEH; B0261 # %B $32& $ & <H <H&#7
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ST
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NXN RQ
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OYOWN BA &')( J|$5%:y 9!;%-<-BA GKBEH!E%#%V-/D79---006-4 /#%- A "!- %!"/--0/!-"8! %!"-0T
OYO PO !-T2/D/EH!E -"& ')( m$77 :}3y"w.-N!-"#%@$" /#%%- !"!/J J$B<AQ!! "#E%%:$A //- "#B%S-EHE%7S#%-"!S -@//4 RA "!--"7 :9K/D/EHEP@E%-0RN$/ "J/DEHBE%TA
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OYO ST -&')( S-~ "!-qr @1!67q /D|EHE ml60l2q$~?"8/BV-A J!/7;-%Q!HE/"N" S-%"!-!@)"!@45"!>O/BEH#E%%- #%V- 3-R %S-@"!/ # %-4 C 14 -@R -""C/#%%-!"N/-3-!<0/-T
OYPO VU M3#/%!-"4RO!R -"N3!J /D EHE%S-T !"!--T2/D@EHE 0-/@"!"/!#%7-!/R-/-4 !?R 3-" !<%!-@"-"/#%0-0/!-!""#RO%$! 3%< S-@"!-/-3@0R5/3"!
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YP OP P -0&')( /!-"m6 |l
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VUP &')( m2nn ml q~ O&')( m2nn ml q~$4
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A -"0&')( *!+-, .4
PON
&')( m2nn)l $m2nn {
QR
747 32 <H G ?4? 747 ( G 4? ? 747 ( G ?4?
0
0
1
1
2
2
ST
3
Lcomm
Rcomm
0
0
1
1
2
2
3
Lcomm
Rcomm
R-%S-J"! / 4 @ /OX!2J!$"6J-!N03J//#!-"84O/DEHE%S/N!"048@/- 3A J /DBEHAE%S//!/"! J%7-$N-@!7"!M%"!! #%-"!@4 "!3!>R
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@>OBEHE%$ #S %V-N"$-:%0S /##%-/DE !/J!C%@" F%J$ @S E/-" 4OPA -" % !"3/-@-FHGK07$6J/@!"!-"VMR M %%!SJ/0!3@-F/D!TE
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.
PON
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QR
ST
0
0
1
1
2
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VU
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NXN VU "!R %3S-"!! > R4 C JX-72!J"/-/!0U$6 /!!-"<"!3J/T2#!/!4 !"4U1 ?A @0/-3BAP7/?/ "!!-T2!@/!"!!" !Q% $"!-!@T
OYOWN M%"!#%-4
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#! 8 $%B EHE%*#' %V- 0) /D EHE& $60/D-EHE% % /0SN3! FT2%/@ET /-"! :8%V--N@#$%- )S R-"!4 R "!-"O!:%V-"!$ /-S 3-)"LR%/ JR -/"!!"6N/B A
OYO RQ
$%M%S!/ %FE% )*,+,-,*,+03 J/")(!30/-)* ! & +>R- ! & +>4
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OYPO VU
Lcomm
Rcomm
0
0
1
1
2
2
3
Lcomm
Rcomm
- $
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"
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SPP T
VUP
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BA !N!"/;A " %M/! $67/J3@F/DE V/DE%BA !N"!-8/"!S-4X2 !8/-3-RIA -"
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