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2)u I2I N . j2 c 2 s , 3L= 93K : CZ5N@ : 3= K . FJK@ :8: 3LFG5N3=*FJ3»= . FG5 gU? , CXHJ3L= T @J3O=>C5 . @J= , 3=MD :>. KL3=>=83@ : =+93LK : C/g13LFG5 , ? < K3L<S3¤gA? , 3@ : 0À=>CXF . F , 3 K . FG583Fi@ HJ3 , ?K3 ,/, @ , 3 : 3L=>583C/FJK7I?AF 0 93A[ n c m y c n m c . 2 c 2 s , ?RgU? , 3L@ : C/FJ=8K : C/583WHI?AFB= , ?KL3 ,/, @ , 3$0i3=(5 D : C/=83? : >JCZj5 : ?UC : 3L<S3LFG5 DI? : <SC , 3=~gU? , 3@ : = D :8. D . =933L= DJ? : 5 . @B= , 3= D :>. KL3=>=83@ : = K?AFJHBCXHI?U58=;? ,43 93LK : C/5N@ : 3 ;?6K35´C/FJ=>5N?AFG5[ azc mtu c m y nrm c . 2 c 2 s . F @5NC , CX=>3 , 3= F@B< 93 :8. =¸H 3 C/FJHJCXKL3= HJ3=¸D :8. K3=>=83L@ : =D . @ : H935N3 : <CXFJ3 : KL3 , @JC H . FG5 , ?*gU? , 3@ : =83 : ? : 3L583Fi@J3A[ FJ3 : 3 , ?U58C . FH 3`.1: H : 3lH . FBF4933SDI? :, ? : 3 , ?U5NC . Fh<SC/FJCX< @B<(0t<»?e@C/< @J< DI? : 3A@3L<SD , 3 r 3=(5 @B58C , C/=93L3D . @ : gA? , CXHB3 :À,43 93LK : CZ5N@ : 3H 3 @JF¤HB3=&D :8. K3L=8=83L@ : =L[a : ?U5NC T @B3<3FG5 , 3=R<S?AK7JCXFB3=RDI? : ? ,X, ;3 , 3L= ;? < 93L< . C : 3 K . << @JFJ3*= . Fi5 , CX<C/593L3=WDJ? :R, 3=R3LFj0A.1:80 3L<S3LFG5N=d=8@ :z, 3)>B@J=dDI? : 5N? 0 93 T @JC : 3 , C/3À5 . @J= , 3=ED :>. KL3=8=>3@ : = ;? , ?W< 93< . C : 3A['m , 3=>5< K3<3D :8. >I?'> , 3'0DJ@BCX= T @J3 , 3=5N3L<SDJ=»HJ3 KA5K , 3 H 3 ?AKLK ;3L= ;? , ? < 93L< . C : 3 H93LK :8. CX=8=>3FG5M< . CXFB=gC/583T @J3 , 3=W5N3L<SDB=HJ3*Kn5K , 36HJ3=RD :>. KL3=8=>3@ : =10 T @J3 , 3L==83@ , ==D5=(5 ;3<3= ;?O< 93< . C : 3K . <S< @BFJ3gCX?$> , 3L=OHI?AFB= , 32/²@5N@ : D :8. K7J3 =83 :8. FG5 K . FJ=>58C/58@493=MH 3 ?A@°D , @J= T @I?V5 : 3 D :8. K3=>=83L@ : = l ? ,X.1: =T @ 3`. F ?*K . FJ=(5 : @BC/5 DI? : , 3DI?A=8=93HB3= <»?UK7JCXFJ3L= ;? P 0I y FR@JHJ= r [

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After sorting pivots

P1 (sorted) P2 (sorted) P3(sorted)

we keep 3rd and 7thvalue( ) = k * lcm(p_i)

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9 3G1:G1 S"#C# % 1 4 P4= | e |?> % 1 95 !1 : 1 %:US " F "#13 UC?[. & D?V11 "G@$ =" 9 E6 ?Y1:? MUC 1H "G CY T O 1 9 " UC.> 11 :I1 / @ n"#"G: :9=: I :KA$ [9 =ZQ0 : FV : :K V ? " K,:#"G"G : UC[K F= V ) gA@^ :!d_K t+bS -"#' 9 = " C!" W B :+0Sd K Y@ K;6aUC 9 7dB 77+bS -"#K 1 = 7MY"G"$ )3 @. / E+ 9 C UC2 1 = 1 = t 9 :'0 o;1M" *.`476< A .[4 @ USK9 GUS- Y#+0Sd 3"#@M1;6' DC 1 1 EK '"#1E6 O ?$UC ?1)@D = G1 G = $"~ UCKXE6'@C UCE6< ="G@Y2;6' yo 1 Y A.> 95 z~?KNSUC@ = + =9 ?K @ "#1 @ =UC..: + 95 NyK] p B - :FE B5: - DG8 4 28D ACB5476 2 +FD G] J6 x ~=" 9 :P?DV : D. / !6 == QV@PE6< =9 . / M6 3L : n n n +0Sd UC "#1 @7IH 0D BKJ6 8D p 8 ALE,E D p KSabS1 UC"#CK dB dBK: K5" T E.> $" =BSFE6 D V@PW V ?I $x@fO=P1 @ + G^5= :"#CPM " 9 T E68%3" [ 21 _'M=" 9 :! USEW.NMY$@=OS 'D=" 9 :! USEW'+ 11HPO 6 -RQS; 6A 8 .| [ O"G1K 3 $T@ Qh 9 $UC Dn P1 3 d nE6 Q " N =: "G EKC + + P =" 9 : s+s ? v v : UCEW7 2@Y UCEW=2%abS1H$s+s dB dBIE6 @ V :Ev+v. & 1V ? VUXW ZY[Y 2jS\:? 5 C;6 fO F t"E:F1 [ y^c?i@ C=i1 fO"#13:q_f. : 4 n U Y 232S\;K: M6 C = @ L $ O% "# .> VO 6 -,QS; 6A 8 4KqN=B? = ' ;6 fO EK W :t A1 :"#@ GB? = M- "G1:fO # ? 9 .4768 )J68 @ "G1:fO 3 W # = = S. | F [K 1H$ UCE6< G = 1 " :MO 6 -RQS; 6A 8 . / )6 ! = = K1 dB UC?O 6 -RQS; 6A 8 Ls s' 1 v+v

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dB?" NE6 O 1= :9 . > B? = $%;6 O " SF1 / Q EK W =1 R ? | 1 " U /[W | 2S\J.g 2 =#I9 2" 9 29 S ^d_t UC@^cd_'@ @ 1=$ UCEW @?3?2 9 :D" 9 y 9 S S1 d[ ;6 + y ? . / '+I1= :9 D4 Y VI2 $ FA6 " n" MN -h K3L6 C = ALEB D : - 8D - D8 6 28 A 2 E D UC !? T H @= V"#@?"G"#: 11 @ -:Y 5J68 2 Q =" 9 :72;6 N S= :N EJ6 S.4==i" = US7V 4 =UCE6 HE6b 1 [. / A6 ! V :9 M"#1 " !@ i" 9 E6 YY1 =UCi S./ )6 1 !A6h O1? "G@ :"G@ " :! 2? 1 Oy =UC US- + = Y+ "#1"G@ Y" + :9 ? V/ @= N"#"G = E6 @ fO E. / 6 3$1 $ : KH1 " : dB?" !A6 HKUC:?@ O#UC 1HV@W 7 S ) 1 = UC2!6 " E6 7^1 11 O#CUC V@@GY" 4 = "G@+ M 2% F1 = KHL =UC-_.47dB 1 Y+!& SY& N#= V C=.: :Y1 = 1B7ei 11) Q Y"G"G@& =Nw1 = ="G V w" = ]1 :2 =UC.: &1 = 1By @ S 7N?. : 1 = 1BNj3!1 @0:?= V ! 95 =G ?1qb !21 = "#Y2 95 :1 $ = = V Pn+0Sd . : *31 [ = 1B#wD1 =@D Q " 9 :Y2+ = !Y??C 1 OG UC??US @! 1 6 @ 1 "Gi 95 @V . : 1:N1 = = 1B3 O1M1 = 1 :"#@ 1 9 " UC2 dB dBNE68 " # w 1 1 1 ^q= _?F 0Sd t\ ]6 2i@ W: 9 3" 9 '"#= dB 1 E H '?. | : X : 9 :] F6 @ -K`1 ? T iE6<I =1 1 [: 1 [: KD 1 4: 7E6 " - 95 .Ag' T AK] +$1 = = 1BCn31 "#"G@721 4 0E6 @ :7+ =9 =@1 =@ r1 1BTP 1 D+0Sd % 95 b @2:1 1 = O1S O1 = = 1BDYj.

, 77 7"! ?< :$# !&% :8 ?8 ! ?(' : ?

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: 1) = 1H + " .4768 Y1 1H7UC V C% :7 ! = =UCi%" 3B? i= = .> =dB UCUSn / : ^JM @ bS* / O1H V: =C_N 9 S1 1 D O 1 9 ;"#GL1H + " . MY / : =L "G1:"#@y bS+-"GN1 ! =UCM$ =EC 5A= @ P UC=1 E6 = [.4=Y T = "~ 95 21 = @Y 1? '-= IE6h = nx" =UC @*:. IW O i$ UC.t 11H 1 3UCE6<3 = | 4 V3 @ + G" = $ / : ZQ oy]W= 4 E68BC @V : e K51 O"#1 V. = @ / W = Q / :$.g' K 65 C=y V Ox / : O +CL^ V woP1 $1 = 1 O V OP / :N_. / :!1H "#=@ E6' 5A :? O3 = KS 3P V r^ _K2 1H + " 1P iS = i% MN1 .> % / : Q " = 11 P UC"G@G1H + " P "GP 9 y S F?.Eg' 5 -K:F / : Q 1) "G L@ W: I7+bS -"# =UC?E6h " M^ V F No`_t :D1 1 = 5 @ DP UCy" =L =1 E. woK ~1) " UC:T dB +G 0Sd'L :P1 " USK : T dB = PO "G% =UC.

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n" ybS UC[.'1HI H x1 ;: O T dB 1 fO"G1:[.> y / : Q oD $1 " "S V [. > y / : Q o$6<"G1`b 1 : O UC OUS:YV @ V@=:"G@7= 5 UC2I .]4"SN1 UC: " E6<% UCF a^cd_ @^_. USA6c 3^= o 0 _ USY^G? O_K ' +C C =' @ W!: ^ 4 / K / :g K@=...d_= V -K + #= =i "#" R ="G@tC "~ # UCnL 1 3? ";6 " . > 31H + " G = 3#@$ "G@ % %iE6< UCn UC#VS UC&i?' V@3W ~ = i dB UC3 =UC[. > i1) " N(:= y)CF*? 9 1:G" V =GUCE6< = )~+ " %,SV LE6<% A6hUS 9 .> # / : Q oy" = - 68" : 6t^ V! Po`_1H "Gi#G1 UC :'?= SO w =UC. / i .:"qbxS = " O " :" +w ndB 3 Y#"#"G / .;6< 1 w UC [ M10 S = Y?.> y / : Q 3 NW "#C$":$1 11 1 $UC 1z)B =D" 9 P'" 9 7 =UC!!P V @M2 F . > / : Q i68"#1qb 1 : ? =UC VnV@%"G@'t =UC!= . 5 ! / : Q K3;6 " 71 = + 1 [ DUC 9 "G@@ 4X 5 @ =UCKV @ 56%[E6h = !"G@n / : Q FUC 56 E6<% = = [.S 1 Q1HyUC7J6 " %1 = =8 z 1 1 1 %E6 1y =UC[. "#@y K D US$" 9 #~1 9:IG#@ Q . > y 1HY"#"G M "#"~ : "#@ 7 =UC2N #@G 1 :9 . O~ =UC @G "I ?"G@:J6cW "#[K);:I?#@71H . > F / : Q Ii= V M1 D ? N1ME68L =UC[. > Y1H hQ " +: h+X = 6 " @!" ) M < :1 V6 : " 9 A.> 6 dB = N / : Q F" %:F^ V! I io`_? =5 "G1"#C = Y 9 71 YUC # M= J68=" 9 :Y? =UC. K@3 ?7? !5;6<Y USK= 1 = S1 + : USi" UC C. > F / : Q 5A i'NNS =11'"G@ : i1 11 O V O io.

> z / : 'w = V[. 1 V6 :n9= V"#C%1 @1:1 " "G@Y >5fO L= :2 V 7 9 =FUS;6?%@V iE6 @ 1' = Qk "G2@7 "*) 9 Ku2 ? 2M F? 1 +Sd i= =UCM2UC 10@ %"G@ 1HV@ 11 Y1H " .1) " US US"P Sd % T dB G1 y | 4 / @ K[68 i 1 ? " #EK10 YW M3 V :9 : 1 "#C = 1 9 .g'% 5 -K1: @A:7+Sd V R / @= A@3

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(X,Y,Z) Event-set

Elastic Edge

Rigid Edge

? To be filled by Discovery Process

[w] Node Constraints

<p,q> Global Constraints

a,b,c Elastic Edge Constraints

a,b Rigid Edge Constraints

(N)? (P,Q)

(N)a1,b1

[w2][w1] [w1] a3,b3a4,b1

shrink

or

? ?(A,B)[w1]

[w2][w1] [w4]

(C,B) (F,E,G)

? ?a1,b4

a2,b2

a2,b3

a3,b1

a3,b3 a1,b1

(D)(A)

(b) (c)

(a)

<ag,bg>

a2,b2,c1

(C,B) (F,E,G)

? ?

[w3][w2]

a1,b4

a2,b2[w3] [w1]

a2,b3,c2

a3,b1

a3,b3 a1,b1

[w4] [w1]

(D)(A)

a3,b1,c1a1,b1

? ?[w3] [w3]

<0,w3>

a2,b2,c2

(N) (P,Q)(L) (M,N)a2,b2 a2,b2

[w2] [w2] [w2] [w1]

<= c1

a2,b2example of extension

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