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O'8 e.&___PPT10+YD ' = @B D ' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8&%(DL' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8&H%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8Hj%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8j%(DL' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(+fK| ..>W@ ,(  @j @  ^?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yDdrs/shapexml.xmlU]o0}G?X~E+mLղ=iM;scxCRr]ߏsu>7ʚOގ9FJuns52{Wgm[`6l4b#om+ j XuK(PGdԐ2|TfW+-q[9*`OO93Ԡ Z  .7Ҋp}A`~t8E*0J x Ģ톅} (!B@xt>N"28$8X/l_QVC4."8H] ͡N>a &Rvh$ !9&z[ ZI&59d}Ked6#̅[\m )$>i ِY$޴)Z1VD`;B8~R[A Y{pC:o-KneW<+B#style.visibility<*@%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*R@%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T@%(D=' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*S@%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*V@%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*U@%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L@%(DU' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*/@%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*U@%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*V@%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2@%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*V@%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*W@%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H@%(++0+@ ++0+/@ ++0+2@ ++0+H@ ++0+L@ +L>~ && 1QP 4$(  Pj P  ^\]?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yDdrs/shapexml.xmlU]o0}G?X~E+mLղ=iM;scxCRr]ߏsu>7ʚOގ9FJuns52{Wgm[`6l4b#om+ j XuK(PGdԐ2|TfW+-q[9*`OO93Ԡ Z  .7Ҋp}A`~t8E*0J x Ģ톅} (!B@xt>N"28$8X/l_QVC4."8H] ͡N>a &Rvh$ !9&z[ ZI&59d}Ked6#̅[\m )$>i ِY$޴)Z1VD`;B8~R[A Y{pC:o-KneW<, (&@ ` EP \`?,Content Placeholder 2` 0,$ 0 'On query Qconn(L(u),L(w)): check labelsL(   (&@ `Dl `   KP`  ,$@ 0`B IP 0DԔP  `B JP 0DԔ` P  LP B  ,$D 0 M0  Pl  0 @ PP 0 @,$@  0fB NP 6DԔ 0 @fB OP 6DԔ @ QP BI`0,$@  0 M1  H P 0޽h ?PPPPPPPPPPPPPPPPPP PPPP PP P PP P PP P PP P PP PPP P PP P P P O'8 eXP___PPT100+B6D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*DP%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*CP%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*EP%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*BP%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%P%(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*KP%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*LP%(D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*PP%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*KP%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*QP%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*LP%(+P+0+%P ++0+BP ++0+CP ++0+DP ++0+EP ++0+LP +8}   H (  H H  ^Ζ?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yDdrs/shapexml.xmlU]o0}G?X~E+mLղ=iM;scxCRr]ߏsu>7ʚOގ9FJuns52{Wgm[`6l4b#om+ j XuK(PGdԐ2|TfW+-q[9*`OO93Ԡ Z  .7Ҋp}A`~t8E*0J x Ģ톅} (!B@xt>N"28$8X/l_QVC4."8H] ͡N>a &Rvh$ !9&z[ ZI&59d}Ked6#̅[\m )$>i ِY$޴)Z1VD`;B8~R[A Y{pC:o-KneW<+B#style.visibility<*H%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*H0%(+m^   H; (  He H  ^?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yDdrs/shapexml.xmlU]o0}G?X~E+mLղ=iM;scxCRr]ߏsu>7ʚOގ9FJuns52{Wgm[`6l4b#om+ j XuK(PGdԐ2|TfW+-q[9*`OO93Ԡ Z  .7Ҋp}A`~t8E*0J x Ģ톅} (!B@xt>N"28$8X/l_QVC4."8H] ͡N>a &Rvh$ !9&z[ ZI&59d}Ked6#̅[\m )$>i ِY$޴)Z1VD`;B8~R[A Y{pC:o-KneW<+B#style.visibility<*H%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*HD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*HDA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(+p+0+H ++0+H ++   ) (  e   ^?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yDdrs/shapexml.xmlU]o0}G?X~E+mLղ=iM;scxCRr]ߏsu>7ʚOގ9FJuns52{Wgm[`6l4b#om+ j XuK(PGdԐ2|TfW+-q[9*`OO93Ԡ Z  .7Ҋp}A`~t8E*0J x Ģ톅} (!B@xt>N"28$8X/l_QVC4."8H] ͡N>a &Rvh$ !9&z[ ZI&59d}Ked6#̅[\m )$>i ِY$޴)Z1VD`;B8~R[A Y{pC:o-KneW<+B#style.visibility<*!E%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Ec%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*c%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(+`   ` X8 (  Xx X  ^x?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yDdrs/shapexml.xmlU]o0}G?X~E+mLղ=iM;scxCRr]ߏsu>7ʚOގ9FJuns52{Wgm[`6l4b#om+ j XuK(PGdԐ2|TfW+-q[9*`OO93Ԡ Z  .7Ҋp}A`~t8E*0J x Ģ톅} (!B@xt>N"28$8X/l_QVC4."8H] ͡N>a &Rvh$ !9&z[ ZI&59d}Ked6#̅[\m )$>i ِY$޴)Z1VD`;B8~R[A Y{pC:o-KneW<+B#style.visibility<*X%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*X7%(+u P _(   }    ^lN?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yDdrs/shapexml.xmlU]o0}G?X~E+mLղ=iM;scxCRr]ߏsu>7ʚOގ9FJuns52{Wgm[`6l4b#om+ j XuK(PGdԐ2|TfW+-q[9*`OO93Ԡ Z  .7Ҋp}A`~t8E*0J x Ģ톅} (!B@xt>N"28$8X/l_QVC4."8H] ͡N>a &Rvh$ !9&z[ ZI&59d}Ked6#̅[\m )$>i ِY$޴)Z1VD`;B8~R[A Y{pC:o-KneW<&e6 D`   \䃕?,Content Placeholder 20P,$ 0 T! Useful for services (oracles, routing,& )>+e6 D`H   0޽h ? O'8 eN F ___PPT10& +D* ' = @B D ' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(++0+  ++0+  ++0+  ++0+  + | (  t   ^p?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yDdrs/shapexml.xmlU]o0}G?X~E+mLղ=iM;scxCRr]ߏsu>7ʚOގ9FJuns52{Wgm[`6l4b#om+ j XuK(PGdԐ2|TfW+-q[9*`OO93Ԡ Z  .7Ҋp}A`~t8E*0J x Ģ톅} (!B@xt>N"28$8X/l_QVC4."8H] ͡N>a &Rvh$ !9&z[ ZI&59d}Ked6#̅[\m )$>i ِY$޴)Z1VD`;B8~R[A Y{pC:o-KneW<+B#style.visibility<*%(+8+0+ +   h (  h h  ^?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yDdrs/shapexml.xmlU]o0}G?X~E+mLղ=iM;scxCRr]ߏsu>7ʚOގ9FJuns52{Wgm[`6l4b#om+ j XuK(PGdԐ2|TfW+-q[9*`OO93Ԡ Z  .7Ҋp}A`~t8E*0J x Ģ톅} (!B@xt>N"28$8X/l_QVC4."8H] ͡N>a &Rvh$ !9&z[ ZI&59d}Ked6#̅[\m )$>i ِY$޴)Z1VD`;B8~R[A Y{pC:o-KneW<?@AH h 0޽h ? O'8 e: 2 ___PPT10 +YD ' = @B D ' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*h"%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*h"L%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*hM]%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*h]%(+: 0 (  q   ^H?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yDdrs/shapexml.xmlU]o0}G?X~E+mLղ=iM;scxCRr]ߏsu>7ʚOގ9FJuns52{Wgm[`6l4b#om+ j XuK(PGdԐ2|TfW+-q[9*`OO93Ԡ Z  .7Ҋp}A`~t8E*0J x Ģ톅} (!B@xt>N"28$8X/l_QVC4."8H] ͡N>a &Rvh$ !9&z[ ZI&59d}Ked6#̅[\m )$>i ِY$޴)Z1VD`;B8~R[A Y{pC:o-KneW<?@A  0(H` # Rreceive a query Qconn(s,t,F) for vertices s,t, and failure event F"E (for |F|d"f) answer whether s and t are connected in G = G \ F PC G O G %C G C G 1C G J ;  WWH  0޽h ? O'8 e___PPT10++B#style.visibility<*%(+8+0+H +t &&&MX&(  q   ^XIH?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yDdrs/shapexml.xmlU]o0}G?X~E+mLղ=iM;scxCRr]ߏsu>7ʚOގ9FJuns52{Wgm[`6l4b#om+ j XuK(PGdԐ2|TfW+-q[9*`OO93Ԡ Z  .7Ҋp}A`~t8E*0J x Ģ톅} (!B@xt>N"28$8X/l_QVC4."8H] ͡N>a &Rvh$ !9&z[ ZI&59d}Ked6#̅[\m )$>i ِY$޴)Z1VD`;B8~R[A Y{pC:o-KneW<?@A2   b[H8c?Oval 5K S  N   2   bcH8c?Oval 6 \  N   2   bnH8c?Oval 7'0 N   2   bvH8c?Oval 8 S "  N   2   b,qH8c?Oval 9KN N   2  d,H8c?Oval 10K  N   2  dH8c?Oval 11 V \  N   2  dH8c?Oval 12 '"  N   zB  R8c?Line 13" YYzB  R8c?Line 14 Y* zB  R8c?Line 15* 'zB  R8c?Line 16 Y# zB  R8c?Line 17* # 2  dPH8c?Oval 18KV  N   zB  R8c?Line 19Y# zB  R8c?Line 20# # * zB  R8c?Line 21 #  * 2  dH8c?Oval 22 N"  N   2  dH8c?Oval 23 S \  N   2  dH8c?Oval 24 N\  N   2  dxH8c?Oval 25 Q \  N   zB  R8c?Line 26# NzB  R8c?Line 27 * zB   R8c?Line 28* B !  ReHBIDENFQRUVW8c? :Ij+:Ij+`T @ @ `I`TArc 29y  N   B "  .HBIDE$FQRUVW8c? {-:Ij+{-:Ij+`T @ @ `I`TArc 30   N   B #  X[AHBIDENFQRUVW8c? :Ij+:Ij+`T @ @ `I`TArc 31 *  N   zB $ R8c?Line 32Q  zB % R8c?Line 33 Q \ zB & R8c?Line 34  * zB ' R8c?Line 35 # * zB ( R8c?Line 36*  B )  X%HBIDENFQRUVW8c? :Ij+:Ij+`T @ @ `I`TArc 37  - N   tB L L8c?Line 21 [ tB M L8c?Line 21  H  0޽h ? O'8 eH@___PPT10 +D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DN' =4@BBBB%()))D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*D ' =+ 4 8? CB ppt_xBC2B]ppt_x+-0.0500*(ppt_x*0.9511+(1-ppt_y)*0.3090)BCdB]ppt_x+-0.1000*(ppt_x*0.8090+(1-ppt_y)*0.5878)BCB]ppt_x+-0.1500*(ppt_x*0.5878+(1-ppt_y)*0.8090)BCB]ppt_x+-0.2000*(ppt_x*0.3090+(1-ppt_y)*0.9511)BCB_ppt_x+-0.2500*(ppt_x*-0.0000+(1-ppt_y)*1.0000)BC,B_ppt_x+-0.3000*(ppt_x*-0.3090+(1-ppt_y)*0.9511)BC^B_ppt_x+-0.3500*(ppt_x*-0.5878+(1-ppt_y)*0.8090)BCB_ppt_x+-0.4000*(ppt_x*-0.8090+(1-ppt_y)*0.5878)BCB_ppt_x+-0.4500*(ppt_x*-0.9511+(1-ppt_y)*0.3090)BCBappt_x+-0.5000*(ppt_x*-1.0000+(1-ppt_y)*-0.0000)BC&Bappt_x+-0.5500*(ppt_x*-0.9511+(1-ppt_y)*-0.3090)BCXBappt_x+-0.6000*(ppt_x*-0.8090+(1-ppt_y)*-0.5878)BCBappt_x+-0.6500*(ppt_x*-0.5878+(1-ppt_y)*-0.8090)BCBappt_x+-0.7000*(ppt_x*-0.3090+(1-ppt_y)*-0.9511)BCB_ppt_x+-0.7500*(ppt_x*0.0000+(1-ppt_y)*-1.0000)BC B_ppt_x+-0.8000*(ppt_x*0.3090+(1-ppt_y)*-0.9511)BCRB_ppt_x+-0.8500*(ppt_x*0.5878+(1-ppt_y)*-0.8090)BCB_ppt_x+-0.9000*(ppt_x*0.8090+(1-ppt_y)*-0.5878)BCB_ppt_x+-0.9500*(ppt_x*0.9511+(1-ppt_y)*-0.3090)BCB]ppt_x+-1.0000*(ppt_x*1.0000+(1-ppt_y)*0.0000)B*Y3>B ppt_x<*D ' =+ 4 8? CB ppt_yBC2B]ppt_y+-0.0500*(ppt_x*0.3090-(1-ppt_y)*0.9511)BCdB]ppt_y+-0.1000*(ppt_x*0.5878-(1-ppt_y)*0.8090)BCB]ppt_y+-0.1500*(ppt_x*0.8090-(1-ppt_y)*0.5878)BCB]ppt_y+-0.2000*(ppt_x*0.9511-(1-ppt_y)*0.3090)BCB_ppt_y+-0.2500*(ppt_x*1.0000-(1-ppt_y)*-0.0000)BC,B_ppt_y+-0.3000*(ppt_x*0.9511-(1-ppt_y)*-0.3090)BC^B_ppt_y+-0.3500*(ppt_x*0.8090-(1-ppt_y)*-0.5878)BCB_ppt_y+-0.4000*(ppt_x*0.5878-(1-ppt_y)*-0.8090)BCB_ppt_y+-0.4500*(ppt_x*0.3090-(1-ppt_y)*-0.9511)BCBappt_y+-0.5000*(ppt_x*-0.0000-(1-ppt_y)*-1.0000)BC&Bappt_y+-0.5500*(ppt_x*-0.3090-(1-ppt_y)*-0.9511)BCXBappt_y+-0.6000*(ppt_x*-0.5878-(1-ppt_y)*-0.8090)BCBappt_y+-0.6500*(ppt_x*-0.8090-(1-ppt_y)*-0.5878)BCBappt_y+-0.7000*(ppt_x*-0.9511-(1-ppt_y)*-0.3090)BCB_ppt_y+-0.7500*(ppt_x*-1.0000-(1-ppt_y)*0.0000)BC B_ppt_y+-0.8000*(ppt_x*-0.9511-(1-ppt_y)*0.3090)BCRB_ppt_y+-0.8500*(ppt_x*-0.8090-(1-ppt_y)*0.5878)BCB_ppt_y+-0.9000*(ppt_x*-0.5878-(1-ppt_y)*0.8090)BCB_ppt_y+-0.9500*(ppt_x*-0.3090-(1-ppt_y)*0.9511)BCB]ppt_y+-1.0000*(ppt_x*0.0000-(1-ppt_y)*1.0000)B*Y3>B ppt_y<*D' =1:Bhidden*o3>+B#style.visibility<*%(Dv' =%(D' =4@BBBB%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<* D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<* D ' =+ 4 8? CB ppt_xBC2B]ppt_x+-0.0500*(ppt_x*0.9511+(1-ppt_y)*0.3090)BCdB]ppt_x+-0.1000*(ppt_x*0.8090+(1-ppt_y)*0.5878)BCB]ppt_x+-0.1500*(ppt_x*0.5878+(1-ppt_y)*0.8090)BCB]ppt_x+-0.2000*(ppt_x*0.3090+(1-ppt_y)*0.9511)BCB_ppt_x+-0.2500*(ppt_x*-0.0000+(1-ppt_y)*1.0000)BC,B_ppt_x+-0.3000*(ppt_x*-0.3090+(1-ppt_y)*0.9511)BC^B_ppt_x+-0.3500*(ppt_x*-0.5878+(1-ppt_y)*0.8090)BCB_ppt_x+-0.4000*(ppt_x*-0.8090+(1-ppt_y)*0.5878)BCB_ppt_x+-0.4500*(ppt_x*-0.9511+(1-ppt_y)*0.3090)BCBappt_x+-0.5000*(ppt_x*-1.0000+(1-ppt_y)*-0.0000)BC&Bappt_x+-0.5500*(ppt_x*-0.9511+(1-ppt_y)*-0.3090)BCXBappt_x+-0.6000*(ppt_x*-0.8090+(1-ppt_y)*-0.5878)BCBappt_x+-0.6500*(ppt_x*-0.5878+(1-ppt_y)*-0.8090)BCBappt_x+-0.7000*(ppt_x*-0.3090+(1-ppt_y)*-0.9511)BCB_ppt_x+-0.7500*(ppt_x*0.0000+(1-ppt_y)*-1.0000)BC B_ppt_x+-0.8000*(ppt_x*0.3090+(1-ppt_y)*-0.9511)BCRB_ppt_x+-0.8500*(ppt_x*0.5878+(1-ppt_y)*-0.8090)BCB_ppt_x+-0.9000*(ppt_x*0.8090+(1-ppt_y)*-0.5878)BCB_ppt_x+-0.9500*(ppt_x*0.9511+(1-ppt_y)*-0.3090)BCB]ppt_x+-1.0000*(ppt_x*1.0000+(1-ppt_y)*0.0000)B*Y3>B ppt_x<* D ' =+ 4 8? CB ppt_yBC2B]ppt_y+-0.0500*(ppt_x*0.3090-(1-ppt_y)*0.9511)BCdB]ppt_y+-0.1000*(ppt_x*0.5878-(1-ppt_y)*0.8090)BCB]ppt_y+-0.1500*(ppt_x*0.8090-(1-ppt_y)*0.5878)BCB]ppt_y+-0.2000*(ppt_x*0.9511-(1-ppt_y)*0.3090)BCB_ppt_y+-0.2500*(ppt_x*1.0000-(1-ppt_y)*-0.0000)BC,B_ppt_y+-0.3000*(ppt_x*0.9511-(1-ppt_y)*-0.3090)BC^B_ppt_y+-0.3500*(ppt_x*0.8090-(1-ppt_y)*-0.5878)BCB_ppt_y+-0.4000*(ppt_x*0.5878-(1-ppt_y)*-0.8090)BCB_ppt_y+-0.4500*(ppt_x*0.3090-(1-ppt_y)*-0.9511)BCBappt_y+-0.5000*(ppt_x*-0.0000-(1-ppt_y)*-1.0000)BC&Bappt_y+-0.5500*(ppt_x*-0.3090-(1-ppt_y)*-0.9511)BCXBappt_y+-0.6000*(ppt_x*-0.5878-(1-ppt_y)*-0.8090)BCBappt_y+-0.6500*(ppt_x*-0.8090-(1-ppt_y)*-0.5878)BCBappt_y+-0.7000*(ppt_x*-0.9511-(1-ppt_y)*-0.3090)BCB_ppt_y+-0.7500*(ppt_x*-1.0000-(1-ppt_y)*0.0000)BC B_ppt_y+-0.8000*(ppt_x*-0.9511-(1-ppt_y)*0.3090)BCRB_ppt_y+-0.8500*(ppt_x*-0.8090-(1-ppt_y)*0.5878)BCB_ppt_y+-0.9000*(ppt_x*-0.5878-(1-ppt_y)*0.8090)BCB_ppt_y+-0.9500*(ppt_x*-0.3090-(1-ppt_y)*0.9511)BCB]ppt_y+-1.0000*(ppt_x*0.0000-(1-ppt_y)*1.0000)B*Y3>B ppt_y<* D' =1:Bhidden*o3>+B#style.visibility<* %(Dv' =%(D' =4@BBBB%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*D ' =+ 4 8? CB ppt_xBC2B]ppt_x+-0.0500*(ppt_x*0.9511+(1-ppt_y)*0.3090)BCdB]ppt_x+-0.1000*(ppt_x*0.8090+(1-ppt_y)*0.5878)BCB]ppt_x+-0.1500*(ppt_x*0.5878+(1-ppt_y)*0.8090)BCB]ppt_x+-0.2000*(ppt_x*0.3090+(1-ppt_y)*0.9511)BCB_ppt_x+-0.2500*(ppt_x*-0.0000+(1-ppt_y)*1.0000)BC,B_ppt_x+-0.3000*(ppt_x*-0.3090+(1-ppt_y)*0.9511)BC^B_ppt_x+-0.3500*(ppt_x*-0.5878+(1-ppt_y)*0.8090)BCB_ppt_x+-0.4000*(ppt_x*-0.8090+(1-ppt_y)*0.5878)BCB_ppt_x+-0.4500*(ppt_x*-0.9511+(1-ppt_y)*0.3090)BCBappt_x+-0.5000*(ppt_x*-1.0000+(1-ppt_y)*-0.0000)BC&Bappt_x+-0.5500*(ppt_x*-0.9511+(1-ppt_y)*-0.3090)BCXBappt_x+-0.6000*(ppt_x*-0.8090+(1-ppt_y)*-0.5878)BCBappt_x+-0.6500*(ppt_x*-0.5878+(1-ppt_y)*-0.8090)BCBappt_x+-0.7000*(ppt_x*-0.3090+(1-ppt_y)*-0.9511)BCB_ppt_x+-0.7500*(ppt_x*0.0000+(1-ppt_y)*-1.0000)BC B_ppt_x+-0.8000*(ppt_x*0.3090+(1-ppt_y)*-0.9511)BCRB_ppt_x+-0.8500*(ppt_x*0.5878+(1-ppt_y)*-0.8090)BCB_ppt_x+-0.9000*(ppt_x*0.8090+(1-ppt_y)*-0.5878)BCB_ppt_x+-0.9500*(ppt_x*0.9511+(1-ppt_y)*-0.3090)BCB]ppt_x+-1.0000*(ppt_x*1.0000+(1-ppt_y)*0.0000)B*Y3>B ppt_x<*D ' =+ 4 8? CB ppt_yBC2B]ppt_y+-0.0500*(ppt_x*0.3090-(1-ppt_y)*0.9511)BCdB]ppt_y+-0.1000*(ppt_x*0.5878-(1-ppt_y)*0.8090)BCB]ppt_y+-0.1500*(ppt_x*0.8090-(1-ppt_y)*0.5878)BCB]ppt_y+-0.2000*(ppt_x*0.9511-(1-ppt_y)*0.3090)BCB_ppt_y+-0.2500*(ppt_x*1.0000-(1-ppt_y)*-0.0000)BC,B_ppt_y+-0.3000*(ppt_x*0.9511-(1-ppt_y)*-0.3090)BC^B_ppt_y+-0.3500*(ppt_x*0.8090-(1-ppt_y)*-0.5878)BCB_ppt_y+-0.4000*(ppt_x*0.5878-(1-ppt_y)*-0.8090)BCB_ppt_y+-0.4500*(ppt_x*0.3090-(1-ppt_y)*-0.9511)BCBappt_y+-0.5000*(ppt_x*-0.0000-(1-ppt_y)*-1.0000)BC&Bappt_y+-0.5500*(ppt_x*-0.3090-(1-ppt_y)*-0.9511)BCXBappt_y+-0.6000*(ppt_x*-0.5878-(1-ppt_y)*-0.8090)BCBappt_y+-0.6500*(ppt_x*-0.8090-(1-ppt_y)*-0.5878)BCBappt_y+-0.7000*(ppt_x*-0.9511-(1-ppt_y)*-0.3090)BCB_ppt_y+-0.7500*(ppt_x*-1.0000-(1-ppt_y)*0.0000)BC B_ppt_y+-0.8000*(ppt_x*-0.9511-(1-ppt_y)*0.3090)BCRB_ppt_y+-0.8500*(ppt_x*-0.8090-(1-ppt_y)*0.5878)BCB_ppt_y+-0.9000*(ppt_x*-0.5878-(1-ppt_y)*0.8090)BCB_ppt_y+-0.9500*(ppt_x*-0.3090-(1-ppt_y)*0.9511)BCB]ppt_y+-1.0000*(ppt_x*0.0000-(1-ppt_y)*1.0000)B*Y3>B ppt_y<*D' =1:Bhidden*o3>+B#style.visibility<*%(Dv' =%(pD' =4@BBBB%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*LD' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*LD ' =+ 4 8? CB ppt_xBC2B]ppt_x+-0.0500*(ppt_x*0.9511+(1-ppt_y)*0.3090)BCdB]ppt_x+-0.1000*(ppt_x*0.8090+(1-ppt_y)*0.5878)BCB]ppt_x+-0.1500*(ppt_x*0.5878+(1-ppt_y)*0.8090)BCB]ppt_x+-0.2000*(ppt_x*0.3090+(1-ppt_y)*0.9511)BCB_ppt_x+-0.2500*(ppt_x*-0.0000+(1-ppt_y)*1.0000)BC,B_ppt_x+-0.3000*(ppt_x*-0.3090+(1-ppt_y)*0.9511)BC^B_ppt_x+-0.3500*(ppt_x*-0.5878+(1-ppt_y)*0.8090)BCB_ppt_x+-0.4000*(ppt_x*-0.8090+(1-ppt_y)*0.5878)BCB_ppt_x+-0.4500*(ppt_x*-0.9511+(1-ppt_y)*0.3090)BCBappt_x+-0.5000*(ppt_x*-1.0000+(1-ppt_y)*-0.0000)BC&Bappt_x+-0.5500*(ppt_x*-0.9511+(1-ppt_y)*-0.3090)BCXBappt_x+-0.6000*(ppt_x*-0.8090+(1-ppt_y)*-0.5878)BCBappt_x+-0.6500*(ppt_x*-0.5878+(1-ppt_y)*-0.8090)BCBappt_x+-0.7000*(ppt_x*-0.3090+(1-ppt_y)*-0.9511)BCB_ppt_x+-0.7500*(ppt_x*0.0000+(1-ppt_y)*-1.0000)BC B_ppt_x+-0.8000*(ppt_x*0.3090+(1-ppt_y)*-0.9511)BCRB_ppt_x+-0.8500*(ppt_x*0.5878+(1-ppt_y)*-0.8090)BCB_ppt_x+-0.9000*(ppt_x*0.8090+(1-ppt_y)*-0.5878)BCB_ppt_x+-0.9500*(ppt_x*0.9511+(1-ppt_y)*-0.3090)BCB]ppt_x+-1.0000*(ppt_x*1.0000+(1-ppt_y)*0.0000)B*Y3>B ppt_x<*LD ' =+ 4 8? CB ppt_yBC2B]ppt_y+-0.0500*(ppt_x*0.3090-(1-ppt_y)*0.9511)BCdB]ppt_y+-0.1000*(ppt_x*0.5878-(1-ppt_y)*0.8090)BCB]ppt_y+-0.1500*(ppt_x*0.8090-(1-ppt_y)*0.5878)BCB]ppt_y+-0.2000*(ppt_x*0.9511-(1-ppt_y)*0.3090)BCB_ppt_y+-0.2500*(ppt_x*1.0000-(1-ppt_y)*-0.0000)BC,B_ppt_y+-0.3000*(ppt_x*0.9511-(1-ppt_y)*-0.3090)BC^B_ppt_y+-0.3500*(ppt_x*0.8090-(1-ppt_y)*-0.5878)BCB_ppt_y+-0.4000*(ppt_x*0.5878-(1-ppt_y)*-0.8090)BCB_ppt_y+-0.4500*(ppt_x*0.3090-(1-ppt_y)*-0.9511)BCBappt_y+-0.5000*(ppt_x*-0.0000-(1-ppt_y)*-1.0000)BC&Bappt_y+-0.5500*(ppt_x*-0.3090-(1-ppt_y)*-0.9511)BCXBappt_y+-0.6000*(ppt_x*-0.5878-(1-ppt_y)*-0.8090)BCBappt_y+-0.6500*(ppt_x*-0.8090-(1-ppt_y)*-0.5878)BCBappt_y+-0.7000*(ppt_x*-0.9511-(1-ppt_y)*-0.3090)BCB_ppt_y+-0.7500*(ppt_x*-1.0000-(1-ppt_y)*0.0000)BC B_ppt_y+-0.8000*(ppt_x*-0.9511-(1-ppt_y)*0.3090)BCRB_ppt_y+-0.8500*(ppt_x*-0.8090-(1-ppt_y)*0.5878)BCB_ppt_y+-0.9000*(ppt_x*-0.5878-(1-ppt_y)*0.8090)BCB_ppt_y+-0.9500*(ppt_x*-0.3090-(1-ppt_y)*0.9511)BCB]ppt_y+-1.0000*(ppt_x*0.0000-(1-ppt_y)*1.0000)B*Y3>B ppt_y<*LD' =1:Bhidden*o3>+B#style.visibility<*L%(Dv' =%(@D' =4@BBBB%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*D ' =+ 4 8? CB ppt_xBC2B]ppt_x+-0.0500*(ppt_x*0.9511+(1-ppt_y)*0.3090)BCdB]ppt_x+-0.1000*(ppt_x*0.8090+(1-ppt_y)*0.5878)BCB]ppt_x+-0.1500*(ppt_x*0.5878+(1-ppt_y)*0.8090)BCB]ppt_x+-0.2000*(ppt_x*0.3090+(1-ppt_y)*0.9511)BCB_ppt_x+-0.2500*(ppt_x*-0.0000+(1-ppt_y)*1.0000)BC,B_ppt_x+-0.3000*(ppt_x*-0.3090+(1-ppt_y)*0.9511)BC^B_ppt_x+-0.3500*(ppt_x*-0.5878+(1-ppt_y)*0.8090)BCB_ppt_x+-0.4000*(ppt_x*-0.8090+(1-ppt_y)*0.5878)BCB_ppt_x+-0.4500*(ppt_x*-0.9511+(1-ppt_y)*0.3090)BCBappt_x+-0.5000*(ppt_x*-1.0000+(1-ppt_y)*-0.0000)BC&Bappt_x+-0.5500*(ppt_x*-0.9511+(1-ppt_y)*-0.3090)BCXBappt_x+-0.6000*(ppt_x*-0.8090+(1-ppt_y)*-0.5878)BCBappt_x+-0.6500*(ppt_x*-0.5878+(1-ppt_y)*-0.8090)BCBappt_x+-0.7000*(ppt_x*-0.3090+(1-ppt_y)*-0.9511)BCB_ppt_x+-0.7500*(ppt_x*0.0000+(1-ppt_y)*-1.0000)BC B_ppt_x+-0.8000*(ppt_x*0.3090+(1-ppt_y)*-0.9511)BCRB_ppt_x+-0.8500*(ppt_x*0.5878+(1-ppt_y)*-0.8090)BCB_ppt_x+-0.9000*(ppt_x*0.8090+(1-ppt_y)*-0.5878)BCB_ppt_x+-0.9500*(ppt_x*0.9511+(1-ppt_y)*-0.3090)BCB]ppt_x+-1.0000*(ppt_x*1.0000+(1-ppt_y)*0.0000)B*Y3>B ppt_x<*D ' =+ 4 8? CB ppt_yBC2B]ppt_y+-0.0500*(ppt_x*0.3090-(1-ppt_y)*0.9511)BCdB]ppt_y+-0.1000*(ppt_x*0.5878-(1-ppt_y)*0.8090)BCB]ppt_y+-0.1500*(ppt_x*0.8090-(1-ppt_y)*0.5878)BCB]ppt_y+-0.2000*(ppt_x*0.9511-(1-ppt_y)*0.3090)BCB_ppt_y+-0.2500*(ppt_x*1.0000-(1-ppt_y)*-0.0000)BC,B_ppt_y+-0.3000*(ppt_x*0.9511-(1-ppt_y)*-0.3090)BC^B_ppt_y+-0.3500*(ppt_x*0.8090-(1-ppt_y)*-0.5878)BCB_ppt_y+-0.4000*(ppt_x*0.5878-(1-ppt_y)*-0.8090)BCB_ppt_y+-0.4500*(ppt_x*0.3090-(1-ppt_y)*-0.9511)BCBappt_y+-0.5000*(ppt_x*-0.0000-(1-ppt_y)*-1.0000)BC&Bappt_y+-0.5500*(ppt_x*-0.3090-(1-ppt_y)*-0.9511)BCXBappt_y+-0.6000*(ppt_x*-0.5878-(1-ppt_y)*-0.8090)BCBappt_y+-0.6500*(ppt_x*-0.8090-(1-ppt_y)*-0.5878)BCBappt_y+-0.7000*(ppt_x*-0.9511-(1-ppt_y)*-0.3090)BCB_ppt_y+-0.7500*(ppt_x*-1.0000-(1-ppt_y)*0.0000)BC B_ppt_y+-0.8000*(ppt_x*-0.9511-(1-ppt_y)*0.3090)BCRB_ppt_y+-0.8500*(ppt_x*-0.8090-(1-ppt_y)*0.5878)BCB_ppt_y+-0.9000*(ppt_x*-0.5878-(1-ppt_y)*0.8090)BCB_ppt_y+-0.9500*(ppt_x*-0.3090-(1-ppt_y)*0.9511)BCB]ppt_y+-1.0000*(ppt_x*0.0000-(1-ppt_y)*1.0000)B*Y3>B ppt_y<*D' =1:Bhidden*o3>+B#style.visibility<*%(+ 77:A0 87(  q   ^$BH?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yDdrs/shapexml.xmlU]o0}G?X~E+mLղ=iM;scxCRr]ߏsu>7ʚOގ9FJuns52{Wgm[`6l4b#om+ j XuK(PGdԐ2|TfW+-q[9*`OO93Ԡ Z  .7Ҋp}A`~t8E*0J x Ģ톅} (!B@xt>N"28$8X/l_QVC4."8H] ͡N>a &Rvh$ !9&z[ ZI&59d}Ked6#̅[\m )$>i ِY$޴)Z1VD`;B8~R[A Y{pC:o-KneW<?@A2  \#J8c?Oval 5K S  N   2  \X&J8c?Oval 6 \  N   2  \h6J8c?Oval 7'0 N   2  \J8c?Oval 8 S "  N   2  \HJ8c?Oval 9KN N   2   ^QJ8c?Oval 10K  N   2   ^[J8c?Oval 11 V \  N   2   ^HdJ8c?Oval 12 '"  N   tB   L8c?Line 13" YYtB  L8c?Line 16 Y# tB  L8c?Line 17* # 2  ^oJ8c?Oval 18KV  N   tB  L8c?Line 20# # * 2  ^qJ8c?Oval 22 N"  N   2  ^́J8c?Oval 23 S \  N   2  ^J8c?Oval 24 N\  N   2  ^ēJ8c?Oval 25 Q \  N   tB  L8c?Line 27 * tB  L8c?Line 28* B   Le`JBIDENFQRUVW8c? :Ij+:Ij+`T @ @ `I`TArc 29y  N   B   (JBIDE$FQRUVW8c? {-:Ij+{-:Ij+`T @ @ `I`TArc 30   N   tB  L8c?Line 32Q  tB   L8c?Line 33 Q \ \l  1,$@  0|B  L8c?Line 15* 'B   R[AJBIDENFQRUVW8c? :Ij+:Ij+`T @ @ `I`TArc 31 *  N   |B ! L8c?Line 34 * tB " L8c?Line 35 # * tB # L8c?Line 36*  B $  R%pJBIDENFQRUVW8c? :Ij+:Ij+`T @ @ `I`TArc 37  - N   tB & L8c?Line 21  l p*  ,p* ,$@  0|B   L8c?Line 14 Y* |B  L8c?Line 21#  * |B ' L8c?Line 21P pp l Yp[  +pY[ ,$@  0|B % L8c?Line 21 [ B  R8c?Line 19Y# B ( R8c?Line 21 p ptB ) L8c?Line 21p0  z . BJ p- ,$@ 0 lF12 G O   / BJ  p ,$@  0 lF22 G O   0 BJc k ,$@ 0 lF32 G O  W 8 HJ ` ,$ 0  Q(s1,t1)?j G O G O G   Vl P AP,$D 0 4 H J  ls32 G O   9 BHJP  lt32 G O  Vl  =,$@ 0 3 HJP lt12 G O   : BJ  ls12 G O  Pl @  @@ ,$D  0 ; BJG @  lt22 G O   < B`JS ls22 G O  Q > BJ P ,$  0  Q(s2,t2)?j G O G O G   Q ? BJF ,$ 0  Q(s3,t3)?j G O G O G   H  0޽h ? O'8 e}|___PPT10|+k;Dz' = @B Dz' = @BA?%,( < +O%,( < +DZ' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*.%(D' =4@BBBB%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*+D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*+D ' =+ 4 8? CB ppt_xBC2B]ppt_x+-0.0500*(ppt_x*0.9511+(1-ppt_y)*0.3090)BCdB]ppt_x+-0.1000*(ppt_x*0.8090+(1-ppt_y)*0.5878)BCB]ppt_x+-0.1500*(ppt_x*0.5878+(1-ppt_y)*0.8090)BCB]ppt_x+-0.2000*(ppt_x*0.3090+(1-ppt_y)*0.9511)BCB_ppt_x+-0.2500*(ppt_x*-0.0000+(1-ppt_y)*1.0000)BC,B_ppt_x+-0.3000*(ppt_x*-0.3090+(1-ppt_y)*0.9511)BC^B_ppt_x+-0.3500*(ppt_x*-0.5878+(1-ppt_y)*0.8090)BCB_ppt_x+-0.4000*(ppt_x*-0.8090+(1-ppt_y)*0.5878)BCB_ppt_x+-0.4500*(ppt_x*-0.9511+(1-ppt_y)*0.3090)BCBappt_x+-0.5000*(ppt_x*-1.0000+(1-ppt_y)*-0.0000)BC&Bappt_x+-0.5500*(ppt_x*-0.9511+(1-ppt_y)*-0.3090)BCXBappt_x+-0.6000*(ppt_x*-0.8090+(1-ppt_y)*-0.5878)BCBappt_x+-0.6500*(ppt_x*-0.5878+(1-ppt_y)*-0.8090)BCBappt_x+-0.7000*(ppt_x*-0.3090+(1-ppt_y)*-0.9511)BCB_ppt_x+-0.7500*(ppt_x*0.0000+(1-ppt_y)*-1.0000)BC B_ppt_x+-0.8000*(ppt_x*0.3090+(1-ppt_y)*-0.9511)BCRB_ppt_x+-0.8500*(ppt_x*0.5878+(1-ppt_y)*-0.8090)BCB_ppt_x+-0.9000*(ppt_x*0.8090+(1-ppt_y)*-0.5878)BCB_ppt_x+-0.9500*(ppt_x*0.9511+(1-ppt_y)*-0.3090)BCB]ppt_x+-1.0000*(ppt_x*1.0000+(1-ppt_y)*0.0000)B*Y3>B ppt_x<*+D ' =+ 4 8? CB ppt_yBC2B]ppt_y+-0.0500*(ppt_x*0.3090-(1-ppt_y)*0.9511)BCdB]ppt_y+-0.1000*(ppt_x*0.5878-(1-ppt_y)*0.8090)BCB]ppt_y+-0.1500*(ppt_x*0.8090-(1-ppt_y)*0.5878)BCB]ppt_y+-0.2000*(ppt_x*0.9511-(1-ppt_y)*0.3090)BCB_ppt_y+-0.2500*(ppt_x*1.0000-(1-ppt_y)*-0.0000)BC,B_ppt_y+-0.3000*(ppt_x*0.9511-(1-ppt_y)*-0.3090)BC^B_ppt_y+-0.3500*(ppt_x*0.8090-(1-ppt_y)*-0.5878)BCB_ppt_y+-0.4000*(ppt_x*0.5878-(1-ppt_y)*-0.8090)BCB_ppt_y+-0.4500*(ppt_x*0.3090-(1-ppt_y)*-0.9511)BCBappt_y+-0.5000*(ppt_x*-0.0000-(1-ppt_y)*-1.0000)BC&Bappt_y+-0.5500*(ppt_x*-0.3090-(1-ppt_y)*-0.9511)BCXBappt_y+-0.6000*(ppt_x*-0.5878-(1-ppt_y)*-0.8090)BCBappt_y+-0.6500*(ppt_x*-0.8090-(1-ppt_y)*-0.5878)BCBappt_y+-0.7000*(ppt_x*-0.9511-(1-ppt_y)*-0.3090)BCB_ppt_y+-0.7500*(ppt_x*-1.0000-(1-ppt_y)*0.0000)BC B_ppt_y+-0.8000*(ppt_x*-0.9511-(1-ppt_y)*0.3090)BCRB_ppt_y+-0.8500*(ppt_x*-0.8090-(1-ppt_y)*0.5878)BCB_ppt_y+-0.9000*(ppt_x*-0.5878-(1-ppt_y)*0.8090)BCB_ppt_y+-0.9500*(ppt_x*-0.3090-(1-ppt_y)*0.9511)BCB]ppt_y+-1.0000*(ppt_x*0.0000-(1-ppt_y)*1.0000)B*Y3>B ppt_y<*+D' =1:Bhidden*o3>+B#style.visibility<*+%(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*=%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(DV ' =%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*.%(D' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*+%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*+D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*+D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*8%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*=%(DZ' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*/%(D' =4@BBBB%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*,D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*,D ' =+ 4 8? CB ppt_xBC2B]ppt_x+-0.0500*(ppt_x*0.9511+(1-ppt_y)*0.3090)BCdB]ppt_x+-0.1000*(ppt_x*0.8090+(1-ppt_y)*0.5878)BCB]ppt_x+-0.1500*(ppt_x*0.5878+(1-ppt_y)*0.8090)BCB]ppt_x+-0.2000*(ppt_x*0.3090+(1-ppt_y)*0.9511)BCB_ppt_x+-0.2500*(ppt_x*-0.0000+(1-ppt_y)*1.0000)BC,B_ppt_x+-0.3000*(ppt_x*-0.3090+(1-ppt_y)*0.9511)BC^B_ppt_x+-0.3500*(ppt_x*-0.5878+(1-ppt_y)*0.8090)BCB_ppt_x+-0.4000*(ppt_x*-0.8090+(1-ppt_y)*0.5878)BCB_ppt_x+-0.4500*(ppt_x*-0.9511+(1-ppt_y)*0.3090)BCBappt_x+-0.5000*(ppt_x*-1.0000+(1-ppt_y)*-0.0000)BC&Bappt_x+-0.5500*(ppt_x*-0.9511+(1-ppt_y)*-0.3090)BCXBappt_x+-0.6000*(ppt_x*-0.8090+(1-ppt_y)*-0.5878)BCBappt_x+-0.6500*(ppt_x*-0.5878+(1-ppt_y)*-0.8090)BCBappt_x+-0.7000*(ppt_x*-0.3090+(1-ppt_y)*-0.9511)BCB_ppt_x+-0.7500*(ppt_x*0.0000+(1-ppt_y)*-1.0000)BC B_ppt_x+-0.8000*(ppt_x*0.3090+(1-ppt_y)*-0.9511)BCRB_ppt_x+-0.8500*(ppt_x*0.5878+(1-ppt_y)*-0.8090)BCB_ppt_x+-0.9000*(ppt_x*0.8090+(1-ppt_y)*-0.5878)BCB_ppt_x+-0.9500*(ppt_x*0.9511+(1-ppt_y)*-0.3090)BCB]ppt_x+-1.0000*(ppt_x*1.0000+(1-ppt_y)*0.0000)B*Y3>B ppt_x<*,D ' =+ 4 8? CB ppt_yBC2B]ppt_y+-0.0500*(ppt_x*0.3090-(1-ppt_y)*0.9511)BCdB]ppt_y+-0.1000*(ppt_x*0.5878-(1-ppt_y)*0.8090)BCB]ppt_y+-0.1500*(ppt_x*0.8090-(1-ppt_y)*0.5878)BCB]ppt_y+-0.2000*(ppt_x*0.9511-(1-ppt_y)*0.3090)BCB_ppt_y+-0.2500*(ppt_x*1.0000-(1-ppt_y)*-0.0000)BC,B_ppt_y+-0.3000*(ppt_x*0.9511-(1-ppt_y)*-0.3090)BC^B_ppt_y+-0.3500*(ppt_x*0.8090-(1-ppt_y)*-0.5878)BCB_ppt_y+-0.4000*(ppt_x*0.5878-(1-ppt_y)*-0.8090)BCB_ppt_y+-0.4500*(ppt_x*0.3090-(1-ppt_y)*-0.9511)BCBappt_y+-0.5000*(ppt_x*-0.0000-(1-ppt_y)*-1.0000)BC&Bappt_y+-0.5500*(ppt_x*-0.3090-(1-ppt_y)*-0.9511)BCXBappt_y+-0.6000*(ppt_x*-0.5878-(1-ppt_y)*-0.8090)BCBappt_y+-0.6500*(ppt_x*-0.8090-(1-ppt_y)*-0.5878)BCBappt_y+-0.7000*(ppt_x*-0.9511-(1-ppt_y)*-0.3090)BCB_ppt_y+-0.7500*(ppt_x*-1.0000-(1-ppt_y)*0.0000)BC B_ppt_y+-0.8000*(ppt_x*-0.9511-(1-ppt_y)*0.3090)BCRB_ppt_y+-0.8500*(ppt_x*-0.8090-(1-ppt_y)*0.5878)BCB_ppt_y+-0.9000*(ppt_x*-0.5878-(1-ppt_y)*0.8090)BCB_ppt_y+-0.9500*(ppt_x*-0.3090-(1-ppt_y)*0.9511)BCB]ppt_y+-1.0000*(ppt_x*0.0000-(1-ppt_y)*1.0000)B*Y3>B ppt_y<*,D' =1:Bhidden*o3>+B#style.visibility<*,%(D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*>%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(DV ' =%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*/%(D' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*,D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*,D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*>%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*@%(DZ' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =4@BBBB%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*1D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*1D ' =+ 4 8? CB ppt_xBC2B]ppt_x+-0.0500*(ppt_x*0.9511+(1-ppt_y)*0.3090)BCdB]ppt_x+-0.1000*(ppt_x*0.8090+(1-ppt_y)*0.5878)BCB]ppt_x+-0.1500*(ppt_x*0.5878+(1-ppt_y)*0.8090)BCB]ppt_x+-0.2000*(ppt_x*0.3090+(1-ppt_y)*0.9511)BCB_ppt_x+-0.2500*(ppt_x*-0.0000+(1-ppt_y)*1.0000)BC,B_ppt_x+-0.3000*(ppt_x*-0.3090+(1-ppt_y)*0.9511)BC^B_ppt_x+-0.3500*(ppt_x*-0.5878+(1-ppt_y)*0.8090)BCB_ppt_x+-0.4000*(ppt_x*-0.8090+(1-ppt_y)*0.5878)BCB_ppt_x+-0.4500*(ppt_x*-0.9511+(1-ppt_y)*0.3090)BCBappt_x+-0.5000*(ppt_x*-1.0000+(1-ppt_y)*-0.0000)BC&Bappt_x+-0.5500*(ppt_x*-0.9511+(1-ppt_y)*-0.3090)BCXBappt_x+-0.6000*(ppt_x*-0.8090+(1-ppt_y)*-0.5878)BCBappt_x+-0.6500*(ppt_x*-0.5878+(1-ppt_y)*-0.8090)BCBappt_x+-0.7000*(ppt_x*-0.3090+(1-ppt_y)*-0.9511)BCB_ppt_x+-0.7500*(ppt_x*0.0000+(1-ppt_y)*-1.0000)BC B_ppt_x+-0.8000*(ppt_x*0.3090+(1-ppt_y)*-0.9511)BCRB_ppt_x+-0.8500*(ppt_x*0.5878+(1-ppt_y)*-0.8090)BCB_ppt_x+-0.9000*(ppt_x*0.8090+(1-ppt_y)*-0.5878)BCB_ppt_x+-0.9500*(ppt_x*0.9511+(1-ppt_y)*-0.3090)BCB]ppt_x+-1.0000*(ppt_x*1.0000+(1-ppt_y)*0.0000)B*Y3>B ppt_x<*1D ' =+ 4 8? CB ppt_yBC2B]ppt_y+-0.0500*(ppt_x*0.3090-(1-ppt_y)*0.9511)BCdB]ppt_y+-0.1000*(ppt_x*0.5878-(1-ppt_y)*0.8090)BCB]ppt_y+-0.1500*(ppt_x*0.8090-(1-ppt_y)*0.5878)BCB]ppt_y+-0.2000*(ppt_x*0.9511-(1-ppt_y)*0.3090)BCB_ppt_y+-0.2500*(ppt_x*1.0000-(1-ppt_y)*-0.0000)BC,B_ppt_y+-0.3000*(ppt_x*0.9511-(1-ppt_y)*-0.3090)BC^B_ppt_y+-0.3500*(ppt_x*0.8090-(1-ppt_y)*-0.5878)BCB_ppt_y+-0.4000*(ppt_x*0.5878-(1-ppt_y)*-0.8090)BCB_ppt_y+-0.4500*(ppt_x*0.3090-(1-ppt_y)*-0.9511)BCBappt_y+-0.5000*(ppt_x*-0.0000-(1-ppt_y)*-1.0000)BC&Bappt_y+-0.5500*(ppt_x*-0.3090-(1-ppt_y)*-0.9511)BCXBappt_y+-0.6000*(ppt_x*-0.5878-(1-ppt_y)*-0.8090)BCBappt_y+-0.6500*(ppt_x*-0.8090-(1-ppt_y)*-0.5878)BCBappt_y+-0.7000*(ppt_x*-0.9511-(1-ppt_y)*-0.3090)BCB_ppt_y+-0.7500*(ppt_x*-1.0000-(1-ppt_y)*0.0000)BC B_ppt_y+-0.8000*(ppt_x*-0.9511-(1-ppt_y)*0.3090)BCRB_ppt_y+-0.8500*(ppt_x*-0.8090-(1-ppt_y)*0.5878)BCB_ppt_y+-0.9000*(ppt_x*-0.5878-(1-ppt_y)*0.8090)BCB_ppt_y+-0.9500*(ppt_x*-0.3090-(1-ppt_y)*0.9511)BCB]ppt_y+-1.0000*(ppt_x*0.0000-(1-ppt_y)*1.0000)B*Y3>B ppt_y<*1D' =1:Bhidden*o3>+B#style.visibility<*1%(D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*?%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*A%(DV ' =%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*0%(D' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*1%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*1D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*1D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*A%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*?%(++0+.m ++0+/m ++0+0m ++0+8m ++0+8m ++0+>m ++0+>m ++0+?m ++0+?m +  0 (  (  q   ^87m?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yDdrs/shapexml.xmlU]o0}G?X~E+mLղ=iM;scxCRr]ߏsu>7ʚOގ9FJuns52{Wgm[`6l4b#om+ j XuK(PGdԐ2|TfW+-q[9*`OO93Ԡ Z  .7Ҋp}A`~t8E*0J x Ģ톅} (!B@xt>N"28$8X/l_QVC4."8H] ͡N>a &Rvh$ !9&z[ ZI&59d}Ked6#̅[\m )$>i ِY$޴)Z1VD`;B8~R[A Y{pC:o-KneW<?@AH  0޽h ? O'8 ey___PPT10Y+D=' = @B + 0(P (  q   ^Wm?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yDdrs/shapexml.xmlU]o0}G?X~E+mLղ=iM;scxCRr]ߏsu>7ʚOގ9FJuns52{Wgm[`6l4b#om+ j XuK(PGdԐ2|TfW+-q[9*`OO93Ԡ Z  .7Ҋp}A`~t8E*0J x Ģ톅} (!B@xt>N"28$8X/l_QVC4."8H] ͡N>a &Rvh$ !9&z[ ZI&59d}Ked6#̅[\m )$>i ِY$޴)Z1VD`;B8~R[A Y{pC:o-KneW<+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*F%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*F%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(+    pc (  q   ^0xm?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yDdrs/shapexml.xmlU]o0}G?X~E+mLղ=iM;scxCRr]ߏsu>7ʚOގ9FJuns52{Wgm[`6l4b#om+ j XuK(PGdԐ2|TfW+-q[9*`OO93Ԡ Z  .7Ҋp}A`~t8E*0J x Ģ톅} (!B@xt>N"28$8X/l_QVC4."8H] ͡N>a &Rvh$ !9&z[ ZI&59d}Ked6#̅[\m )$>i ِY$޴)Z1VD`;B8~R[A Y{pC:o-KneW<?@A{  \*m?,Content Placeholder 2P  -Space O(|E(G)|) Query time O(f log2n loglogn)T.    ,>?@AH  0޽h ? O'8 ey___PPT10Y+D=' = @B + '   (  q   ^Tm?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yDdrs/shapexml.xmlU]o0}G?X~E+mLղ=iM;scxCRr]ߏsu>7ʚOގ9FJuns52{Wgm[`6l4b#om+ j XuK(PGdԐ2|TfW+-q[9*`OO93Ԡ Z  .7Ҋp}A`~t8E*0J x Ģ톅} (!B@xt>N"28$8X/l_QVC4."8H] ͡N>a &Rvh$ !9&z[ ZI&59d}Ked6#̅[\m )$>i ِY$޴)Z1VD`;B8~R[A Y{pC:o-KneW<?@AH  0޽h ? O'8 e~___PPT10^+YDB' = @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*a%(+K  b Z  (  h   m0e0e ?,Content Placeholder 200p m (Approximate) Distance Oracle: Data-structure that can answer (approximate) distance queries Qdist(s,t) for any two vertices s, t (with a stretch of at most k)   ,^ :: C`J  F m?Title 1"~PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!Cedrs/shapexml.xmlTMo6 x-6BE 0,z,FeqMIy>R`x >{eMI#l̮_^~,D2 ikdO2sEp &]͂dOuவ͜AHz=[7k2m}3Քv@mC=%[2z l؇ ohf] N*:OPbXvu{:!C蝍s2x|i}GE_49ɈA"lѶ*&4:JX(5yNzCq0:*@+$05gl_^j5Gy4?Zs 4gktdvv07m*'VDv ]'xg7{{Ƴ_ c7~m=>jIH:O}RZ1tMjդ?!=+T<2l3 ]]敟dJbk(}5XLxus֨}9q]CrHo_*vUGa ~W_Ү;{yAO3aHLvv~Z@h{%XE&OSQtO+ on0|y$ z%) a+95{K|d;خ8u0[PK!z)}vdrs/downrev.xmlDKK1!\LqlZ( wIt0tf./͗iّB N `dk'mO%Jl%#EX.NOXI57abcTJ<֊ Ɖdsvp`gh gi(nAmsBO+Eצ3NK~;h q~6<K4}_zfӼ<ke(PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!Ce*drs/shapexml.xmlPK-!z)}vkdrs/downrev.xmlPKs@ HDistance oracles ,H  0޽h ? O'8 ey___PPT10Y+D=' = @B +"" D<P (      Fhm?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!Y%drs/shapexml.xmlXn8/@H-َ$@ڃ0(fMIv&=mz XCqy|8|~(IsK(JuN??ܝ)q)ENj3 .ksF#7aiF_mlbQDp%m7Z@ }Nb|ya`.e6sq2Sd6'H!dL@`{1g!MH"Zat;sz:csʽEnY!ΛZzR Y9_("G}z-2Hf90v*ޥ h2RT~`e5iH`K}cAk8dRzƐ k(uiȤE&d0mx<F?0{u7ݭHkO2]<+Glܯ,Ly S,u51_dO)VS>(9`oPRFz.!BEr iSD~@ yply<)(>f\PSGck &6wR~5JGތUxv]>3I:){&ZpyaM o2GV!$6UGMg4wEnu`GbW3znM#9)v_oX#H@Y'/g:0B  $+&lI6]6GDת&V7Q~NEm++͛j椕ʩ4{9U$^/ޙ-.v PK!drs/downrev.xmlDN0EH5HluxDnxvۂMilvX^X zVp1+@^[n> bBz&EX-Xi?Ԉ XRWIkCwĹ0Z9/kr~0ѽk;Wwown>]:=nA$aΡ+Qk! /.X((n4[\PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!Y%*drs/shapexml.xmlPK-!drs/downrev.xmlPK`p VDistance Oracles* ,3   0m,$D 0 BThm [Thorup-Zwick-05]: For every weighted undirected graph G it is possible to construct a data structure of size O(n1+1/k) that is capable of answering distance queries Qdist(s,t) in O(k) time, with multiplicative approximation factor d" 2k-1 (returns a distance estimate  such that dist(s,t,G)  (2k-1)" dist(s,t,G) )  P PG C G 3_C G O G /C G O G C G 0C G C G G G C G C G  G    G C t V* *H   0޽h ? O'8 e~___PPT10^+YDB' = @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* F%(+M 3 + p (  :   F8m?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!Y%drs/shapexml.xmlXn8/@H-َ$@ڃ0(fMIv&=mz XCqy|8|~(IsK(JuN??ܝ)q)ENj3 .ksF#7aiF_mlbQDp%m7Z@ }Nb|ya`.e6sq2Sd6'H!dL@`{1g!MH"Zat;sz:csʽEnY!ΛZzR Y9_("G}z-2Hf90v*ޥ h2RT~`e5iH`K}cAk8dRzƐ k(uiȤE&d0mx<F?0{u7ݭHkO2]<+Glܯ,Ly S,u51_dO)VS>(9`oPRFz.!BEr iSD~@ yply<)(>f\PSGck &6wR~5JGތUxv]>3I:){&ZpyaM o2GV!$6UGMg4wEnu`GbW3znM#9)v_oX#H@Y'/g:0B  $+&lI6]6GDת&V7Q~NEm++͛j椕ʩ4{9U$^/ޙ-.v PK!drs/downrev.xmlDN0EH5HluxDnxvۂMilvX^X zVp1+@^[n> bBz&EX-Xi?Ԉ XRWIkCwĹ0Z9/kr~0ѽk;Wwown>]:=nA$aΡ+Qk! /.X((n4[\PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!Y%*drs/shapexml.xmlPK-!drs/downrev.xmlPK`` Distributed distance oracles  Distance labeling schemes [P-99]6A 9,#3I  0s ,$D 0 Data structure stored in pieces at the graph vertices (as vertex labels) To answer distance query Qdist(s,t), it suffices to consult the labels L(s), L(T)I  f cC G O  G  8C G 8c 9  WWH  0޽h ? O'8 e___PPT10+YD~' = @B D9' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*I%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*J%(+    F (  :   Fm?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!Y%drs/shapexml.xmlXn8/@H-َ$@ڃ0(fMIv&=mz XCqy|8|~(IsK(JuN??ܝ)q)ENj3 .ksF#7aiF_mlbQDp%m7Z@ }Nb|ya`.e6sq2Sd6'H!dL@`{1g!MH"Zat;sz:csʽEnY!ΛZzR Y9_("G}z-2Hf90v*ޥ h2RT~`e5iH`K}cAk8dRzƐ k(uiȤE&d0mx<F?0{u7ݭHkO2]<+Glܯ,Ly S,u51_dO)VS>(9`oPRFz.!BEr iSD~@ yply<)(>f\PSGck &6wR~5JGތUxv]>3I:){&ZpyaM o2GV!$6UGMg4wEnu`GbW3znM#9)v_oX#H@Y'/g:0B  $+&lI6]6GDת&V7Q~NEm++͛j椕ʩ4{9U$^/ޙ-.v PK!drs/downrev.xmlDN0EH5HluxDnxvۂMilvX^X zVp1+@^[n> bBz&EX-Xi?Ԉ XRWIkCwĹ0Z9/kr~0ѽk;Wwown>]:=nA$aΡ+Qk! /.X((n4[\PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!Y%*drs/shapexml.xmlPK-!drs/downrev.xmlPK` Distributed distance oracles  Distance labeling schemes [P-99]6A 9,#3  0\%sR lThm [P-99]: For every weighted undirected graph G it is possible to construct an approximate distance labeling scheme of size (n1/k) capable of answering distance queries Qdist(s,t) with multiplicative approximation factor O(k)  G C G3CuC g G O G 'C G O G *C G B + H  0޽h ? O'8 ey___PPT10Y+D=' = @B +%  L D $ (  $ $ # Ls0e0e ?,Content Placeholder 4``0 s F-T distance oracle: Data structure capable of answering distance queries Qdist(s,t,F) between vertex pairs s,t, on the surviving graph G\F, subsequent to a failure event F 5,,J >: C`  $  v8?s0e0e?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK! ^udrs/shapexml.xmlUKo8@H$B"1n`D.z,FeH.I9v~}8=yFoxh%sV9SӕPۜ~<\\S< V@fv3\d0$pVj)-d =>XcNW2~z0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK! ^udrs/shapexml.xmlUKo8@H$B"1n`D.z,FeH.I9v~}8=yFoxh%sV9SӕPۜ~<\\S< V@fv3\d0$pVj)-d =>XcNW2~z3/  ,} @` 4 Fs?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK! ^udrs/shapexml.xmlUKo8@H$B"1n`D.z,FeH.I9v~}8=yFoxh%sV9SӕPۜ~<\\S< V@fv3\d0$pVj)-d =>XcNW2~z0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK! ^udrs/shapexml.xmlUKo8@H$B"1n`D.z,FeH.I9v~}8=yFoxh%sV9SӕPۜ~<\\S< V@fv3\d0$pVj)-d =>XcNW2~z t BB >B 3 Ԕ  BB ?B 3 Ԕe  BB @B 3 Ԕ / BB AB 3 Ԕ  BB BB 3 Ԕ  V BB CB 3 Ԕ  BB DB 3 ԔH ~  E B6CDE FԔ6-@  z y t F y t,$D 0BB G 3 Ԕy jz BB H 3 Ԕy z BB I 3 Ԕy B z y BB J 3 Ԕy z BB K 3 Ԕy  z Q BB L 3 Ԕy z BB M 3 Ԕy z * BB N 3 Ԕy ` z BB O 3 Ԕy z  BB P 3 Ԕy 8 z n BB Q 3 Ԕy z BB R 3 Ԕy  z G BB S 3 Ԕy } z BB T 3 Ԕy z BB U 3 Ԕy Vz BB V 3 Ԕy z  W BCDE FԔ@y   X B6CDE FԔ 6@  BB Y 3 Ԕ J BB Z 3 Ԕ  BB [ 3 Ԕ #BB \ 3 ԔYBB ] 3 ԔBB ^ 3 Ԕ1hBB _ 3 ԔBB ` 3 Ԕ @BB a 3 ԔvBB b 3 ԔBB c 3 ԔOBB d 3 ԔBB e 3 Ԕ']BB f 3 ԔBB g 3 Ԕ6BB h 3 Ԕen i BC'DE FԔ'@nsBB j 3 ԔsctBB k 3 Ԕs t-BB l 3 Ԕs t BB m 3 Ԕs tT BB n 3 Ԕs t BB o 3 ԔsF t| BB p 3 Ԕs t BB q 3 Ԕsm t BB r 3 Ԕs t7 BB s 3 Ԕs t BB t 3 Ԕs) t_ BB u 3 Ԕs t BB v 3 ԔsP t BB w 3 Ԕst BB x 3 ԔswtBB y 3 Ԕn?oABB z 3 Ԕc-n? { BC DE FԔ @H c-BB |B 3 ԔBB }B 3 ԔoBB ~B 3 Ԕ9BB B 3 ԔBB B 3 Ԕ+aBB B 3 ԔBB B 3 ԔRBB B 3 ԔBB B 3 ԔzBB B 3 Ԕ CBB B 3 ԔBB B 3 Ԕ5kBB B 3 Ԕ  BB B 3 Ԕ\  BB B 3 Ԕ &   B6CDE FԔ6-@  6aF        BQCEDE FQEQ @`0 Su<B B # 0 Su   BECDE FEE @`  <B  #      BECDE FEE @` 0  <B B #  0     BCEDE FE @``u<B B # `u   BCEDE FE @`u<B  # u   BCEDE FE @`u<B  # u   BCDDE FDD @`    B8CDE F88 @` 0 S1 <B B #  0 S1    BCDE F @``  <B  # `     BC8DE F8 @`` S0 <B  # ` S0    BDCDE FD @`  <B  #      BDCDE FD @`  <B  #      BCDE F @`  0 <B  #   0    BECDE FE @` = `0 <B  #  = `0    BECDE FEE @` ` <B B #  `    BECDE FEE @` `= <B  #  `=    BECEDE FEEEE @`{   BECDE FE @`I Z <B  # I Z    BECDE FE @` Z <B  #  Z    BECDE FE @` Z <B  #  Z BB  3 7  X   (BfCnDEF77$' )+ -20?2Z9Q=M?HBDH;O4R/T+X&[ [XVRM K KORV]af f fda _&X/R8HF?S=V9X4_-e$n nD$   pt@`K K    BECDE FE @`I Z0 <B  # I Z0    BCEDE FEE @`{   BECDE FE @` Z0 <B  #  Z0    BECDE FE @`0 Z <B  # 0 Z    BECDE FE @` 0 <B  #  0    BECDE FE @`  <B  #      BECDE FE @`S0 1 <B  # S0 1    BRCQDE4F> R(M<=L)QL<()=MR( @`M+  BRCQDE4F<8c R(M<=L)QL<()=MR(@M+   BQCRDE4F> Q)L==M(RM=)(=LQ) @`e    BQCRDE4F<8c Q)L==M(RM=)(=LQ)@e     BQCQDE4F> Q)L==M(QM=)(=LQ) @`~    BQCQDE4F<8c Q)L==M(QM=)(=LQ)@~     BQCQDE4F> Q)L=<M(QM=)(<LQ) @`   BQCQDE4F> Q)L=<M(QM=)(<LQ) @` ~   BQCQDE4F<8c Q)L=<M(QM=)(<LQ)@ ~    BQCQDE4F> Q(M==L)QL=()=MQ( @`  C Y   BQCQDE4F<8c Q(M==L)QL=()=MQ(@  C Y    BQCQDE4F> Q(M==L)QL=()=MQ( @`r    BQCQDE4F<8c Q(M==L)QL=()=MQ(@r    BQCQDE4F<8c Q(M==M)QM=()=MQ(@ -    BQCRDE4F> Q)M==M)RM=))=MQ) @`7 !   BQCRDE4F<8c Q)M==M)RM=))=MQ)@7 !    BQCQDE4F> Q)M==M)QM=))=MQ) @`7 e   BQCQDE4F<8c Q)M==M)QM=))=MQ)@7 e    BQCQDE4F> Q(M==L)QL=()=MQ( @` r C   BQCQDE4F<8c Q(M==L)QL=()=MQ(@ r C    BQCQDE4F> Q(M==L)QL=()=MQ( @`cr    BQCQDE4F<8c Q(M==L)QL=()=MQ(@cr     BRCQDE4F> R(M==L)QL=()=MR( @`o Y   BRCQDE4F<8c R(M==L)QL=()=MR(@o Y    BQCQDE4F> Q(L==L(QL=((=LQ( @`+ |Y   BQCQDE4F<8c Q(L==L(QL=((=LQ(@+ |Y    BQCQDE4F> Q)L=<M(QM=)(<LQ) @`   BQCQDE4F<8c Q)L=<M(QM=)(<LQ)@    BCDE F @`  <B  #      BCDE F @``  <B  # `     BCDE F @`S 0 <B B # S 0    BCDE F @` 0 <B  #  0    BCDE F @`  <B  #      BCDE F @`` = <B B # ` = <B  #  <B  # {<B  # {   BECEDE FEEE @`6.{<B  # 6.{   BCEDE FEE @`G6{<B  # G6{   BCEDE FEE @``6{<B  # `6{  BQCQDE4F<8c Q)L=<M(QM=)(<LQ)@   BQCQDE4F> Q)L=<M(QM=)(<LQ) @`R  BQCQDE4F<8c Q)L=<M(QM=)(<LQ)@R   BQCQDE4F> Q)M==M(QM=)(=MQ) @`|R  BQCQDE4F<8c Q)M==M(QM=)(=MQ)@|R   BQCQDE4F> Q(M==M)QM=()=MQ( @` -    BQCQDE4F> Q(M<=L)QL<()=MQ( @`o_  BQCQDE4F<8c Q(M<=L)QL<()=MQ(@o_   BQCQDE4F> Q(M<=L)QL<()=MQ( @`7_  BQCQDE4F<8c Q(M<=L)QL<()=MQ(@7_   BRCQDE4F> R(M<=L)QL<()=MR( @`W_  BRCQDE4F<8c R(M<=L)QL<()=MR(@W_   BQCQDE4F> Q)M==M)QM=))=MQ) @`7  BQCQDE4F<8c Q)M==M)QM=))=MQ)@7   BQCQDE4F> Q)M==M(QM=)(=MQ) @`|  BQCQDE4F<8c Q)M==M(QM=)(=MQ)@|   BQCQDE4F> Q)L=<M(QM=)(<LQ) @`  BQCQDE4F<8c Q)L=<M(QM=)(<LQ)@   BQCQDE4F> Q(L=<L(QL=((<LQ( @` >Y   BQCQDE4F<8c Q(L=<L(QL=((<LQ(@ >Y    BQCQDE4F> Q(M<=L)QL<()=MQ( @`1! r   BQCQDE4F<8c Q(M<=L)QL<()=MQ(@1! r     BQCRDE4F> Q)M==M)RM=))=MQ) @`1e     BQCRDE4F<8c Q)M==M)RM=))=MQ)@1e      BQCQDE4F> Q)M==M)QM=))=MQ) @`1     BQCQDE4F<8c Q)M==M)QM=))=MQ)@1      BQCQDE4F> Q)L=<M(QM=)(<LQ) @` >   BQCQDE4F<8c Q)L=<M(QM=)(<LQ)@ > '  B(fpm ,$ 0 B0(v)D G$O$G$ '  Bpl pN ,$ 0 B1(v)D G$33O$33G$33 '  Btq pm ,$ 0 B2(v)D G$O$G$ P  s *޽h ?"` 33 y ___PPT10Y .sn+(D ' = @B D@ ' = @BA?%,( < +O%,( < +D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*F%(++0+ ++0+ ++0+ +&wL0 022(  x  c $40`    0|` p jnBasic notion: A tree T covering the -neighborhood of v8 G C G C B  f G fB C G $8X F x   x Z2  s *8  ] Z2  s * P Z2  s *6 x Z2  s *8 Z2   s * ] Z2   s *  5] Z2   s *  P Z2   s *  TB   c $D 6 TB  c $D 0 TB  c $D0 W TB  c $D  TB  c $D0 W Z2  s *  ] TB  c $D< TB  c $D < 0 TB  c $D 0 0 Z2  s *  Z2  s *8  P Z2  s * P Z2  s *  P TB  c $D < < TB  c $D_ < _ 0 TB  c $D< 0 2  BIENG}THQ `T|Ij+`T|Ij+`T|Ij+`T  2  [ABIENHQ `TIj+`TIj+`TIj+`T ~ 0 TB  c $D<  TB   c $D_ P TB ! c $D 0 TB " c $D _ 0 TB # c $D0 _ W z   $ 0  ,$@ 0ZB % s *D) v ZB & s *D) i ZB ' s *D) ZB ( s *D) ZB ) s *D) ! ZB * s *D) ZB + s *D)H! Hi ZB , s *D)p  ZB - s *D)@  . B m ,$ 0 Uv F  2 / s * p  ,$D 02 0 Bod ,$D 0' 1 BԦ  ,$ 0 B2(v)D G O G  & 2 B& D,$ 0  covering T> G C G   H  0޽h ?/  33 y ___PPT10Y .sn+dD ' = @B D@ ' = @BA?%,( < +O%,( < +D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*.%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*/%(D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*1%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2%(++0+. ++0+1 ++0+2 +, p! !(    # Ʀ0e0e ?,Content Placeholder 4``00$@ 0 H@___PPT9" 2G = weighted undirected graph A tree cover TC(r,k) : collection of trees {T1,& ,Tl} such that For every v there exists a tree Ti such that Br(v) Ti For every Ti and every vTi, dist(v,ri,Ti) (2k-1) r For every v, the number of trees that contain v is O(kn1/k)._                  / b+: W$&n    v0e0e?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!Sdrs/shapexml.xmlUn:_@p[~q!rȽp#rѥ1(5E$Iq(vCh<<}+Ɏ['ÐAU 9=pG?sk2g+6ޛl0p-pZ0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!Sdrs/shapexml.xmlUn:_@p[~q!rȽp#rѥ1(5E$Iq(vCh<<}+Ɏ['ÐAU 9=pG?sk2g+6ޛl0p-pZ'$$"@`$  $  v4L0e0e?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!G+&drs/shapexml.xmlUKo8@H$B"1n`D.z\(bM\rIqz(yFoxh%sV9SӕPۜ~<\\S< VLk %Yid6C>*˫)*R[T. !f)vPug5W0,!A!;hW]u-zc%?b/!EV6X*S CVpr-)xxɛJ]Ő\Ҁ;0}[&gؚyP5B=0zWֲ[J9DZˮx9x+x(S!C66G2VHsŗ!7UFKSGuiE(q+cyVH~%րuMol jv9]!a*>UHpi|Q/E ?;e!ܒi>PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!G+&*drs/shapexml.xmlPK-!*9:drs/downrev.xmlPK``   dConnectivity Oracle (reminder)* , ,H $ 0޽h ? O'8 ey___PPT10Y+D=' = @B +f   4 (  4 4 # |0e0e ?,Content Placeholder 4``00<$D 0  *Construction The algorithm has log(nW) iterations Iteration i handles distances d" 2i Gi = graph obtained by removing from G all edges of weight > 2i      #  ,1> @` 4 Fo?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK! ^udrs/shapexml.xmlUKo8@H$B"1n`D.z,FeH.I9v~}8=yFoxh%sV9SӕPۜ~<\\S< V@fv3\d0$pVj)-d =>XcNW2~z+B#style.visibility<*4 2%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*42V%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4V%(+ <(  <  < # l¨0e0e ?,Content Placeholder 4`<$D 0  Iteration i: Construct a tree cover TCi with =2i and k Gi|T = subgraph of Gi induced by T vertices For each TTCi , construct connectivity oracle Conn_OrT on Gi|T For each vertex v store pointer to tree Ti(v) TCi containing B(v)$     e          $$$$$$  $     m $ !%) @` < Fd?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK! ^udrs/shapexml.xmlUKo8@H$B"1n`D.z,FeH.I9v~}8=yFoxh%sV9SӕPۜ~<\\S< V@fv3\d0$pVj)-d =>XcNW2~z+B#style.visibility<*< 9%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<9f%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<f%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(+  (  PL (  L L # 誨0e0e ?,Content Placeholder 4``0  :Lemma The size of the data structure is O(fkn1+1/klog(nW))X; "   @` L F?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK! ^udrs/shapexml.xmlUKo8@H$B"1n`D.z,FeH.I9v~}8=yFoxh%sV9SӕPۜ~<\\S< V@fv3\d0$pVj)-d =>XcNW2~z0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!Cꂍdrs/shapexml.xmlUKo8@H$B"1n`D.z\(bM\rIqz(yFoxh%sV9SӕPۜ~<\\S< VLk %Yid6C>*˫)*R[T. !f)vPug5W0,!A!;hW]u-zc%?b/!EV6X*S CVpr-)xxɛJ]Ő\Ҁ;0}[&gؚyP5B=0zWֲ[J9DZˮx9x+x(S!C66G2VHsŗ!7UFKSGuiE(q+cyVH~%րu+4N 8쟯K`1xGF^M.XI߻-uXXR[qkM̷rwb1(.n~S nѸGMlݪ97>m4 qu9l%[MbW^x Fn1& [6͖W?PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!Cꂍ*drs/shapexml.xmlPK-!drs/downrev.xmlPK``   IAnswering Queries ,H T 0޽h ? O'8 ey___PPT10Y+D=' = @B +I p h \ (  \ \ # l$0e0e ?,Content Placeholder 4``0  ZLemma Consider vertices s,t and failure set F. Let d=dist(s,t,G\F). The estimated distance  returned by Qdist(s,t,F) satisfies d  (8k-2)(f+1)d   ,  j * $*H @` \ F,5?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK! ^udrs/shapexml.xmlUKo8@H$B"1n`D.z,FeH.I9v~}8=yFoxh%sV9SӕPۜ~<\\S< V@fv3\d0$pVj)-d =>XcNW2~z0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK! ^udrs/shapexml.xmlUKo8@H$B"1n`D.z,FeH.I9v~}8=yFoxh%sV9SӕPۜ~<\\S< V@fv3\d0$pVj)-d =>XcNW2~z0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!vdrs/shapexml.xmlUKo8@H$B"1n`D.z\(bM\rIqz(yFoxh%sV9SӕPۜ~<\\S< VLk %Yid6C>*˫)*R[T. !f)vPug5W0,!A!;hW]u-zc%?b/!EV6X*S CVpr-)xxɛJ]Ő\Ҁ;0}[&gؚyP5B=0zWֲ[J9DZˮx9x+x(S!C66G2VHsŗ!7UFKSGuiE(q+cyVH~%րu+B#style.visibility<*l<{%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*l{%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*l)%(+" t(  t t # 0e0e ?,Content Placeholder 4p`<$D 0  Use hierarchy of tree covers as in distance oracle. To route from s to t, try increasingly higher levels Suppose dist(s,t,G) d" 2i There is a tree T TCi that contains Br(s) for r=2i ! T contains also the destination t ` % q   g,e$e e >q 0 @`  t F?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!vdrs/shapexml.xmlUKo8@H$B"1n`D.z\(bM\rIqz(yFoxh%sV9SӕPۜ~<\\S< VLk %Yid6C>*˫)*R[T. !f)vPug5W0,!A!;hW]u-zc%?b/!EV6X*S CVpr-)xxɛJ]Ő\Ҁ;0}[&gؚyP5B=0zWֲ[J9DZˮx9x+x(S!C66G2VHsŗ!7UFKSGuiE(q+cyVH~%րu` `ZB t s *D> ` 0`ZB tB s *D>`0` t <v@   oT6 G O  N T p t T pf2 t 6>` p t <ԌTP pp  Br(s)N G l } tc},$D 0Z2 t s * ` t <Ȩ} Wt G  H t 0޽h ? O'8 eR J ___PPT10* +&D ' = @B D ' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*t4i%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*ti%(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* t%(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(+ {p(  ~  # ̪0e0e ?,Content Placeholder 4p <$D 0  rT is of depth d" (2k-1)"2i The route from s to t is at most k"2i+2 = O(k" dist(s,t,G)) Only remaining problem: handle edge disconnections&  $ e   #   e e 7,F : @`  F<?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!vdrs/shapexml.xmlUKo8@H$B"1n`D.z\(bM\rIqz(yFoxh%sV9SӕPۜ~<\\S< VLk %Yid6C>*˫)*R[T. !f)vPug5W0,!A!;hW]u-zc%?b/!EV6X*S CVpr-)xxɛJ]Ő\Ҁ;0}[&gؚyP5B=0zWֲ[J9DZˮx9x+x(S!C66G2VHsŗ!7UFKSGuiE(q+cyVH~%րu` `ZB  s *D> ` 0`ZB  B s *D>`0`   <Lêv@   oT6 G O  N T p   T pf2   6>` p   <٪TP pp  Br(s)N G F }  }Z2  s * `  <4} Wt G  H  0޽h ? O'8 e___PPT10+ CD~' = @B D9' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*X%(+=# yP0 (  R  # 0e0e ?,Content Placeholder 4`   rConsider this tree T" $# @`z  RA??Picture 2`Y  DTextBox 7  4___PPT11 B___PPT9$  Ou  Y  D(TextBox 8 w 4___PPT11 B___PPT9$  Ov    F?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!vdrs/shapexml.xmlUKo8@H$B"1n`D.z\(bM\rIqz(yFoxh%sV9SӕPۜ~<\\S< VLk %Yid6C>*˫)*R[T. !f)vPug5W0,!A!;hW]u-zc%?b/!EV6X*S CVpr-)xxɛJ]Ő\Ҁ;0}[&gؚyP5B=0zWֲ[J9DZˮx9x+x(S!C66G2VHsŗ!7UFKSGuiE(q+cyVH~%րu@ `B  0D>@ `B  0D>   BN- M Tu(e)H GOG l p: pf ,$@ 0  F*TextBox 11 : 4___PPT11 B___PPT9$  Tv(e)X G3O3G3G3 ZB  s *D3) ZB B s *D3)ZB  s *D3)@ ZB  s *D3)p@ ZB B s *D3)p ZB B s *D3)  ZB  s *D3)    \H=?,Content Placeholder 4@`` ,$ 0 2<disconnects T into two connected components, Tu(e) and Tv(e)=     ,-$# @`H  0޽h ? O'8 ed \ ___PPT10< +:D' = @B Dk' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(DY' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(+p+0+  ++0+ +! ,$ | (  | | # h_0e0e ?,Content Placeholder 40 <$@ 0  A recovery edge of e is any edge e of G that connects Tu(e) and Tv(e). Define for each edge eT a recovery edge rec(e).z     P7$ @`z | RA??Picture 2`Y | DLNTextBox 7  4___PPT11 B___PPT9$  Ou  Y | DQTextBox 8 P  4___PPT11 B___PPT9$  Ov  l  |,$D 0B  | hp0),Straight Connector 12#"@ PK!!|[Content_Types].xmlN0DH+J8 @Mb- ߳i Hݙ77i3$.+)mp{-߷Oŝ :3-@r\^}Fr9+EvP" O&z0=U6`E^>Bt>Cq({Q6|GvS̤Vv(dzdߦ⳼8әt@)jJO7VS$)&Zí0 U\+@|H-"4ڇO5yUsz[j:dM>ͯE=)aijjaE(a~>?<;P״N"VR[튿WBJC*4.-~Z./M?M~eoPK!a=drs/downrev.xmlDOMk@Սƪ"B^4}N`v6d1Pms5.Ԟ L' (ۚK Tdg2K3|,!24P֡a8r߾s(v^ck,Iaͱ–3|_\>yPB6OK<@onPK-!!|[Content_Types].xmlPK-!3X 2_rels/.relsPK-!\/drs/connectorxml.xmlPK-!a=drs/downrev.xmlPK  | FxTextBox 13>`4___PPT11 B___PPT9$  rec(e)* 33   | Ft?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!vdrs/shapexml.xmlUKo8@H$B"1n`D.z\(bM\rIqz(yFoxh%sV9SӕPۜ~<\\S< VLk %Yid6C>*˫)*R[T. !f)vPug5W0,!A!;hW]u-zc%?b/!EV6X*S CVpr-)xxɛJ]Ő\Ҁ;0}[&gؚyP5B=0zWֲ[J9DZˮx9x+x(S!C66G2VHsŗ!7UFKSGuiE(q+cyVH~%րu+B#style.visibility<*|Iz%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*|%(+    0 (    # IJ0e0e ?,Content Placeholder 4`0  .Slight simplification for analysis: Assume the graph edges are sorted - e1,& ,em, and choose rec(e) for every e to be the first recovery edge ei of e $$   3>N- @`  Fx?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!vdrs/shapexml.xmlUKo8@H$B"1n`D.z\(bM\rIqz(yFoxh%sV9SӕPۜ~<\\S< VLk %Yid6C>*˫)*R[T. !f)vPug5W0,!A!;hW]u-zc%?b/!EV6X*S CVpr-)xxɛJ]Ő\Ҁ;0}[&gؚyP5B=0zWֲ[J9DZˮx9x+x(S!C66G2VHsŗ!7UFKSGuiE(q+cyVH~%րu   63#. @`B  f3)*Straight Connector 4#"@PK!!|[Content_Types].xmlN0DH+J8 @Mb- ߳i Hݙ77i3$.+)mp{-߷Oŝ :3-@r\^}Fr9+EvP" O&z0=U6`E^kKdr2J7}֓זd)M!7|Ij odW=7iP?/t]xȞ|Bt0ɳBJtnƘ!'QVp4{O1$^ o"܋PUqZj% ɝݼ-%-W8+'kJDqOگg%+{ՅGI,q!a 5?8G,~u#\mk-#/N?N3wPK!̳drs/downrev.xmlDOj@ă*Rj$$;vGM߾+zwVF! qm˵ Tdg2C6BRjB8h cՐ8q}p( Zۀz=ϲvrjhp:]mYԝ c&/v Jh`PK-!!|[Content_Types].xmlPK-!3X 2_rels/.relsPK-!k/drs/connectorxml.xmlPK-!̳drs/downrev.xmlPKp  B  hZ),Straight Connector 14#"@PK!!|[Content_Types].xmlN0DH+J8 @Mb- ߳i Hݙ77i3$.+)mp{-߷Oŝ :3-@r\^}Fr9+EvP" O&z0=U6`E^W`9˺4l٥a{'(8g*t:KsEhNQ xHćI= 6suD(R:"+Qbߓo'?IbE 4Pa=gxy4*} .o(]]wlyxaal^PK!ʰdrs/downrev.xmlDOj@}/)RBERWBQ(R!;MBawB9,ףՅBl=f9(ۖkߧ({d"WK,.*p,@#2ZǪ!1q~|p( Zۀz=vrjhp<;ݴ۰.?w_}wZ<7PBM_t^PK-!!|[Content_Types].xmlPK-!3X 2_rels/.relsPK-!eOq/drs/connectorxml.xmlPK-!ʰdrs/downrev.xmlPK p B  B hZ),Straight Connector 18#"@ PK!!|[Content_Types].xmlN0DH+J8 @Mb- ߳i Hݙ77i3$.+)mp{-߷Oŝ :3-@r\^}Fr9+EvP" O&z0=U6`E^$vkY[ҿgmH9yݝٙ)s뤆n%ljpq4y-SxMw!X 25zo,s͖wMwBێy &3;yT62VЯ3k_["[Xw2zڒbN1},!`1M]lΪAn;C xǘX\3GP\UZ2ԴEtVጴXOL8b6=IYbu߳ j$H^!_4NaVJnWʒ4/HMF s,0S<(kܶ&[=),CX 8O Gk;NMEK';|PK!}Cdrs/downrev.xmlDOj0b% YZiC,&XcByu`SkA\8Ssro@lqLF'D9"OQCBJ鋊,k#:!®[ |Tj%-*l鵢zT?~qո\$eM3@CLdPK-!!|[Content_Types].xmlPK-!3X 2_rels/.relsPK-!B^/drs/connectorxml.xmlPK-!}C drs/downrev.xmlPK pB  B hZ),Straight Connector 20#"@PK!!|[Content_Types].xmlN0DH+J8 @Mb- ߳i Hݙ77i3$.+)mp{-߷Oŝ :3-@r\^}Fr9+EvP" O&z0=U6`E^t8 0#G/n">Z|Ct4 fDžڃ+HZi)A*fܜLD'z*X|OI*0L·]M82uI? 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Subcase 1 (not too hard): e2 does not appear on the alternative path P(e1) via rec(e1) (and s,t are connected in Gi|T\{e1,e2}):   k     )      ,Z"@`  RA??Picture 2G ,$D 0  F?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!vdrs/shapexml.xmlUKo8@H$B"1n`D.z\(bM\rIqz(yFoxh%sV9SӕPۜ~<\\S< VLk %Yid6C>*˫)*R[T. !f)vPug5W0,!A!;hW]u-zc%?b/!EV6X*S CVpr-)xxɛJ]Ő\Ҁ;0}[&gؚyP5B=0zWֲ[J9DZˮx9x+x(S!C66G2VHsŗ!7UFKSGuiE(q+cyVH~%րu+B#style.visibility<*6%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*6t%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(DL' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(DL' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(+8+0+  +   k (    #  0e0e ?,Content Placeholder 4`T <4___PPT9 >Subcase 2 (hardest): both e1 is on P(e2) and e2 is on P(e1). )                 8 @`  F` ?Title 1"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!vdrs/shapexml.xmlUKo8@H$B"1n`D.z\(bM\rIqz(yFoxh%sV9SӕPۜ~<\\S< VLk %Yid6C>*˫)*R[T. !f)vPug5W0,!A!;hW]u-zc%?b/!EV6X*S CVpr-)xxɛJ]Ő\Ҁ;0}[&gؚyP5B=0zWֲ[J9DZˮx9x+x(S!C66G2VHsŗ!7UFKSGuiE(q+cyVH~%րu+B#style.visibility<*%(+8+0+ +   _ (  Z  # $;0e0e ?,Content Placeholder 4``0  zStore for e1 (similarly, for each edge eT) two additional recovery edges recu1(e1) and recv1(e1). 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