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 % ?On the Memory Requirements of XPath Evaluation over XML Streams@@(NZiv Bar-Yossef Marcus Fontoura Vanja Josifovski IBM Almaden Research Center *OP3Preliminaries: XML  Preliminaries: XPath 1.0  XML Streams  Streaming XML AlgorithmsXFilter and YFilter [Altinel and Franklin 00] [Diao et al 02] X-scan [Ives, Levy, and Weld 00] XMLTK [Avila-Campillo et al 02] XTrie [Chan et al 02] SPEX [Olteanu, Kiesling, and Bry 03] Lazy DFAs [Green et al 03] The XPush Machine [Gupta and Suciu 03] XSQ [Peng and Chawathe 03] TurboXPath [Josifovski, Fontoura, and Barta 04] & S+3333"3 333 &33 ;       Our ResultsSpace lower bounds for evaluating XPath on XML streams A streaming XML algorithm Matches the lower bounds on a large fragment of the language Uses space sub-linear in the query size rather than exponential in the query sizexS$lP AH   Related Work  Data Complexity [Vardi 82]  3F(Q,D) Evaluation function of a query Q on document D. FQ(D) Evaluation function of a fixed query Q on document D. Data complexity on Q: Complexity of best algorithm for FQ on worst D. Worst-case data complexity: maxQ (complexity of FQ). We characterize the data complexity of FQ separately for each Q (not just the worst-case one). e3323333/3JB(%xA+XPath Fragment B,XPath Fragment (cont.)D.XPath Fragment (cont.) Query Frontier Size Document Recursion Depth Document Depth  New algorithm #Proof of Theorem 1 Critical Document   Main Lemmas  One-way Communication Complexity !  3! Reduction  3"Fooling Set Technique -&Proof of Lemma 1 .'Proof of Lemma 1 Proof of Lemma 1 (cont) E/Proof of Claim (example) 2 +$ AlgorithmUses the query as an NFA Based on three global data structures Pointer array Validation array Level array Matches the lower bounds for a fragment of XPath.6?+2?+2$Algorithm Example Run %&' (!)"*#1*Conclusion: our Contributions!Space lower bounds on the instance data complexity of XPath on XML streams: In terms of Query Frontier Size In terms of Document Recursion Depth In terms of Document Depth A streaming XML algorithm Matches the lower bounds on a fragment of the language Does not use finite-state automataL$ald$ZlP3 33 3 Z  XPath 1.0   XPath 1.0 ,% Reduction  3/P456789:;= > ? @  ` Ot{h______` M <ff33̙3` +ffO=ff̙H7` fff3f̙` Tff33ff` 0Ky{kOz` )R{f` GiIfff̙fR` ̙|̙3f` 3ff~>?" dd@'?lFd@  nK'o`P( n?" dd@   @@``PT     o (`0p>>  ''(  ZB  c $D"`   6D "M }  X Click to edit Master title style!!  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X Click to edit Master title style!!    0 PODS Josifovski 1 Fagin 3 0<2B F3BF3BFfBF3BF3BF3B FfBF3B F3BFfB F3BF3BF3BF3BFfBF3B F3BFfB F3BF3B F3 BPS  <  %2  0\/-,$@ 0 @ conference  32  0X- ,$@ 0 :name32  0\-(  ,$@ 0 =speaker32  0h`- 5 + ,$@ 0 :name32   0t[-  ,$@ 0 Y paper_cnt  3 2   0W-,$@ 0 :root3z  S ,$@ 0z @ S K ,$@  0z @ S  0 - ,$@  0z  S  -^ ,$@  0z @ S { ,$@  02  0l- i ,$@  0 =speaker32  0q-W blG ,$@ 0 :name32  0t- F ,$@ 0 Y paper_cnt  3 z  S R> ,$@ 0z @ S  g0W ,$@ 0z  S  0 ,$@ 0  s *+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(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<*%(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<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(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<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*!%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*#%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*&%(++0+- ++0+- ++0+- ++0+- ++0+ - ++0+ - ++0+- ++0+- ++0+- ++0+- ++0+- ++0+- ++0+- ++0+- ++0+- ++0+- ++0+ - ++0+!- ++0+"- ++0+#- ++0+$- ++0+%- ++0+&- +& g ZK0 !!P2o(  ~"  s *X-M }  -  " 0z! ~4/conference[name = PODS]/speaker[paper_cnt > 1]/name50 2 3333 333,  2 # 6 zS"`?  @ conference  32 $ 0z [5  :name32 % 0TzRMa :root3F & S aF ' S    + 0z ;, @Document 0 2  , 0 z 1D+ =Query0 2 - s * z0 },$D 0 kResult: { x7 }@0 2 2 / 0&z"` yY  =speaker32 1 0|*z"`, M :name32 3 0-z ) Y paper_cnt  3 L 5@ c $ & L 6 c $Y &., L 7@ c $Y \&  O 6$3z ?"6@ NNN?N   F= PODS$0 2 P <T7z ?"6@ NNN?N u  C> 1$0 22 Q 0:z( M  @ conference  32 R 0?zH 8  :name32 S 0Bz   =speaker32 T 0lGzF 5 + 6 :name32 U 0Ez  Y paper_cnt  3 2 V 0Nzxh :root3F W S h( F X@ S M  F Y@ S  0 -F F Z S  -^ F [@ S M { k 2 \ 0Rz i  =speaker32 ] 0Vz bl :name32 ^ 0 [z. FS Y paper_cnt  3 F _ S M R F `@ S  g0 F a S  0.  b s *(_zC"?  :PODS 2f c s *XczC"?o  @ Josifovski 2 f d s *fzC"?o ;Fagin 2f e s * jzC"?&z 71 2f f s *lnzC"?C0* 73 2f g s *qzC"?dK Dx0& 2  h s *luzC"?5   Dx1& 2  i s *yzC"?5 ,  Dx2& 2  j s *~zC"?x W_  Dx3& 2  k s *dzC"? <  Dx6& 2  l s *4zC"? 4  Dx4& 2  m s *zC"?   Dx5& 2  n s *zC"? b  Dx7& 2  o s *zC"?Z 0A  Dx8& 2 H  0޽h ? %#& #$' #/5/16/37VQWQSXSTYSUZQR[Q\_\]`\^a 3fffff3̙3f̙___PPT10.IpU+Ӭ!DO' = @B D ' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*-%(+8+0+-z +J  g  &(  r  S zM }  z   0z * y5XML stream: XML document arriving as a one-way stream(60 2 *$  0lzP lm",$ 0 ,Critical resources: Memory Processing timeH0 21 2g  0tz^!30 ,$ 0 aWhy XML streams? For transferring XML between systems For efficient access to large XML documentsH0 2Q1 2PjH  0޽h ? 3ff~\T___PPT104.IPFY+TD' = @B DS' = @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<*%(+p+0+z ++0+z +} g $(  r  S zM }  z r  S z;  z H  0޽h ? 3ff~___PPT10i.I`?+D=' = @B + g n(  r  S pM }     S z; `<$@ 0  *Ft`H  0޽h ? 3ff~___PPT10.I+EDZ' = @B D' = @BA?%,( < +O%,( < +DL' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*9S%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*S%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(+ g ((  (r ( S 4zM }  z  ( 0&! ; ` 4Space complexity of XPath evaluation over non-streaming XML documents [Gottlob, Koch, Pichler 03], [Segoufin 03] Space complexity of XPath evaluation over streams of indexed XML data [Choi, Mahoui, Wood 03] Space complexity of select-project-join queries over relational data streams [Arasu et al 02] sZZZ* 3+363 33 33tIN\ H ( 0޽h ? 3ff~___PPT10i.vJ`+D=' = @B +  g ( (  r  S |M }  |   s * | "6 ?; W<$@ 0 | *XYYhH  0޽h ? 3ff~ZR___PPT102.I`|V+;Y"vD' = @B D' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*c%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*ce%(+ g  (  r  S T-|M }  | *  <9! ?"6@ NNN?Ny  1. Queries are subsumption-free "!0 2! 2  6d6!S"`? O  @ conference  32  0t  C<&0 22  6$|S"`?S d  @ conference  32  0,| 1 u&  Y paper_cnt  3 2  0l|' :root3F  S vS F @ S   2  08|   Z author_cnt  3    6?"0@NNN?N   ! 6?"0@NNN?N   " <| ?"6@ NNN?N   F< 30&0 2 # < | ?"6@ NNN?N *  D> 30$0 2H  0޽h ?       ! 3ff~___PPT10i.Op1j+D=' = @B +[ g rj (  x  c $ĄM }     < ?"6@ NNN?Nb[ f(3. Queries consist of conjunctions only ")0 2)*  <؊ ?"6@ NNN?Nf B4. Queries are  star-restricted ""0 2"H  0޽h ? 3ff~___PPT10i.Op1j+D=' = @B +!" g  <(  r  S M }   J ' 0( D<4___PPT9 BFrontier at u: u, its siblings, and the siblings of its ancestors.*C1 2 68X\ , s *C"?! ,$D 0 Theorem 1: For all queries Q in the fragment, stream-space(FQ) = W(FrontierSize(Q)).W0 2  333,7 - 0<6yV R Definitions:* 0 2 P . 0( H@8___PPT9 *FrontierSize(Q): size of largest frontier.*+1 28X2 / 6йS"`?Gv @ conference  32 0 0/ $  :name32 1 0 :root3F 2@ S RGF 3 S vRnd  4 0ŁrWa =Query0 22 5 0ʁ"`S .  =speaker32 6 0́"` ,  :name32 7 0 с R v  Y paper_cnt  3 L 8@ c $vRS L 9 c $  L :@ c $ 4  ; 6ց ?"6@ NNN?Nv ]  F= PODS$0 2 < <ځ ?"6@ NNN?NP ~7  C> 1$0 2H  0޽h ?_1/2/03/5856957: 3ff~___PPT10.IX]+RWDS' = @B D' = @BA?%,( < +O%,( < +D' =%(Dy' =%(D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*7D' =1:B solid*a3>Bfill.type<*7D' =1:B true*]3>Bfill.on<*7D# ' =%(D ' =%(D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*7D' =1:B solid*a3>Bfill.type<*7D' =1:B true*]3>Bfill.on<*7D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*6D' =1:B solid*a3>Bfill.type<*6D' =1:B true*]3>Bfill.on<*6D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*0D' =1:B solid*a3>Bfill.type<*0D' =1:B true*]3>Bfill.on<*0DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(+8+0+, +`3 g PH)Y(   Q s *C"? W,$D 0 Theorem 2: For all queries Q in the fragment that have at least one  // node, stream-space(FQ) = W(recDepthQ(D)).v0 2 E 3 3333,X r  S XM }   2  6S"`?   T//part232  0   <number2  0dhG X :root3F  S X F   S  H2   0"`  :nameL @ c $ 2 & 0!0  :part32 ' 0,    <number32 ) 0P e(  :name32 + 0Gu :root3F , S uF - S 0 " F .@ S @ a F / S q  2 1 0b   :name3F 4 S t^  < s *C"?h O Dx0& 2  = s *xC"? Dx1& 2  > s *C"?   Dx3& 2  ? s *<$C"? Z  Dx4& 2  A s *(C"? Q  Dx4& 2  B s *&C"?0 Dx6& 2  C s *0C"? 0  Dx7& 2  D s *5C"?loS  Dx2& 2 L E c $ L H c $@ [  J 09  9  Definition: recDepthQ(D): Max number of nodes in D that lie on one root-to-leaf path and  path match the same node in Q.Bz0 2 a c 8X K 0|=;9j5 B Document D 0 2  L 0K  ?Query Q0 22 R 0|N" $q  :part32 S 0Q ,& :part32 T 0U  <number3 U s *tYC"?   Dx5& 2  V s *h^C"? v@ @ Compressor 2 f W s *TaC"?   812 2f X s *4eC"?y t`  B Refrigerator 2 f Y s *iC"? 9456 2fH  0޽h ?@  +&,&R-R).RS/1&4STE'RH 3ff~___PPT10.I`є+ LD<D,' = @B D' = @BA?%,( < +O%,( < +D' =%(Dy' =%(D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*D# ' =%(D ' =%(D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*&D' =1:B solid*a3>Bfill.type<*&D' =1:B true*]3>Bfill.on<*&D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*RD' =1:B solid*a3>Bfill.type<*RD' =1:B true*]3>Bfill.on<*RD!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*SD' =1:B solid*a3>Bfill.type<*SD' =1:B true*]3>Bfill.on<*SD' =%(Dy' =%(D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*RD' =1:B solid*a3>Bfill.type<*RD' =1:B true*]3>Bfill.on<*RDA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Q%(+8+0+Q +{, g !Vs(  x  c $tM }   T 8 Bv ?"6@ NNN?N; / :Definition: depth(D): Length of longest root-to-leaf path.,;0 2B&B (2 9 0{O :part32 : 0h   <number32 ; 0Ă !G  :name32 < 0 f :root3F = S F > S OAF ?@ S _ ) F @ S   2 A 0h~ :name3F B S 0 C s *ЎC"?vn Dx0& 2  D s *XC"?$_  Dx1& 2  E s *C"?n Dx3& 2  F s *C"? H  Dx4& 2  G s *C"?$    Dx4& 2  H s *C"? s  Dx6& 2  I s *hC"? 0  Dx7& 2  J s *\C"?+r Dx2& 2 L K c $ Nl L L c $_ F[  M 0Z._T B Document D 0 2 2 N 0صA  :part32 O 0 E  :part32 P 0 L* <number3 Q s *8C"? V  Dx5& 2  R s *C"?? 2 &  @ Compressor 2 f S s *C"?   812 2f T s *C"?zo Xa  B Refrigerator 2 f U s *PC"?{ i,$D 0 Theorem 2: For all queries Q in the fragment that have at least one  / node, stream-space(FQ) = W(log depth(D)).u0 2 D 333,W  V s *tC"?BB) 9456 2fH  0޽h ?<9=9N>N;?NO@A9BOPK:NL 3ff~XP___PPT100.I`є+ GFD' = @B D' = @BA?%,( < +O%,( < +Du' =%(D' =%(D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*9D' =1:B solid*a3>Bfill.type<*9D' =1:B true*]3>Bfill.on<*9D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*ND' =1:B solid*a3>Bfill.type<*ND' =1:B true*]3>Bfill.on<*ND!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*OD' =1:B solid*a3>Bfill.type<*OD' =1:B true*]3>Bfill.on<*OD!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*<D' =1:B solid*a3>Bfill.type<*<D' =1:B true*]3>Bfill.on<*<D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*PD' =1:B solid*a3>Bfill.type<*PD' =1:B true*]3>Bfill.on<*PDA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*U%(+8+0+U +v  g C;(  r  S LM }      s *C"?  ,Theorem 4(a): For all queries Q in a  Univariate XPath : Space: O(|Q| recDepth(D) log depth(D)). Time: O(|D| |Q| recDepth(D)).d0 2!043F3F3 B3F3F3P'   k  s *DC"?E v,$D 0 Theorem 4(b): For all queries Q in a subset of our fragment and for non-recursive documents D, Space: O(FrontierSize(Q) log depth(D)). Time: O(|D| FrontierSize(Q)).`0 2J0YB3F3F3 B3F3F3>hH  0޽h ? 3ff~___PPT10.I#+Y DO' = @B D ' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(+8+0+ + g   0 8L (  Lx L c $hM }    &L 0 ( / <Fragment:  subsumption-free  univariate Conjunctions only  star-restricted @ 0 2E10F2 E,  'H( *L s *XC"? Theorem 1: For all queries Q in the fragment, stream-space(FQ) = W(FrontierSize(Q)).W0 2  333,72 +L 6)S"`? x  @ conference  32 ,L 0.    :name32 -L 0p- E3.  :root3F .L S . <D F /L S  D`  0L 06)  =Query0 22 1L 0T:"`  =speaker32 2L 0>"`2 :name32 3L 0p5ID h Y paper_cnt  3 L 4L@ c $ D L 5L c $L 6L@ c $  7L 6F ?"6@ NNN?N   F= PODS$0 2 8L <I ?"6@ NNN?Np C> 1$0 2H L 0޽h ?_-L+L.L+L,L/L+L1L4L1L2L5L1L3L6L 3ff~___PPT10i.IX]+D=' = @B +}I gZK0 G ? 14/(  4~" 4 s *|M }   V I4 0O)[5 Definition: Document D is critical for query Q, if: (1) D matches Q. (2) If we remove from D any node, it no longer matches Q. R90 2P00P2e2 Y4 6XS"`? 4  @ conference  32 Z4 0L]  :name32 [4 04W4 X  :root3F \4 S X  F ]4 S    ^4 0c ?Query Q0 22 _4 0 h"` I; =speaker32 `4 0k"`\ :name32 a4 0os$  Y paper_cnt  3 L b4@ c $  L c4 c $;L d4@ c $; e4 6t ?"6@ NNN?N `  F= PODS$0 2 f4 <x ?"6@ NNN?N,s C> 1$0 22 g4 0d|\   @ conference  32 h4 0p| l  :name32 i4 0(   =speaker32 j4 0z5 + j :name32 k4 0  Y paper_cnt  3 2 l4 0,  :root3F m4 S  \ F n4@ S   F o4@ S  0 -zF p4 S  -^F q4@ S  {  2 r4 0 i  =speaker32 s4 0tbl :name32 t4 0bF Y paper_cnt  3 F u4 S  R F v4@ S  g0F w4 S  0b x4 s *C"?l f v S  :PODS 2f y4 s *C"?No 5 @ Josifovski 2 f z4 s *C"?o ;Fagin 2f {4 s *ЫC"?& 71 2f |4 s *0C"?w0^ 73 2f }4 s *DC"?  Dx0& 2  ~4 s *0C"?i P  Dx1& 2  4 s *C"?i ,P  Dx2& 2  4 s *C"? W  Dx3& 2  4 s *(C"?B <)  Dx6& 2  4 s *C"? 4 Dx4& 2  4 s *xC"? Dx5& 2  4 s *HC"??b& Dx7& 2  4 s *C"? 0u Dx8& 2  4 0 B Document D 0 2 H 4 0޽h ?[4Y4\4Y4Z4]4Y4_4b4_4`4c4_4a4d4 l4g4m4!g4i4n4"i4j4o4#i4k4p4$g4h4q4%g4r4u4&r4s4v4'r4t4w4 3fffff3̙3f̙((___PPT10(.IpU+D&' = @B Dm&' = @BA?%,( < +O%,( < +D' =%(DF' =%(D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*l4D' =1:B solid*a3>Bfill.type<*l4D' =1:B true*]3>Bfill.on<*l4D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*g4D' =1:B solid*a3>Bfill.type<*g4D' =1:B true*]3>Bfill.on<*g4D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*h4D' =1:B solid*a3>Bfill.type<*h4D' =1:B true*]3>Bfill.on<*h4D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*r4D' =1:B solid*a3>Bfill.type<*r4D' =1:B true*]3>Bfill.on<*r4D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*t4D' =1:B solid*a3>Bfill.type<*t4D' =1:B true*]3>Bfill.on<*t4D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*s4D' =1:B solid*a3>Bfill.type<*s4D' =1:B true*]3>Bfill.on<*s4D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*i4%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*j4%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*k4%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*o4%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*p4%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*y4%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*4%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*4%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*n4%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*{4%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*4%(++0+i4 ++0+j4 ++0+k4 ++0+y4 ++0+{4 ++0+4 ++0+4 ++0+4 + g  8'(  8r 8 S \M }    8 s *C"??; ,$D 0 Lemma 1: For all queries Q in the fragment and any critical document D for Q, stream-space(FQ) = W(FrontierSize(D)).w0 2 F 333,W 8 s *C"?e !=W,$D 0 Lemma 2: For all queries Q in the fragment, there is a critical document D so that FrontierSize(D) = FrontierSize(Q).80 2 U#,_  8 <D ,$D 0 B show proof 0 >  8 s *hC"?'} Theorem 1: For all queries Q in the fragment, stream-space(FQ) = W(FrontierSize(Q)).W0 2  333,7H 8 0޽h ? 3ff~___PPT10.{J@+2D' = @B D' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(++0+8 ++0+8 ++0+ 8 + g   0 #  (   r   S .M }      `A j0195384O9     \A 1man82i G     0/+ CAlice"0 2   0(4Kw ABob"0 23   07V ?x"0 2   0;q" ?y"0 23   0?IM v 0,$ 0 Mm00 2    0C  rf: (X, Y) Z<0 2    0I; ,$ 0 ^f(x,y)"0 233T "  0M q ,$ 0 bCC(f) = number of communication bits used by the best protocol on the worst-case choice of inputs.(c0 2[_B #  BD)?"0@NNN?No& y,$D 0H   0޽h ? 3ff~  ___PPT10w .JfQU+~zID ' = @B D^ ' = @BA?%,( < +O%,( < +DL' =%(DT' =%(Dp' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*# %(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*" %(++0+  ++0+  ++0+"  + 9 g  7D?(  D D <_9G3,$@ 0 9D0 )D <c5D /,$@ 0 Ja,0 *D <h2 ,,$D 0 Jb,0x  D c $jM }     D `A j0195384Z  <$@  0   D \A 1man82) _ <$@ 0   D 0@9 ,$  0 CAlice"0 2  D 0Tgl ,$ 0 ABob"0 23B D 0D) x  ,$D 0> D 0dv z P ,$ 0 stateA(a)| 0 2N" D 0\~L XA : streaming algorithm for FQ using space SN-0 2& D 0T!i ,$ 0 stateA(a)d 0 2J  &D s *w= ,$D 0 3D s *m,$D 0 $HTheorem: stream-space(FQ) >= CC(FQ)%0 2    5D 0 !,$ 0 p FQ(D)J0 2333333 6D <29 ,,$@  0 Ja,0 7D </ ),$D  0 Jb,0H D 0޽h ? 3ff~('___PPT10'.JfQU+h,D$' = @B D$' = @BA?%,( < +O%,( < +D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*&D%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*)D%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<**D%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* D%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* D%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* D%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* D%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*6D%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*7D%(D' =%(D8' =A@BBBB0B%()?)?D' =.G7 BBBBBYM 1.94444E-6 -4.81481E-6 L -0.2217 0.30255 *3>*B ppt_xB ppt_y=@0BBAApBB33㽐B><*6DD0' =A@BBBB0B%()?)?Dw' =.?7 BBBBBQM -2.22222E-6 -3.7037E-7 L 0.31702 0.3 *3>*B ppt_xB ppt_y=@0BBAApBBO">B><*7DD' =%(D3' =%(Dp' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-o6Bdissolve*<3<*DDc' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-o6Bdissolve*<3<*DDA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*5D%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*3D%(++0+D ++0+)D ++0+*D ++0+ D ++0+ D ++0+D ++0+D ++0+3D ++0+5D ++0+6D ++0+6D ++0+7D ++0+7D +! g    H! (  H H <ZT xDa,bT0r H S 8M }    H s *C"? P,$D  0 .vTheorem: For any fooling set T, CC(FQ) = W(log |T|).<0(2 3 33V H 0<   _|$ 0H@___PPT9" rDefinition A set T of partitioned documents is a fooling set for FQ if: All documents in T match Q. For any two distinct documents Da,b, Dg,d in T, either Da,d does not match Q or Dg,b does not match Q. H%Z " ZZ " ZZ & =]%)9 H <8 ?"6@ NNN?N 3 QPartitioned document: 0 2 H <`dL ^,$@ 0 Ja,0 H <,\G "V,$@ 0 Jb,0) H <` ?"6@ NNN?N*m ,$ 0 KDocument prefix 0 2) H <  ?"6@ NNN?Nh,$ 0 KDocument suffix 0 2H H 0޽h ? 3ff~___PPT10n.J]+x9hWD' = @B D=' = @BA?%,( < +O%,( < +D ' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D8' =A@BBBB0B%()?)?D' =.G7 BBBBBYM 3.88889E-6 2.23301E-6 L -0.05243 0.15719 *3>*B ppt_xB ppt_y=@0BBAApBBlּB-=<*HD6' =A@BBBB0B%()?)?D}' =.E7 BBBBBWM 3.33333E-6 1.51641E-6 L 0.05295 0.16343 *3>*B ppt_xB ppt_y=@0BBAApBB-<B=<*HD' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(++0+H ++0+H ++0+H ++0+H ++0+H ++0+H ++0+H ++0+H + g 0 &ltP(  tx t c $`$M }   < =t s *%C"? O2q Lemma 1: For all queries Q in the fragment nd any critical document D for Q, stream-space(FQ) = W(FS(D)).l0 2 E 333,,(2 >t 6L2S"`? 4  @ conference  32 ?t 0 7  :name32 @t 094 X  :root3F At S X  F Bt S    Ct 0> ?Query Q0 22 Dt 0DB"` I; =speaker32 Et 0dF"`\ :name3L Ft@ c $  L Gt c $;L Ht@ c $; It 6J ?"6@ NNN?N `  F= PODS$0 2 Jt <M ?"6@ NNN?N,s C> 1$0 22 Kt 0D\   @ conference  32 Lt 0O   :name32 Pt 0T  :root3F Qt S  \ F Ut@ S  7< 2 Vt 0\ 9  =speaker32 Wt 0Ta3Wa# :name32 Xt 0c Y paper_cnt  3 F Yt S   F Zt@ S  \3F [t S   ^t s *4iC"?n ;Fagin 2f `t s *dmC"?[ 73 2f at s * qC"?  Dx0& 2  bt s *uC"?i P  Dx1& 2  ct s *\yC"?   Dx2& 2  et s *P~C"? %ug  Dx3& 2  ht s *C"?s5Z Dx4& 2  it s *C"?  Dx5& 2  jt 0 B Document D 0 2 2 kt 0(ss$  Y paper_cnt  3  lt s *0C"? l |  :PODS 2fH t 0޽h ?@@t>tAt>t?tBt>tDtFtDtEtGtDtHtPtKtQtKtLtUtKtVtYtVtWtZtVtXt[t 3ff~___PPT10i.JXZ+D=' = @B +5 g 6.@ (gx~(  xx x c $<M }    x < ?"6@ NNN?N ,$ 0 S = { x2, x5 }\0 22 Dx 6S"`? 4  @ conference  32 Ex 0  :name32 Fx 04 X  :root3F Gx S X  F Hx S    Ix 0Ȳ ?Query Q0 22 Jx 0"` I; =speaker32 Kx 0̺"`\ :name3L Lx@ c $  L Mx c $;L Nx@ c $; Ox 6d ?"6@ NNN?N `  F= PODS$0 2 Px < ?"6@ NNN?N,s C> 1$0 22 Qx 0\   @ conference  32 Rx 0$   :name32 Sx 0  :root3F Tx S  \ F Ux@ S  7< 2 Vx 0 9  =speaker32 Wx 0l :name32 Xx 0` Y paper_cnt  3 F Yx S   F Zx@ S  F [x S   \x s *C"?[ ;Fagin 2f ]x s *C"?[ 73 2f ^x s *C"?  Dx0& 2  _x s *xC"?i P  Dx1& 2  `x s *8C"?   Dx2& 2  ax s *C"? %ug  Dx3& 2  bx s *C"?sZ Dx4& 2  cx s *C"?  Dx5& 2  dx 0x O Document DS( 0 2  2 ex 0s$  Y paper_cnt  3  fx s * C"? l |  :PODS 2fB gx BD)?"0@NNN?N:,$D  0H x 0޽h ?@FxDxGxDxExHxDxJxLxJxKxMxJxNxSxQxTxQxRxUxQxVxYxVxWxZxVxXx[x 3ff~WO___PPT10/.JXZ+\-YD{' = @B D6' = @BA?%,( < +O%,( < +D' =%(D;' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*>x%(D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*RxD' =1:B solid*a3>Bfill.type<*RxD' =1:B true*]3>Bfill.on<*RxD!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*XxD' =1:B solid*a3>Bfill.type<*XxD' =1:B true*]3>Bfill.on<*XxD ' =%(D> ' =%(D' =A@BBBB0B%()?)?D<' =.7 BBBBB=M 0.0 0.0 L 0.19097 -0.00254 *3>*B ppt_xB ppt_y=0BBAA<*WxD' =A@BBBB0B%()?)?D<' =.7 BBBBB=M 0.0 0.0 L 0.19097 -0.00254 *3>*B ppt_xB ppt_y=0BBAA<*bxD' =A@BBBB0B%()?)?D<' =.7 BBBBB=M 0.0 0.0 L 0.19097 -0.00254 *3>*B ppt_xB ppt_y=0BBAA<*\xD' =A@BBBB0B%()?)?D<' =.7 BBBBB=M 0.0 0.0 L -0.19826 0.01711 *3>*B ppt_xB ppt_y=0BBAA<*XxD' =A@BBBB0B%()?)?D<' =.7 BBBBB=M 0.0 0.0 L -0.19826 0.01711 *3>*B ppt_xB ppt_y=0BBAA<*]xD' =A@BBBB0B%()?)?D<' =.7 BBBBB=M 0.0 0.0 L -0.19826 0.01711 *3>*B ppt_xB ppt_y=0BBAA<*cxD4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*gx%(++0+>x ++0+Wx ++0+Xx ++0+\x ++0+]x ++0+bx ++0+cx + g   P'y (     <- ?"6@ NNN?Nm 7m ,$ 0 .n2. If S T, need: either DST or DTS does not match Q. 80 2BBJBJBBB @h`r  S .M }   z  <p3 ?"6@ NNN?N (2 ,$ 0 1. For all S, DS matches Q. L lBJB8XB   s *6C"?R <Claim: { DS }S is a subset of Frontier(D) is a fooling set.p=0 2   J3   <?"6@ NNN?Nll,$@ 0   <E ?"6@ NNN?N/<,$ 0 Pstream-space(FQ) >= log(2FS(D)) = FS(D).l)0 2   ) ' <LN ?"6@ NNN?N P ,$ 0 KProof of Claim: 0 2H  0޽h ? 3ff~: 2 ___PPT10 .J`+Or!D ' = @B D ' = @BA?%,( < +O%,( < +D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'%(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+' +f g 99 El7(     Ft!0e0e     @  5% 8c8c     ?A)BCD|E||# "0e@       @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abM }  ! 2  0_In @ conference  32  0`do _ :name32  08h :root3F  S IF  S n#2  0Xl  =speaker32  0o   :name32   0r  Y paper_cnt  3 F !@ S nvF "@ S v F # S v# $ s *\xC"? l Dx0& 2  % s * }C"?a; H Dx1& 2  & s *`C"? Dx3& 2  ' s *TC"?0 :  Dx2& 2  ( s * C"?Vu  Dx4& 2  ) s *C"? Dx5& 2  * 0FL Document DT T = { x4,x5 } 0 2  BJBJB  + s *C"?G .  :PODS 2f P 0 z ,$ 0 T Document DTS, 0 2  2 S 0$4 @ conference  32 T 0Z J :name32 U 05 :root3F V S F W@ S }2 X 0D#  =speaker32 Y 0   :name32 Z 0 X  Y paper_cnt  3 F [ S O#F \ S  O F ]@ S  O  ^ s *HC"?& Dx0& 2  _ s * C"?W Dx1& 2  ` s *LC"?(M Dx2& 2  a s *@C"?t Dx3& 2  b s *C"?C %*  Dx5& 2  c s *C"?# G  Dx4& 2   d 0l  Document DS S = { x2,x5 }v0 2  BJBJB e s *C"?@ '  :PODS 2f f s *<C"?   ;Fagin 2f g s *PC"? =  ;Fagin 2f h s *tC"? Z  73 2f i s *C"? e  73 2fB j BD)?"0@NNN?N2 ]h B k BD)?"0@NNN?N4I 2 l 0   ,$@ 0 @ conference  32 n 0; + ,$@ 0 :root3z o S + ,$@ 0 w s *C"?'  ,$ 0 Dx0& 2  x s *DC"?  ,$ 0 Dx1& 2 B  BD)?"0@NNN?N  ,$@ 0F  NtGJH Ԕ?"6@ NNN?N K W,$D 0 VConference name missing!"0(22  0D  V ,$@  0 =speaker32  0` ,$@  0 :name32  08 ,$@  0 Y paper_cnt  3 z @ S    ,$D 0z @ S ,$@  0z  S  ,$@ 0  s *C"?  f ,$ 0 Dx3& 2   s *C"?u,$ 0 Dx4& 2   s *C"?,$ 0 ;Fagin 2f  s *h!C"?f ,$ 0 73 2f2  0$ ,$@ 0 :name3z  S  ,$@ 0  s *0)C"? ,$ 0 ;Fagin 2f  s *|C"?#^ ,$ 0 Dx4& 2   s *$0C"? = s,$ 0 Dx5& 2 H  0޽h ?! "  #USVSTWSX[XY\XZ]nlo !l"#$ 3ff~o,g,___PPT10G,.O~ +<Dc(' = @B D(' = @BA?%,( < +O%,( < +D %' =%(D$' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*n%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*o%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*w%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(++0+P ++0+l ++0+n ++0+w ++0+x ++0+ ++0+ ++0+ ++0+ ++0+ ++0+ ++0+ ++0+ ++0+ ++0+ ++0+ ++0+ +} g  l$(  lr l S !M }  ! r l S !; ` ! H l 0޽h ? 3ff~___PPT10i.>Mp K+D=' = @B +a g xp@ 0P(  Pr P S dM }    P Hf))?@P  n$ c1 b1 ....%!  P 0l9^4  3a P 0q9^ ?F"  P 0t^4  ?1" dB P <DԔO  dB P@ <DԔ!   P <y   G Level array 0 F !P <d~  LValidation array 0FdB "P <DԔi# #P <@G  VPointer array with one entry0D2 $P 0H ,  F/a(2 %P 0,x&V F/b(32 &P 0 %  7$3F 'P S   F (P@ S  x )P s *C"? L  Du0& 2  *P s *|C"?u Q\  Du1& 2  +P s *C"?pMW Du2& 2 2 ,P 0s!Q B/c$3F -P S  s .P s * C"?c \J Du3& 2 0 /P <ȧ  Query: /a[b and c]t 0P <İOs6 C Input XML H P 0޽h ??`&P$P'P$P%P(P$P,P-P 3ff~___PPT10i.9MP1+D=' = @B +=g TL` "=T|(  T T 6H M } )Algorithm Example Run T H))?@P  b$ c1 b1 ..."%$  T 09^4  3a T 09^ ?F"  T 0`^4  ?1"  T <0# 7$ #T H 8c?"6@`NNN?NRA8 }? :  ,T? :  $T 04}?& :  3b %T 0& ?  ?F"  &T 00&  :  ?2"  'T <@) # 7aA8 8 3  +T8  3  (T 008 , 3  3c )T 0x, 8  ?F"  *T 0<, 3  ?2" B -T@ BD8c?"0@NNN?NT  .T < "   =Index 0B /T@ BD8c?"0@NNN?N Q   0T <Z  T  =Index 10 1T <  Query: /a[b and c]t 2T <Os6 C Input XML 2 3T 0 ,  F/a(2 4T 0 x&V F/b(32 5T 0@ %  7$3F 6T S   F 7T@ S  x 8T s *C"? L  Du0& 2  9T s *TC"?u Q\  Du1& 2  :T s *C"?pMW Du2& 2 2 ;T 0ls!Q B/c$3F  c1 b1 ..."%$ X </Os6 C Input XML  X 019^4  3a X 0<89^ ?F"   X 0P>^4  ?1"   X <@# 7$0  X <`E  Query: /a[b and c]t X H 8c?"6@`NNN?N!OF }? :  X ? :  X 0N}?& :  3b X 0Q& ?  ?F"  X 0 V&  :  ?2"  X <|Z) # 7aOF 8 3  X 8  3  X 00^8 , 3  3c X 0Da, 8  ?F"   X 0e, 3  ?2" B !X@ BD8c?"0@NNN?N(  "X <$j" y  =Index 0B #X@ BD8c?"0@NNN?N %  $X <mZ vT  =Index 1OF }? :  %X <Z 7  &X 0pp}?& :  3b 'X 0s& ?  ?F"  (X 0|x&  :  ?2"  )X <L}& f  7cOF 8 3  *X 5 Z 0  +X 0P{8 , 3  3c ,X 0, 8  ?F"  -X 0, 3  ?2" 2 /X 0 ,  F/a(2 0X 0x&V F/b(32 1X 0h %  7$3F 2X S   F 3X@ S  x 4X s *C"? L  Du0& 2  5X s * C"?u Q\  Du1& 2  6X s *ȡC"?pMW Du2& 2 2 7X 0ps!Q B/c$3F 8X S  s 9X s *C"?c \J Du3& 2 H X 0޽h ??`1X/X2X/X0X3X/X7X8X 3ff~___PPT10i. c1 b1 ..."%$ \ 09^4  3a \ 0<9^ ?F"  \ 0^4  ?1"   \ <# 7$ \ B 8c?"6@`NNN?Na!OF }? :  \ ? :  \ 00}?& :  3b \ 0& ?  ?F"  \ 0&  :  ?2"  \ <\) # 7aOF 8 3  \ 8  3  \ 088 , 3  3c \ 0, 8  ?F"  \ 0, 3  ?2" B  \@ BD8c?"0@NNN?N  !\ <"2  =Index 0B "\@ BD8c?"0@NNN?N   #\ <Z /T  =Index 1OF }? :  $\ <Z 7  %\ 0}?& :  3b &\ 0d& ?  ?F"  '\ 0&  :  ?2"  (\ <D& f  7cOF 8 3  )\ 5 Z 0  *\ 0`8 , 3  3c +\ 0D, 8  ?F"  ,\ 0, 3  ?2" OF }? :  -\ 9" s 4  .\ 0x }?& :  3b /\ 0& ?  ?F"  0\ 0 &  :  ?2"  1\ <#a Z  8/cOF 8 3  2\ 2 " s -  3\ 08 , 3  3c 4\ 0, 8  ?T"  5\ 0@, 3  ?2"  H\ 6# M } )Algorithm Example Run0 I\ <$  Query: /a[b and c]t J\ <p/Os6 C Input XML 2 K\ 0x4 ,  F/a(2 L\ 0T&x&V F/b(32 M\ 0 = %  7$3F N\ S   F O\@ S  x P\ s *@C"? L  Du0& 2  Q\ s *EC"?u Q\  Du1& 2  R\ s *pIC"?pMW Du2& 2 2 S\ 0dNs!Q B/c$3F T\ S  s U\ s *RC"?c \J Du3& 2 H \ 0޽h ??`M\K\N\K\L\O\K\S\T\ 3ff~___PPT10i.=M=!K+D=' = @B +e'g |&t& =L`%(  ` ` HX))?@P  b$ c1 b1 ..."%$ ` 0(^9^4  3a ` 0`9^ ?F"  ` 0e^4  ?1"   ` <Pj# 7$ ` H 8c?"6@`NNN?N+OF }? :  ` ? :  ` 0Th}?& :  3b ` 0l& ?  ?F"  ` 0Pv&  :  ?2"  ` <`t) # 7aOF 8 3  ` 8  3  ` 0P}8 , 3  3c ` 0, 8  ?F"  ` 0\, 3  ?2" B  `@ BD8c?"0@NNN?Nl !` <,"k  =Index 0B "`@ BD8c?"0@NNN?N i  #` <Z hT  =Index 1OF }? :  $` <Z 7  %` 08}?& :  3b &` 0ԕ& ?  ?F"  '` 0D&  :  ?2"  (` <`& f  7cOF 8 3  )` 5 Z 0  *` 08 , 3  3c +` 0d, 8  ?F"  ,` 0h, 3  ?2" OF }? :  -` 9 G4  .` 0l}?& :  3b /` 0& ?  ?F"  0` 0P&  :  ?2"  1` <س#5  7bOF 8 3  2` 2 G-  3` 0,8 , 3  3c 4` 0, 8  ?T"  5` 0, 3  ?2"  6` 6 M } )Algorithm Example RunOF }? :  7` H p C  8` 0P}?& :  3b 9` 0d& ?  ?F"  :` 0&  :  ?2"  ;` <2^ W , 8/cOF 8 3  <` A  p <  =` 08 , 3  3c >` 0B, 8  ?T"  ?` 0, 3  ?2" 0 @` <  Query: /a[b and c]t A` <8Os6 C Input XML 2 B` 0 ,  F/a(2 C` 0Hx&V F/b(32 D` 0D %  7$3F E` S   F F`@ S  x G` s *$C"? L  Du0& 2  H` s *C"?u Q\  Du1& 2  I` s *C"?pMW Du2& 2 2 J` 0 s!Q B/c$3F K` S  s L` s *C"?c \J Du3& 2 H ` 0޽h ??`D`B`E`B`C`F`B`J`K` 3ff~___PPT10i.=M`n +D=' = @B +,g ++ FUd*(  d d H<))?@P  b$ c1 b1 ..."%$ d 09^4  3a d 0(9^ ?F"  d 0&^4  ?1"   d <## 7$ d B 8c?"6@`NNN?N,VuOF }? :  d ? :  d 0 /}?& :  3b d 0(& ?  ?F"  d 0,-&  :  ?2"  d < 5) # 7aOF 8 3  d 8  3  d 0=8 , 3  3c d 0B, 8  ?F"  d 0@, 3  ?2" B  d@ BD8c?"0@NNN?N7 !d <XA"6  =Index 0B "d@ BD8c?"0@NNN?N }4  #d <NZ 3T  =Index 1OF }? :  $d <Z 7  %d 0R}?& :  3b &d 0`Q& ?  ?F"  'd 0M&  :  ?2"  (d <X& f  7cOF 8 3  )d 5 Z 0  *d 0a8 , 3  3c +d 0xe, 8  ?F"  ,d 0i, 3  ?2" OF }? :  -d 9 G4  .d 0o}?& :  3b /d 0m& ?  ?F"  0d 0w&  :  ?2"  1d <x{#5  7bOF 8 3  2d 2 G-  3d 0y8 , 3  3c 4d 0ԁ, 8  ?T"  5d 0 , 3  ?2"  6d 6 M } )Algorithm Example RunOF }? :  7d H p C  8d 0Ԍ}?& :  3b 9d 0`& ?  ?F"  :d 0d&  :  ?2"  ;d <2^ W , 8/cOF 8 3  d 0, 8  ?T"  ?d 0p, 3  ?2" OF }? :  @d 61  Ad 0@}?& :  3b Bd 0L& ?  ?T"  Cd 00&  :  ?2"  Dd <  8/bOF 8 3  Ed / *  Fd 08 , 3  3c Gd 0, 8  ?T"  Hd 0H, 3  ?2" 0 Id <(  Query: /a[b and c]t Jd <,Os6 C Input XML 2 Kd 04 ,  F/a(2 Ld 0x&V F/b(32 Md 0 %  7$3F Nd S   F Od@ S  x Pd s *C"? L  Du0& 2  Qd s *C"?u Q\  Du1& 2  Rd s *pC"?pMW Du2& 2 2 Sd 0ds!Q B/c$3F Td S  s Ud s *C"?c \J Du3& 2 H d 0޽h ??`MdKdNdKdLdOdKdSdTd 3ff~___PPT10i.=M+D=' = @B +.g -- I\h,(  h h H))?@P  b$ c1 b1 ..."%$ h 09^4  3a h 089^ ?F"  h 0< ^4  ?1"   h <$# 7$ h B 8c?"6@`NNN?N6OF }? :  h ? :  h 0}?& :  3b h 0& ?  ?F"  h 0&  :  ?2"  h <) # 7aOF 8 3  h 8  3  h 08 , 3  3c h 0(#, 8  ?F"  h 0(, 3  ?2" OF }? :  $h <Z 7  %h 0&}?& :  3b &h 0/& ?  ?F"  'h 0$4&  :  ?2"  (h <(9& f  7cOF 8 3  )h 5 Z 0  *h 0=8 , 3  3c +h 06, 8  ?F"  ,h 0D, 3  ?2" OF }? :  -h 9 G4  .h 0?}?& :  3b /h 0F& ?  ?F"  0h 0tP&  :  ?2"  1h <T#5  7bOF 8 3  2h 2 G-  3h 0R8 , 3  3c 4h 0D\, 8  ?T"  5h 0`, 3  ?2"  6h 6d M } )Algorithm Example RunOF }? :  7h H p C  8h 0f}?& :  3b 9h 0j& ?  ?F"  :h 0@o&  :  ?2"  ;h <s2^ W , 8/cOF 8 3  h 0 z, 8  ?T"  ?h 0X~, 3  ?2" OF }? :  @h 61  Ah 08}?& :  3b Bh 0t& ?  ?T"  Ch 0&  :  ?2"  Dh <T  8/bOF 8 3  Eh / *  Fh 0p8 , 3  3c Gh 0, 8  ?T"  Hh 0ě, 3  ?2" OF }? :  Ih E@  Jh 0 }?& :  3a Kh 0& ?  ?T"  Lh 0&  :  ?1"  Mh < /) 8/aB Nh <D3?"0@NNN?N  Oh N԰ ?"6@ NNN?N{  I Return TRUE" 0 2 D0 Ph <<  Query: /a[b and c]t Qh < Os6 C Input XML 2 Rh 0 ,  F/a(2 Sh 0x&V F/b(32 Th 0 %  7$3F Uh S   F Vh@ S  x Wh s *C"? L  Du0& 2  Xh s *C"?u Q\  Du1& 2  Yh s *DC"?pMW Du2& 2 2 Zh 0s!Q B/c$3F [h S  s \h s *(C"?c \J Du3& 2 H h 0޽h ??`ThRhUhRhShVhRhZh[h 3ff~___PPT10i.>MД +D=' = @B + g p z(  x  c $M }     c $H; `<$@ 0  *Ft`H  0޽h ? 3ff~___PPT10.I+EDZ' = @B D' = @BA?%,( < +O%,( < +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<*"%(+I gZK0 p..(  ~"  s *M }   2  0p\L 7C32  0  < ,  7N32  0 ~  7S32  0!  7N32  0ԟ! < ,  7P32  0$!K\L; 7$3F   S ;F  @ S   F  @ S [    F   S [  F  @ S s \ 2  0 l\q  7S32  0H    7N32  0   7P3F  S ) F @ S N  F  S N 94   s *C"?  :PODS 2f  s *C"?  @ Josifovski 2 f  s * $C"?   ;Fagin 2f  s *8(C"? X   71 2f  s *+C"? X  73 2f  s *%C"?63 Dx0& 2   s *`3C"?8 Dx1& 2   s *7C"?  h  Dx2& 2   s *x!C"?k ,R  Dx3& 2   s *?C"?u R\  Dx6& 2   s *CC"? n  Dx4& 2   s *GC"? `  Dx5& 2    s *!C"? H  Dx7& 2  ! s *OC"?   Dx8& 2  " 0S|rh,$ 0 z/conference/nameN0 2 332 # 0(Z  ,$@ 0 F/C(32 $ 0,_  ,$@ 0 F/N(32 % 0UL<,$@ 0 7$3z & S <QX ,$@ 0z '@ S  RX ,$@ 0 ( s *gC"?7,$  0 Du0& 2  ) s *XlC"? ,$  0 Du1& 2  * s *oC"?  ,$  0 Du2& 2  + 0s<O 9D0 2 , 0w,$ 0 9Q0 2 - 0@{ J ,$ 0 kResult: { x2 }@0 2  . 0oQK,$D  0H  0޽h ?@      %#& #$' 3fffff3̙3f̙b)Z)___PPT10:).IpU+V`D'' = @B D&' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*#%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*&%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*'%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*)%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<**%(D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*.%(Dy' =%(D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*Dd' =%(D' =%(D3' =4@BB*BB%()?)?D' =.O7 BBBBBaM -1.11111E-6 -3.7037E-7 L -1.11111E-6 0.09792 *3>*B ppt_xB ppt_y=@0BBAApBBB,H=<*.Dy' =%(D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*DV' =%(D}' =%(D%' =4@BB*BB%()?)?Dy' =.A7 BBBBBSM 3.33333E-6 0.09791 L -0.00018 0.21342 *3>*B ppt_xB ppt_y=@0BBAApBBa 6Bl=<*.Dy' =%(D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*-%(++0+" ++0+# ++0+$ ++0+% ++0+( ++0+) ++0+* ++0+, ++0+- +"P gZK0 `..F(  ~"  s *M }   2  05%  7C32  0 U E  7N32  0h r b  7S32  0 H "  8  7N32  0H 8  7P32  0pu 7$3F   S uZZ5F  @ S  ?  F  @ S  H F   S  ? :H F  @ S : U 2  0   7S32  0|; +  7N32  0; B2+  7P3F  S   F @ S  ; F  S  ;   s *TC"?E b r ,  :PODS 2f  s *C"?E , e , @ Josifovski 2 f  s *\C"?E r, ;Fagin 2f  s *C"?E ~, 71 2f  s *(C"?E h, 73 2f  s *C"?p W Dx0& 2   s *C"?"  Dx1& 2   s *C"?B )  Dx2& 2   s *LC"? b   Dx3& 2   s *8C"? (  Dx6& 2   s *C"?C D *  Dx4& 2   s *C"?C *  Dx5& 2    s *0C"?, ~  Dx7& 2  ! s *C"?- n  Dx8& 2  " 0,$ 0 {/conference//nameN0 2 332 # 0\ sw ,$@ 0 F/C(32 $ 0 i }mY ,$@ 0 G//N(32 % 0T|l,$@ 0 7$3z & S  ,$@ 0z '@ S w i ,$@ 0 ( s *C"?S,$  0 Du0& 2  ) s *C"?] XD ,$  0 Du1& 2  * s *4C"?X b? ,$  0 Du2& 2  + 0  9D0 2 , 0\!Bgzb,$ 0 9Q0 23 - 0'  ,$ 0 Result: { x2, x4, x7 }l0 2    . 0,$D  0H  0޽h ?@      %#& #$' 3fffff3̙3f̙//___PPT10/.IpU+̺Dh-' = @B D#-' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*#%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*&%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*'%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*)%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<**%(D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*.%(Dy' =%(D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*Dd' =%(D' =%(D3' =4@BB*BB%()?)?D' =.O7 BBBBBaM -1.11111E-6 -3.7037E-7 L -1.11111E-6 0.09792 *3>*B ppt_xB ppt_y=@0BBAApBBB,H=<*.Dy' =%(D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*D ' =%(D}' =%(D%' =4@BB*BB%()?)?Dy' =.A7 BBBBBSM 3.33333E-6 0.09791 L -0.00018 0.21342 *3>*B ppt_xB ppt_y=@0BBAApBBa 6Bl=<*.D ' =%(D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*-%(++0+" ++0+# ++0+$ ++0+% ++0+( ++0+) ++0+* ++0+, ++0+- +4 g && ,,p&(  p p <TlZ f,$@ 0 9D0 p <lXi] c,$D! 0 Zb3:0 p <]hWb,$@ 0 Za1:0 p <cd^,$@ 0 Zb1:0 p <hh# b,$@ 0 Za2:0 p <mi# c,$@ 0 Zb2:0 p <ri \ c,$@  0 Za3:0  p <wl` f,$@  0 Zb3:0  p <|kQe,$@ 0 Za1:0  p <ga,$@ 0 Zb1:0  p <k& e,$@ 0 Za2:0  p <l& f,$@ 0 Zb2:0 p <l _ f,$@ 0 Za3:0x p c $M }    p `A j0195384J  <$@ 0  p \A 1man82# <$@ 0  p 0 * ,$ 0 CAlice"0 2 p 0f  ,$ 0 ABob"0 23B p 0D);  ; ,$D# 0B p 0D) k ,$D) 0B p 0D) V  ,$D% 0B p 0D)  ,$D' 0 p 0 ) C l  ,$" 0 Ns100 2  p 0# B k ,$$ 0 Ns200 23 3 p 0 C l ,$& 0 Ns300 2  p 0 M v ,$( 0 Ns400 23 3P p 0lD nA : S-space streaming algorithm for FQ. r 1: integer.f80 2 C  p 0`G,$  0 ?(r = 6)0 2 p 0f^M,$  0 Fs0(0 2 p 0H[nB,$  0 Fs1(0 2  p 04[B,$  0 Fs2(0 2 !p 0Zw A,$ 0 Fs3(0 2 "p 0d: K,$ 0 Fs4(0 2 #p 0Z < A,$ 0 Fs5(0 2 $p 0ZW A,$ 0 Fs6(0 2 %p s **  ,$D 0B &p 0D)h ,$D- 0B 'p 0D)  ,$D+ 0 (p 0 @ i ,$* 0 Ns500 2  )p 0| J s ,$, 0 Ns600 23 3t *p s *<WE},$D0 0 2Theorem: S CC(FQr) / rv0 2 C +p 0 ,$/ 0 p FQ(D)J0 2333333 ,p 0X N ,$. 0 p FQ(D)J0 2333333H p 0޽h ? 3ff~kk___PPT10k.JfQU+<DHc' = @B Dc' = @BA?%,( < +O%,( < +D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%p%(D ' =%(D ' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D ' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*!p%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"p%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*#p%(D' =%( D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$p%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =%(D`' =%(D:' =A@BBBB0B%()?)?D' =.I7 BBBBB[M 1.94444E-6 -1.85185E-6 L -0.09011 0.22477 *3>*B ppt_xB ppt_y=@0BBAApBB8B =<* pD6' =A@BBBB0B%()?)?D}' =.E7 BBBBBWM 3.33333E-6 4.07407E-6 L 0.47673 0.21551 *3>*B ppt_xB ppt_y=@0BBAApBBt>Bq=<* pD:' =A@BBBB0B%()?)?D' =.I7 BBBBB[M 2.77778E-6 -1.85185E-6 L -0.23507 0.29144 *3>*B ppt_xB ppt_y=@0BBAApBB B><* pD.' =A@BBBB0B%()?)?Du' =.=7 BBBBBOM 5.E-6 -3.33333E-6 L 0.33664 0.27778 *3>*B ppt_xB ppt_y=@0BBAApBBDD,>B8><* pD:' =A@BBBB0B%()?)?D' =.I7 BBBBB[M 3.61111E-6 -3.33333E-6 L -0.37848 0.35556 *3>*B ppt_xB ppt_y=@0BBAApBBABa 6><*pD8' =A@BBBB0B%()?)?D' =.G7 BBBBBYM 2.22222E-6 -3.33333E-6 L 0.19479 0.34885 *3>*B ppt_xB ppt_y=@0BBAApBBww=B(}2><* pD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =%(D3' =%(Dp' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-o6Bdissolve*<3<*pDc' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-o6Bdissolve*<3<*pD3' =%(Dp' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-o6Bdissolve*<3<*pDc' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-o6Bdissolve*<3<*pD3' =%(Dp' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-o6Bdissolve*<3<*pDc' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-o6Bdissolve*<3<*pD3' =%(Dp' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-o6Bdissolve*<3<*pDc' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-o6Bdissolve*<3<*pD3' =%(Dp' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*(p%(D' =-o6Bdissolve*<3<*(pDc' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*'p%(D' =-o6Bdissolve*<3<*'pD3' =%( Dp' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*)p%(D' =-o6Bdissolve*<3<*)pDc' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*&p%(D' =-o6Bdissolve*<3<*&pD' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*+p%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<**p%(+P+0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+ p ++0+ p ++0+ p ++0+ p ++0+ p ++0+ p ++0+ p ++0+ p ++0+ p ++0+ p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+ p ++0+!p ++0+"p ++0+#p ++0+$p ++0+(p ++0+)p ++0+*p ++0++p ++0+,p +  0 VN (  X  C *8   N  S  J   Fi_Q evaluation of by special algorithm that knows Q in advance compexity of Q is the cost of the algorithm complexity of Fi= min_Alg( max_q_d (space (Alg(Q,D)))) complexity of Fi_Q= min_AlgQ( max_d (space (AlgQ(D)))) Q held fixed not a new complexity measure Why: In the spirit of instance optimality of Fagin et al.  DROP THIS Related to instance optimiality I.d.c. much more comprehensive, in practice we want to estimate the size of the query before it runs, does not get stuck on pathological cases < 1   H  0' ? 3380___PPT10.EO%C 0  S(  X  C *8     S Xz J   U'Lema the frontier size is in terms of D$H  0' ? 3380___PPT10.LOPm#  0  (  X  C *8     S  J    H  0' ? 3380___PPT10.LO[/~ 0  (  X  C *8     S L J   ZAfter the reduction we need to prove lower bounds for the communication complexity of Fi_qVH  0' ? 3380___PPT10.MO>Avf 0  v(  X  C *8     S ܿ J   xBf. s. t. for proving lower bounds communication complexity of Fi_q>H  0' ? 3380___PPT10.MOm& 0   (  X  C *8     S l J   "reminder slideH  0' ? 3380___PPT10.NO)' 0  (  X  C *8     S  J   -for each node in the query, all children that belong to S are put before those that are ins -nodes in S are put before their siblingsH  0' ? 3380___PPT10.OOH 0  X(  X  C *8     S  J   ZDefine Dst and Dts,H  0' ? 3380___PPT10.QO0)*/ 0 @ ?(  X  C *8     S L J   A-explain the scenario: names/ conferences etc.H  0' ? 3380___PPT10.O@pO 0 H@P (  X  C *8   @  S  J   explain more, what is $, what is slash, $ -> root expand names, put PODS, etc take out the arrow, remove predicates remove slashes  only something else remove animation two possible corresp. Only one matchesH  0' ? 3380___PPT10.O 0 QI` (  X  C *8   I  S  J   Document arrives as a stream top down Explan then why it is importatnt remove graphics do not have enough memory to store the document explain the latency ,& VH  0' ? 3380___PPT10.OD8P  0 p `(  X  C *8     S H J   b4emphasise that this is the query define stream-space ,H  0' ? 3380___PPT10.O0>Wrk0/H_i P_h(`<%_3Q{"Iumlz0r+kd1g_c]gE*@=`ǮpU$D 8 eȷEOh+'0h# hp   ( 4@H@On the Memory Requirements of XPath Evaluation over XML Streams IBM_USERmorNetwork IBM_USERmor314Microsoft PowerPointmen@xD@%I@4L_7G"g  F  --$--'--% t `--'3f--F$!>G<G:H8I6J5L4N3P3R3T4V5X6Z8[:\<]>]@]B\D[FZGXHVITIRIPHNGLFJDIBH@G>G--'--F$!]G[GYHWIUJTLSNRPRRRTSVTXUZW[Y\[]]]_]a\c[eZfXgVhThRhPgNfLeJcIaH_G]G--'--F$!|GzGxHvItJsLrNqPqRqTrVsXtZv[x\z]|]~]\[ZXVTRPNLJIH~G|G--'--F$!>f<f:g8h6i5k4m3o3q3s4u5w6y8z:{<|>|@|B{DzFyGwHuIsIqIoHmGkFiDhBg@f>f--'--F$!]f[fYgWhUiTkSmRoRqRsSuTwUyWzY{[|]|_|a{czeyfwguhshqhogmfkeichag_f]f--'--F$!|fzfxgvhtiskrmqoqqqsruswtyvzx{z|||~|{zywusqomkihg~f|f--'f--F$!ffghikmoqsuwyz{|||{zywusqomkihgff--'3f--F$!><:86543334568:<>@BDFGHIIIHGFDB@>--'--F$!][YWUTSRRRSTUWY[]_acefghhhgfeca_]--'f--F$!|zxvtsrqqqrstvxz|~~|--'--F$!--'--F$!--'3f--F$!><:86543334568:<>@BDFGHIIIHGFDB@>--'f--F$!][YWUTSRRRSTUWY[]_acefghhhgfeca_]--'--F$!|zxvtsrqqqrstvxz|~~|--'--F$!--'f--F$!><:86543334568:<>@BDFGHIIIHGFDB@>--'--F$!][YWUTSRRRSTUWY[]_acefghhhgfeca_]--'--F$!|zxvtsrqqqrstvxz|~~|--'--F$!--'--F$!--'f--F$!><:86543334568:<>@BDFGHIIIHGFDB@>--'--F$!][YWUTSRRRSTUWY[]_acefghhhgfeca_]--'--F$!|zxvtsrqqqrstvxz|~~|--'--F$!--'--F$!><:86543 3 34568:<>@BDFGHII I HGFDB@>--'--F$!][YWUTSR R RSTUWY[]_acefghh h gfeca_]--'--F$!|zxvtsrq q qrstvxz|~  ~|--'--F$!    --'--F$!] [ Y!W"U#T%S'R)R+R-S/T1U3W4Y5[6]6_6a5c4e3f1g/h-h+h)g'f%e#c"a!_ ] --'--F$!  !"#%')+-/13456665431/-+)'%#"!  --'--%!44--'@Arial-. 3f2 BjOn the Memory ,""/2"."Systemti-@Arial-. 3f(2 Requirements of XPath (""2"!%%".-@Arial-. 3f%2 Evaluation over XML %""!"$/".-@Arial-. 3f2 #Streams%1.-@Arial-. 2 uZiv Bar  .-@Arial-.  2 ug-.-@Arial-. 2 uwYossef .-@Arial-. 2 Marcus Fontoura%  .-@Arial-. 32 Vanja Josifovski    .-@Arial-. 12 21IBM Almaden Research Center       .-՜.+,0     On-screen ShowuIBM^%  ,ArialTimes New Roman WingdingsSymbolcmsy10 Courier NewNetwork@On the Memory Requirements of XPath Evaluation over XML StreamsPreliminaries: XMLPreliminaries: XPath 1.0 XML StreamsStreaming XML Algorithms Our Results Related WorkData Complexity [Vardi 82]XPath FragmentXPath Fragment (cont.)XPath Fragment (cont.)Query Frontier SizeDocument Recursion DepthDocument DepthNew algorithmProof of Theorem 1Critical Document Main Lemmas!One-way Communication Complexity ReductionFooling Set TechniqueProof of Lemma 1Proof of Lemma 1Proof of Lemma 1 (cont)Proof of Claim (example) AlgorithmAlgorithm Example Run Slide 28 Slide 29 Slide 30 Slide 31 Slide 32 Slide 33Conclusion: our Contributions XPath 1.0 XPath 1.0 Reduction  Fonts UsedDesign Template Slide Titles% _ظ'IBM_USERIBM_USER  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./123456789:;<=>?@ACDEFGHIKLMNOPQZRoot EntrydO)PicturesCurrent UserJSummaryInformation(0#PowerPoint Document(SDocumentSummaryInformation8B