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A % A %A +( + # '( % +% / %% * ' % 5 $4 % /% 7 9 9 9, 93 97 !, ! ! !0 !7 =, = = =9 =! == =0 =3 'B - ( A @ + > D3 D5 @ % @ % -> ? G/"H '> " E = =9 =9 =! =! 0 0 0= 0, 0 0 09 % @B " @B * @B % * @B .B% 7 7 79 7! + 7 I ( 'J C . B * B B B B 'B . * ? B B '%$%# ?B < *% CB ( 'B B + K -% BF + K ' ( +% C + * > B B 4 "% * + # ( -B . # E + K % 'B > A " - ? + . > . ( $) ?> ? B % 'B $< / #D( B * ,,F % & % B L B B + K (B B + K F *% ,, ? (B + K G MNH 5 E B *( B !◦ / A 5 ' B * ,, ( B & , & (B ( +( ( % > & ?> (B & ◦ G-%H B &% B B ' 4 # 4 M#7N F O A & 2 ( C) " ) BP * % > B & B B B & 2 B B A 77 ! ,9 B ◦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i Cj / 6 3 " i = j F Ci ∩ Cj ∈ / {Ci , Cj } %% % ' " 6 ' / 2 12 / / " Ci , Cj ∈ C F Ci ∩ Cj = ∅ Ci , Cj ∈ C i = j %% % -.#. ' 8 6 I / 6 B B 6 ' 8 J I > 6 . 12 * / 6 B B Ci / 8 ? A / / $ Cj ∈ {∅, Ci } Cj ⊂Ci %% % /#. ' " ( 8% > (( + Ci ∩ Cj ∈ {Ci , Cj , ∅} %% 0. * ' ( > / * B : G)H % : / ' : ? 12 > / ( + : / 12 / ( G M'37NH %% + B 12 * B + ( . $ 12 S I 12 xi > > ? * * 12 $ 7 " S + 12 A: & ' ' ' F S F 12 (|S| = n ∈ ℵ) xi F i% 12 S xi,j F j % * i% 12 x1 = x1,1 x2 = x2,1 ··· ··· xn = · · · xn,d xn,1 x1,d x2,d 2 * d ∈ D * 12 * n×d%$: : * D * % :( ?( (< * B %% 1.#.2 ! 3 4 ? ? /5 B (< * * (B ( 12 B * ; (B (B 12 I ( ) ; ' $< ( $ * (B (B 12 ; $ D 1 dist(x, y ) = δi , δi = |D| i=1 0, f alls xi = yi 1, sonst G ,H B . * *B ' B B * 12 > ( > + >F • ∀x, y ∈ S : dist(x, y ) ∈ ≥0 • dist(x, y ) = 0 ⇔ x = y • dist(x, y ) = dist(x, y ) & *B D B & B B 4 ( " $ B dist(x, y ) = d 2 2 (x1 − y1 ) + · · · + (xd − yd ) = (xi − yi )2 i=d , G H " ( " $ > B + F % ∀x, y , z ∈ S : dist(x, z) ≥ dist(x, y ) + dist(y , z) ( (( > B 5 " ( " $ $ ( Lr %$ Gr ≥ 0HG M'37NH > Lr %$ 5"#" ( B G M3,NH F d r dist(x, y ) = |xi − yi |r G H i=d ' " *B Lr %$ * )< * * '% > J G MI$77NH ' $) A( ( B ?B @ * B% - (< ( 5$ G 9H 5< " G !H dist(x, y ) = |x1 − y2 | + · · · + |x1 − y2 | = d |xi − yi | G 9H i=d G !H $ $< ( (B (B 12 > 5= G =H . ( ( ; (B (B 12 dist(x, y ) = max(|x1 − y2 | , · · · , |x1 − y2 |) d xi ∗ yi G =H i=1 sim(x, y ) = d d (x )2 ∗ (xi )yi i i=1 i=1 I )< & > 5= )< ; $ (% ;< G%H; (B 12 B ? B : G * ,9H (% ;: n × n%$: B ( (B ( 12 0 dist(x2 , x1 ) D= dist(xn , x1 ) dist(x1 , x2 ) · · · dist(x1 , xn ) 0 · · · dist(x2 , xn ) d(xn , x2 ) ···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c(Ci ) = |Ci | |Ci | (dist(xir , xis ))2 G 0H r=1 s=1 xir r % ' / Ci # 4 $< > / > B D *B 12 / ( $ µ / c(Ci ) = |Ci | (dist(µi , xir ))2 G 3H r=1 * ? B BF , & ( $ > / & 2 12 x ∈ S / ( $ + > 2 / Ci # > 3 9 + > 2 / Ci $ µi |C | µi = i 1 xi |Ci | r=1 r , " ! & % 9 c(Ci )(∀i) / * ' B *( / > ? % ( )< @ " ( *B B B B B / * B * " E $ % ' B @ " @ ( G ) H / * B / ( * B * 2 12 / ( B 12 B / ' C *< 12 ( * ( @ B " > *B / * * 4 1 1 ' * " -: % O(k ∗ n) ' *B > " * % " G M##NH , & ( / B ' (B ?B > " * % & *( ' ) / B 9 & , B B> *( / $ / # / B . 1/c(Ci ) I ) & /% % " > & $ ) / 1 > / ( 4 * % " J " B % % 378"9 ' J / B B / 12 ) $ % ? %!& G. % ' !'' # & H G M'#7=NH + ? B / / B 4 ( > + K > B • ∈ ≥0 , x ∈ D N (x) = {y ∈ D : dist(x, y) ≤ } % x ,9 " • M inP T S ∈ N.x ∈ D +9" |N (x)| ≥ M inP T S • x ∈ D " y ∈ D 5 #2 x ∈ N (y) • x ∈ D y ∈ D ∃p1 , . . . , pn ∈ D : p1 = y, pn = xund∀i ∈ {1, . . . , n − 1} : pi+1 " pi • x, y ∈ D 2 ∃z ∈ D : x y z • : A9" B #2 % #2 • : A B #% E2 * , 4 B % 12 A B C < # & M in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xi ' D / Ci $ / C (B / ( dist(Ci , Cj ) ( ( / Ck = Ci ∪ Cj > / 12 D ' ? # B / ( B # * (B /% * B + ? * (B ,0 " ( 12 * (B ( 12 $< * ,! B @ B *< ( / B B > 4F • # ()F • $ ()F • * ()F dist(Ci , Cj ) = minx∈Ci ,y∈Cj dist(x, y) G 7H dist(Ci , Cj ) = maxx∈Ci ,y∈Cj dist(x, y) G ,H dist(Ci , Cj ) = 1 dist(x, y) |Ci | |Cj | x∈C ,y∈C i G ,,H j # () ? * (B (B /% ' 12 / ? 12 )<% ' (B (B / ? C( ' (B 12 (B / B /%' - ? / ( " +( + / * ? 2 B /%' 4 B @ ' @ ? / ( / B / ( B ? 4 /% ' ( * / GB " H ' B @ ? / C( GO(N 2 )H * @B + (: . > C( $ () * () # () + B /5 * * + A:% B -% B (B ? ( > /5 ? % A: ( /5 B # % - ( A: %': A2 E B * *B A *B *B ; ( * % ; (B * B * B ; (B 12 /5 * . ,3 " @"A 5 G ME07NH B * A • D T $ A # • di ∈ D % • ti,j E 2% A $ &) T % • w(ti,j ) .B • di = (w(ti,1 ), . . . , w(ti,K )) K = |T | ' B ? A B A .B I 2 * K = |T | * .B > A ( + A4 ( B A4 B 0 G ,H B $ ( E% ( G M/#"7 NH > B > B /5 > *B *B% / (> B ) ; B ( *T / B A2 > & ED ? /% 5 B B B . > ' *K -( > ( % . M/#"7 N B > -( A2 ( > *B / :% B * + *B ( ( # ( A ) *B > B ' / B * ( ( *> A < @ @4 -( ' . * + K B %% :0!: 5#. A%.B 0 A G * 9 !H > * ? /5 ( B B > 0 %.B G ME07N j 0 3 ! 4-! 5 5 -! ! 6 % ,7 " H (B #F ( % 4 G H ( ?4 G H # ( ) B 4 B • li G*( AH • al C D • tfi,j ?4 A 2 • nj *( A 2 $ -(4 ( 4 B F idfj = log |D| nj |D| + 1 G , H ?4 F ntfi,j = tfi,j tfi,j li + 0, 5 + 1, 5 al G ,H 4 B A ) 2 B ?% 4 A ?4 B < ( 2B + (B ? ( ( # * # B 0 %.B A j i w(ti,j ) = idfj ∗ ntfi,j G ,9H A ( A B ( B ,9 B %% + /5 > B ( ? 4 B > G BH A > E% B A % B"$ & ( ( & A G > -H ( B ( K B B ''# B & B ( + * *2 * & C ( & B & % ( & B ( - ? " :% & ((> G ME07NH B B & OP OP OP O(P OP ( & & A ( B @ ?% ? B > ? /5 B B %% ! ;0# + * B * ( /5 ) B " B ( A:% % G H * % B B + / * @B B # ' " 2 5 ( A:5 ( #: ? > B 5 ( # *J) /%E( ' "5 + /5 B ( B " (% ' A: B B ? % $ A ; (B + ( (B A B 5 *5 < B B ) " B ) 55 *>( ( > A: ( A B "5 'K + ( ) " + B ( ( A > > @ " ; 'T(( A% B (B * ? B B% ( A( % + B > ( (B (B %% < :. ! * ? ( /5 B $ 12 ; * B% ! - 7 -!!-!8 -! -! ! 921 . -!-! /0 : 7*-8 * 74! -! 8 7 .8 , " < $ ( A + ( ; % ( *( " ( ( B B / K / B ? G*% ;H (B ( * O+/*@P G * H ' / B ( B B ? ( /5 $ A 2 / ( ( + B A ( (B / ( * .% ( (B /% J< * B B $ > (B ? B B * ? (B > ( * B *( %%% = * O/ A C PM&UC77N > * ) /5 ( *% * B ; *( * M&UC77N B / B B *% ( B /( < 12 *% & B + K ? & (B A ' GH $ A GH * / > ( + K4 • ,$ F ' - ]0, 1] $ > • F ' A *( / % )< G H $( • Largei $ / Ci • F ' A *( / % $( • Smalli $ 1 2 / Ci ' / Ci A / B k > / Ci 4 F k = M inSup∗|Ci | I A B B 4 / " * / B # B B 4F k Intra(C) = Smallj j=1 Inter(C) = Σkj=1 |Largej | − G ,!H j = 1k Largej Cost(C) = w ∗ Intra(C) + Inter(C) G ,=H G ,0H ,! ( Intra(C) # ? % / " C B ? A # / Inter(C) G ,=H B $< > 6 (B / $ Inter(C) B ? / .B w # ,0 B # B B ,0 B / B $ B % # / ( B / < (B "F * ? *% B 2 / ( ' / (% B / )K % 2 B * # Cost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• D = {D1 , . . . , Dn } $ • T = {t1 , . . . , tk } $ A • Dj ⊆ T E $ A • M inSuport ∈ [0, 1] 4 B $ A 4 ( % - ( 4 • cov(T ⊂ T ) = {Di ∈ D|T ⊆ Di } • F = {Fj ⊆ T | |cov(Fj )| ≥ M inSuport ∗ |D|} 4 cov(T ⊂ T ) ( $ % A ' A B 4 B *( ' 4 A B M inSupport > B - G >( H ( F $ - -( k A k% # !' ! % > B * B > > 4 % A B $ ) ! " *( B G M/C*9NH * ( *%' 2 % 4 G M#,NH # B G%,H% B B % ( G%,H% ) % # # k >> # 4 & # B + B > ' "( # B ( B 4 * B $ $ ( ( #% ) # ( ' * ,# G,- ' # % M"VNH * ( 2 - *( ?B "4:%+ + < '( "% B * 'T(( ( B ' (B ' 4 - ⊆% > $ ? < > 2 1 )< * $%' F I A B M+'U N B / ? $ F ( ? J / ( * ?% B B B / + ? ) B 6 ' 2 & ? B / / * ?% > B /5 6 > B ( + / M+'U N ? B ? ( * > / $ - I 4 / # A / 4 ( A / # A 4 B ' &( G,'H (B A % "( ' G 'H B # ' B # > &( $ # B ' B 2B # > /G%H ' > A A ' / A {A, B} # > /G%H A {A} {B} 4 > $ / /G%HF • N (Fi ) = {Fj ∈ F |Fj ⊂ Fi ∧ |Fi − Fj | = 1} Fi ∈ F !-!-! 3 0 9 #-!2; = " & F $ $ / % ( +( Fi ( > A $ A F ( > / A 4 - / / B > ? . ? ( *B / # .% F B / 6 G H B ' > 6 % B A ) B G H A ' GJH /% /G%H B + ( / C # N (C) = {C1 , C2 , ..., Cn } ( *B # 4 @ 2 B 2B B / $ #% B / $ N (C) 2 # + K 6 ( B ( f > Di / C 4 f (Di ) = |{Ci ∈ N (C)|Di ∈ Ci }| G ,3H f # $ / B 6 / / (f (Dj ) − 1) Ci ∈ N (C) Dj ∈Ci M+'U N 4 * B 82'' G % > H / B F SO(Ci ) = (f (Dj ) − 1) Dj ∈Ci |{D ∈ Ci }| G ,7H > / G( 1H % 6 @ 6 / ( B / * ! ( "( > J / " < G- ,H B / B ) ' B +( / C > # ) G 7 H *( B / (> G- % 3H B # +* 0 " * !F / # > B B #% B C B / G 7 H ( B C # G 7 H & 7 $ B / / 'B '# - B $ / ' G 1%H J / / B > 2 B / ? /% B B B / B # 8 B $ ' / '%/ k% ? A $% k − 1 ? / $ /% A B $< >% ,7 ? # ' ? / +( A E B *( 4 A ( ' B * (B B B +( A ( " > (B % / B + G 6 /H +% GA /H ' B ? ( / - ' 3 " / * ? "% B A M inSupport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• '( • /%CF * ) > 2 / B (% B K / • 6 / F ' #%/ % '%/ •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tj ) > .B A tj D ; 5 ! 5 % -! -! , - < = 4 T W (tj ) = tf xidf (tj , di ) G9,H di ∈D∧tj ∈d .B M,N ( B ) A B N T W (tj ) = T W (tj ) max {T W (ti )|ti ∈ T }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{}H & (B B (B A {databas, db2} {databas, oracle} * ! F ? A * !F % A ' A B 4 ? ! ( A B & % % ( ' . > /% I # . / > % '%/ G# H / #%/ G# H %% ,++ ,!# M+'U N B *B / $ / > 6 K B / : @B % ) B * (B " *( ' E ) C) "( 2B /% $ C) ) B % B #: O(2n ) 5 B> + > 6 T( M+'U N B 5%* ( *: >% 6 C( $ / *: @B B ': ( B 1 9 5 (B " B ' @B *( > 6 ( /% $ & B 4 < *( / / B !%! / , # ' $ B ( > B B . > 'K M+'U N K " B > @ $ B B ( ( / (B B # 6 B / * !9F %A +( * !9 B +( (B * !, A% # ( B < # A / 2B A B * * !9 ' #%/ &(%/ G {}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• Ci FS ' / / • d FS ' $ Di Ci • Mi FS $ G BH /G%H Ci G$ #H • Ni FS $ G BH / Ci • Cdi FS $ d > ∃C ∈ Mi d ∈ C • mi (d) FS *( / C > C ∈ Mi ∧ d ∈ C & (B 12 $ Mi 12 $ Ni $ Mi B / * / 4 $ Ni $ 2 I B > / > ? % & '%/ B B > #> " / ( @ / Ci B ( 6 B / Mi B G/H Ni $ 4 6 6 / Ci F costov (d) = mi (d) − 1 G!,H * 6 / OC(Ci ) = costov (d) G! H d∈Cdi > 6 / G1/ % 1 /H $B #%/ " B > B ,. , ! . Di - 9 1, ! % 7- 98 -! 9 5 * 9 ( B ? > ' B / B / > # + * !9 ( ! & ( / 6 ( & / {sql} {column} / > ( 6 % & / # ( & 6 ( B> B & / > B> 'K * . B (B # > % % ( #. ?@#. ( ? 9 B > / % / ( B > ? > B @B ( / % / # B / * 6 " B > 'K A ( 4 *( f ts /% / B B ( ' B / B B ( % 6 * *< 4 B / ' ) C) " > $( /%# > / ( / 6 > % B > B / ( > B B 5%/ > A 5 %/ (% B ( B ? .( > $( /%# B .(B B > ( ' B ' B # > B B 6 I '%/ *( /% # ( # 6 % # > > # > ( $) ( ( # *( /%# • ni (d) FS *( / C > C ∈ Ni ∧ d ∈ C 92& < -! -! 99 5 $ -(4 > # ( $) % ( > 6 G!H costup (d) = ni (d) U C(Ci ) = G!9H costup (d) d∈Di /Cdi * !9 # > (% $) G/ % /H B B / ( Gd ∈ Di /Cdi H # B + * !9 B% + & ( / # ( $) *( / & {sql} = D2 D10 (B /%# ) D6 D9 2B & /% {sql} {column} / > ( # ( $) D9 # > B & / > # ( B ) B B & # % ( $) B & ( A /%# B # ( $) ( $ B / ( ( # 6 % % = 5 * # * . #< > / LCost(Ci ) = U C(Ci ) + OC(Ci ) = d∈Di /Cdi costup (d) + costov (d) G!!H d∈Cdi . / LCost(Ci) G7 H / Ci /% 6 B / ( ( /% # > * # / / > / /% $ . #: B B / ( 6 B B & / > / > B # > *( / / & #B $ % B ' # B / B /%# 9! 5 B 6 # ( $) % / (> *( G% H / # @ ) > / * ( & ( / . B !! - *B / ( 4 B . - ? + * !9 & # B . 6 & # B # ,7 ( $) 6 B % *B # {sql} {column} 6 > D5 D7 D8 B / # ( $) > D9 I 6 (B # # > 2B B ' * !, B ' % B $ # B / B B B & #% < :'' B B ' - # ( $) % 6 B # ( $) + < # ) ': *B # *B % # B *B $) % ' B + > > B F * ? % # B B & *B /% B> ? B # @> .B ( + 6 R (B .B * $) * B B ': !! ' ( . .% / % /% ( ) *( # B . / *( B LCostd(Ci ) = LCost(Ci )/ |Di | G!=H LCostd(Ci ) # B / Ci # > / # ( & B * # B B .> 2B% 9= 5 6 & & 'J * + % % 5 5 * B #< ( J / ( B %B > / & > *( ( '( 8% #< B # .> GA%H ( + B # G! H B B ( /% B LCostd(Ci ) ∗ W (Ci ) + GCost(Ci ) = GCost(Cj ) ∗ W (Cj ) Cj ∈Mi W (Ci ) + W (Cj ) G!0H Cj ∈Mi ∧GCost(Cj )>0 + / > !0 W (C) .B > # LCostd(Ci ) '%/ > # GCost(Cj ) #%/ .B * 2B / ( ' B #% / ? ( '%/ B B ' ) .B B *( 2B / B> '%/ )< .B >B A #% / & # #%/ J< *( C ( B B GCost(Ci ) > 2 / Ci B # A / Ci I # / A B 4 B & # + + /%# # > ( $) 6 ) # - .B / @ B B # / )< - ' * !! *( / % * .B + *( . / # 5 6 # /% # 2B # GC/G/H R ./G/HH @ # C G ( % / / A B + # ( # / C * / 90 5 * !!F + # G ( / C + # >% B + B F GCost(G) = LCostd (G)∗W (G)+GCost(C)∗W (C) W (G)+W (C) = 0,5∗100+0,2∗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⊆ % A ' A B A +B 97 5 {sql} > $ {databas, sql} ( ,% C > B & B - 3 > A B ,B; B A {column, databas, sql} ( + ? {column, databas} {sql} B ( - B ? {column, sql} {databas} > (B %12 : B : # > {column, sql} B G- ,=H & : B % )< .( $ G- 7H B G- ,H > ? A * B #% ( > ( > G- ,,H * ( B ' & > ( > & % * $ *%* G% M*79NH ' B %' B ,% 2B % B B ) B GY,H%A $ > '> A $ B A > O %%P ? > ' % ( B A% >( A A % A B >> B > > B B% .)< 2n 4 A ' " B T( * B B ,?# G M"VNH ' G M-//NH ( B *( 12 G ,%H & M"VN M-//N > B ? ( 4 $ 12 *( 12 G *( 12H B T( *%* + $ ? * '% * ( C( B * .( / %% A ". ! # 8 % *B% ! #< < $ 2B / / B 2 B B ( # > '%/ ( + % # > / # #%/ ) B ' + B $ A% ?( > B * !0 ( .! !,' 5 * AB .-! C6 =66 ! 5 E * !0F +% / "1$ "( B > &( &( 4 A B ,% / B "( > # / "(% "( J 6 '%/ > B A / B # 1 ( 4 "( / B # 2n > ( : -B * B B > C( 1 ( B% C( 2 B : N G *( /H B * (B $4) * W B C( B% >( $4 ' E( * W ? ? + ? B ( > B * ( 1 4 (B $4) % . # B C( T( * B % ? 1 4 *: "1$ "$ %% % 7#.2!2! * !3 ( * B 1% 4 A / B # '%/ * !3 ( "( B "( * !0 > * /% ( * B B% ? / G * ! H *< B "( B * > J /% ( BF * * "$ "$ "$ !, 5 * !3F %% * ( * * ! . * * ! "( * !3 B >> ( B / ( # > G- H # G- H # ( / > '%/ B & B / E B G- !H * B "( > &< $ > + /% G7 H G H E - &< (4 # B G H # G H > $ +∞ 4 > /% $ # 4 B * ! (B ! 9 * ( B "( >> E # / G- 3H & 2 B / GH $ ( - "( !3 A / ( 4 $ # 1 E ) C) O(2n ) ( B 5 A B 1 )% B ( * ? * !7 ( ' > > / : # ' 2B / * + * + / ' ( - # 4 % GAH ' C) " &( ( )$ 2$ ! -! -! & -! A=? . ! 5 * !7F ' # $ # B " % B A / 1 B * !7 > # " > # , , ,, OZP (B , , B (B , ,, # G B H ( , ,, 2B OXP (B # ,, , ( # A > # / * / # ' ( ? - + - % 9 G * !3H + ' ( B 1 ( B * + # (B # B> * A # 9 ! = >> # 0 B * B 2 ? B # ( $ B # G H ((> >> ' +( # #% > # B B A # ∪ 73&<4 >> B ' > * B 1 4 +B "( B B > & > ? > B B # Ck /% k $ E / C / {C1 , C2 , ..., Ck } $ - 1, ..., n .-! ; -! -! 9 -! ! 1! ! 5 ! F "( * !3 B (> % / ( ? # > B $ / % K # / 1 * 1 B & ( E "( B B F " 1, 2, 3, ..., n ' 1 > / C n ≺ C) ≤ GCost(M ≺ C)∀M ∈ P (N ) GCost(C n ≺ C > / C B / C n P (N ) ( C "( / C GCost(Cn ≺ C) # G 1H > / C * " # # Z GCost(C k−1 ≺ C) ≤ GCost(Ck ≺ C)∧ n ≺ C) GCost(Ck−1 ≺ C) ≥ GCost(C k < n > . # .> F , # LCost(C) # /% Ck # GCost(C k−1 ≺ C) # ( / Ck > B ? # # > B GCost(C k−1 ≺ C) ( " ,H & 9 C ! * ,! 9 2 !9 5 # # # / Ck GH% B / C1 , ..., Ck−1 )< # * B ) B ? #K( / % B # * > B /% B #K( / > B B / ( > B *% B # B / Ck /% B / B ) > /% Ck B * + n ' / Ck $ B / C ( # > F n /C ≺ C) < GCost(C n ≺ C) GCost(C k n ≺ C) > ( & * GCost(C 1 . B # ( / Ck ( " H # / C B $ # / B % # / C G !0H # GCost(Ck ) / Ck > # GCost(C k−1 ≺ C) )% GCost(Ck−1 ≺ C) < GCost(Ck ≺ C) * # F GCost(Ck ) > GCost(C k−1 ≺ C) ∧ GCost(Ck ) > GCost(Cn ≺ C) #K( > / ( B% / G " ,H n /Ck ≺ C) < GCost(C n ≺ C) GCost(C ⇒ & ( * ( " H & " ,H H * " , % 1 " * # # [ * B * 1 - & . * -! !! 3 " 5 +B ( + - # < B 1 ) * B +% B + - 9 I + +B , (B B >> # # Ck )< # # & ) # # ∪ 73&<4 # $% ( ? # > G # # Ck H )< 1 * 4 1 B% C( O(2n ) / * ? B C(% 2 ( @ ) > %% % ?!)B A! . ! ' # $4 ? / 6 T( ' 4F • N FS $ / C • n(d) FS |{CC ∈ N |d ∈ CC}| • dc(C) FS *( C 6 T( B F Overlap(Ci ) = n(d)/dc(Ci ) G!3H d∈Ci / 6 ? ( % ( ( B & $ / 6 T( Overlap(Ci ) B ' * ' B - "( !3 B 2 * "( B 6 - *B% E( B * ' B * & *B C( / B %% % ?!)B 25!* + $4 * B 2 E% n / B % B / ( ( * !, ( * * . B "( & > iN ext G : C /H C "2 "4$ != 5 * !,F % 5 $4 > G 7 H * 2 E B n # % G- 9H n *B > - "( n # C / > F I # : )< iN ext G #H ( ( B / 7 > ( # # B : )< iN ext "(% C # (> G CH > C / B "( B * + "% ( B 2B >> ' E B & 4 "( > $ & ∞ (> & ? C % $ / B # B ( ? B > ( ' % G AH : *B *( n A B # ( *B A # / *B * : ( # E n > *( > / > .> & 1 ( 4 *( ? 2 % $"" 2 % $"" "2 "4$ 2$ %% 7!. ! :. ( * * B /% % ' / % ( # G +H B B / #%/ ) > -B / ' / 2B % ) #%/ +B ) / {column, sql} {column, database} % !0 5 @ {column, database, sql} (B % {column, database, sql} 4 A / ) / {column, database, sql}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n ?. B G4 8 12 16H / $4 * B (B E( G, $ , $H > + *: ? * 2 *( ( >> # B > 6 / G F H ?. ? B n # #% ( B * B 2 # ' G * !7 * ! ,H ( 2B n B #%# (B G B $) BH ? %% * B %% * -! -!2 2 ! -!, 1 -! @ (-! &<, 0(2n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• "( F *$ * U" =Y G,7, .(H • F , .+ E*$ G == H ' ( .> / *:% > B 2 @B " @B B B * , $ E , $ E ' ( + ;# @B B ' % *: ' . 0, ( A%%? B '% / %.5 * B ' *: 33 8 % % #. ! :. B ? ? M&'N ( B ? ! B ? * 9 * 0,9 ( ' * #< B $< B * ! B B > ? 'K B #( * 2 ' / B / B A (( ? B > ( B > # B B% > ( # B . > # > 6 @ ? M&'N B . > ? #<G * ! 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n ) C( ( 1% ( 4 B * ( G ! ,H K B B * T( & ' ( ) * *( B 9 A G,%H - ( *: G?. %%H (B T( ( / .> & A ( ? % 'B G =H @ 2 ( B & / *: ? / B G (> H .> B ? B C) ) #: / B *( A * > *< B *( A ( ? % 'B / (( A B F & " /% ? ( *: L ' ' * > E " / % *( > B 73 $ M*+#77N $ * $ $ + %" # 1"A/F1 " A 5 / A / 5 $ ,777 M*# N I * . # C $ B A 5 $ * M*79N E * B E , ! 5 ! 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GH 0" GH 3# GH 7# GH , GH ,, # GH , $ GH C C , C % 9 3, , , 7 , , ,3 709, ==99 909 7= 0079 ! ,77! 3,=! 0 = ,9 =,00 9 ,3 , ,! 0 , 97 ,!= ,099 ,9 , 97 =0 =, 97\ ,!\ !00\ ,07 !0 =!= ,0,\ ,!,\ !93\ C C 9 C ! =,= ,! 3 0 = 9 0 9 0 3 79 , ! 00=! 09,7 97 % % =\ % % 7! % % 7!=\ % % . , !9 03 3 !,= =,,= 0=07 = ,, 0 ,,! 9 9=0 9!\ 037 9 ,\ A * F * @B F E(%/ .B (|N | + |M |) ,, )* ) /" , 9 ! = 0 3 ? ,!3!0 70\ ,!,, 79!\ ,9!9 7! \ ,!! 7!07\ ,,,!7 73!\ ,9=7 730 \ 77=0 77!,\ 77=0 77!,\ 777! 7707\ , ,!3!0 70\ ,!09! 73\ ,!09 73,\ ,!=97 733\ ,, 7073\ ,9 = 7300\ 77=3= 77!\ 7799 7709\ 7799 7709\ ,!3!0 7=77 ,!7!0 7=, ,=07 7 7 9 ,!07! 70!9 ,,, 9 7339 ,,77 73737 77,7, 7777! 77,7, 7777! 77,7, 7777! ,!3!0 70\ ,=, 7!=\ ,=33 7 39\ ,!7,0 7=!\ ,, ,9 73\ ,!0 73=7\ 779 7703\ 77,7, 7777\ 77,7, 7777\ A *F * @B F ( & G ( & ( E(% / H /" , 9 ! = 0 3 7 , ,, ? , 9,0 370=\ , =0 7!9\ , ,=!7 7,!7\ , ,=!7 7,!7\ ,,!,,7 7=07\ ,,9 99 70!9\ ,,9 73,\ ,,, 73!\ ,, 3 73!3\ ,, 3 73!3\ ,, 3 73!3\ ,,,=!3 7707\ , , 9,0 370=\ , 099 30!\ , !09 33=9\ , ,9,, 7,03\ ,,9!7 70 9\ ,,9,3, 70!7\ ,, 7== 73=9\ ,, 79, 73==\ ,,,== 7707\ ,,,== 7707\ ,,,== 7707\ ,,,== 7707\ , 9,0 370=\ , 3=, 3==9\ , 0, 30=0\ , 7, \ ,,9! 70,\ ,,9 7090\ ,, 3 9 730=\ ,, 09! 733\ ,,,9== 7770\ ,,,9== 7770\ ,,,9== 7770\ ,,,9== 7770\ , 90 7 !\ ,= 3!93\ , 779 3!0!\ , 339 377!\ ,,!0! 7=3\ ,,9=,9 70 \ ,, =7 7333\ ,, 00 733,\ ,,,9== 7770\ ,,,9== 7770\ ,,,9== 7770\ ,,,9== 7770\ A *9F " @B F ( & G ( & ( E(% / H , /" , 9 ! = 0 3 7 ? ,, 7 393 \ , =7 7,\ , =7 7,\ , ,,7, 7,7 \ ,,0==0 79=0\ ,,97!9 7=7,\ ,,9 39 7093\ ,,0 7 707!\ ,, , 0 77!\ ,,,9, 7770\ , ,, 7 393 \ , !0 , 33=,\ , !=73 33= \ , ! 37,\ ,,0073 79!0\ ,,= 7! 7!07\ ,, != 77 \ ,, 3 77 ,\ ,,,!!3 773=\ ,,,!!3 773=\ ,, 7 393 \ , !0 7 33=\ , ! ,3 337=\ , 9 9 37==\ ,,0993 793!\ ,,= =0 7!3,\ ,,09 73! \ ,, 9 777\ ,,,=7! 770\ ,,,=7! 770\ ,, 7 393 \ , 003 309=\ , =3= 303,\ , = =, 33 \ ,,0,3 7!=\ ,,=! 7!= \ ,,9 0 7093\ ,,9!,! 70 3\ ,,,=7= 770\ ,,,=7= 770\ A *!F " @B F ( & % G ( & ( E(%/ H /" , 9 ! = 0 3 ? 37!70 7,=9\ 3! 09 7= 7\ 3! 09 7= 7\ 3!7= 7=97\ 39,30 70!\ 3 == 77\ 3 =, 779\ 3 ,,0 7777\ 3 ,,0 7777\ , 37!70 7,=9\ 3!39 7!==\ 3!39 7!==\ 3!!07 7!79\ 3!7 73 \ 3 0, 77 0\ 3 097 77 \ 3 3, 77=0\ 3 3, 77=0\ 37!70 7,=9\ 3!0,3 7!07\ 3!0,3 7!07\ 3!9 7=,9\ 3!= 73!\ 3 =0, 77 \ 3 !7 779,\ 3 7 770 \ 3 7 770 \ 37!70 7,=9\ 3=!7 7!9,\ 3!73 7!97\ 3!3= 7!=\ 30= 737\ 3 79 77\ 3 00 77 0\ 3 7 770 \ 3 7 770 \ A *=F B @B F ( & G ( & ( E(% / H ,