comad-tutorial
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comad-tutorial

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Survey of Approximate Query AcknowledgementsProcessing Techniques Brian Babcock (Stanford) Kaushik Chakrabarti (MSR) Mayur Datar (Stanford)Gautam Das Minos Garofalakis (Bell Labs) Venky Ganti (MSR)University of Texas at Arlingtonhttp://ranger.uta.edu/~gdas/2Outline Introduction Introduction Approximate Query Processing (AQP) Non-Sampling Based Methodsin Relational Databases – Histograms – Wavelets Sampling Based Methods Focus on answering Aggregate queries– Uniform Random Sampling – Aggregation queries often arise in OLAP – Biased/Non-Uniform Random Sampling and Data-Mining for large Databases– Distinct Value Estimation Conclusions3 4Examples of Aggregate Motivation for AQPQueries Answering complex aggregation queries over large data warehouses exactly can be SPJ queries with time consuming– aggregation operators such as If approximate answers are acceptable, • Count, Sum, Count(Distinct), Avgcan we answer these queries much faster? – Group By– Along with approximate answers, an estimate of the error in the approximation is important• Confidence Intervals5 61Example Quantifying ErrorSELECT State, COUNT (*) as ItemCountFROM SalesDataWHERE ProductID = 5437 Consider a simple aggregation queryGROUP BY StateORDER BY ItemCount DESC – Answer is a single numberExact Answer Approximate Answer – Relative error of query QState EstItemCount EstErrorStateItemCountExactAnswer− ApproxAnswer3425 3400WA WA 50 Error(Q) ...

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            !"!
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/!    '(  , & 7  $  2      6- ! 1+   &
5   ;  $     : *8 8 *'(8  2  %
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%    ! 2 *!  2 1! ,$        
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 5 *!     2 $    & 2 ,         7 ,61%D  2 5   =    
  38 48  * ! ! 2 *    -  2  ! !  2 ,   ! ! 2 +  ! :      #
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+1 3   &  1! &#  !   P ! !&  ! Q   $ &# "$ !#$% " !#$%     
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$                         '<(  , $ ? , H= E> H=  $ 7 < I,I%8 $ 2 7 = &  &#8 ! 8      2   J B < I,I% $ @> < I,IC J F> < I,IC
E1 3 .16  &#  G   $ &# K/!8  L>M 6'%<0NB(  !   K;!  8 LOM
+1 3 * * &   !   $ ! K+#   LLM +1! 1! K+#8 4 OOM 2 7  !   ! E8 B8   8 # 2 - = #   !!   &# 2 G % = ! !& 2 7  = E8   8 # :   &#  %  1!    2   &# #& !   &#GR ! ! ! ! !     
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+1 3 * +3/ K 8 /! LA M 2    : *  &# &  %   &   $      !  :  &     '8 =B( &# +3/ &#!   &!   8  $      &#G '  ( 5     1! 
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3    E1   + 1 !  !       & & 2+!     P! ! 3&          
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61 3 4  $ &8   !! !  ,    *                           3 $ !         
6 +1 3 K   LFM 2 $   &# 3 K%   FEM 2 4#! &! 2 *! ! &#
4+    !        !
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3 4 * 3 ! * ST  '# S T(                        '% ( 
41&!  ) !    &  $  K+   LOM 2 * $   $$) ( (#$% 2 * (%'   &HHI*I   & # : #    #$%*()$2 !    P & 2 6  + ! '-B( 5 : !  ! 2 ,  !    !  
+1 3 4% $  ! ! !     ! ! $ & ! 11   S$T  2 !! 3 ! KG   LCM 2 01!! 3 ! K*#&   FFM 
% /!    !     ! ,  $1   ! 2 7    $8      Q ST   2    !   $    !& &  $  
5  ,  'H= UH= &( = *VK&M 1 *VK1EM 2 *V   '( S!T  !& 2  6'W&8 0X(8 $ & = G  $  0= G  !   0YE   !!    *  
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4  &  1 !  5      & +1! $ !  & !!   $ 8 $     &      
 %    58    BFZ              ,   6  '<(  , $ , = F * = EF ,$  > < '<(   $  = F 5  = ><B = EF
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01%!   ! !  !  2 58 !      &  5  P  !     $  && P 2 / !8   !!!    $   = EP       !" # # # $ $ % &&&  &&& &&&  6 ,$  ',(  ,  ' < (   $ ,& H > $ & H > ',( = E@F '<( EF<@ Y >F<B = E@F = 
5 5 - , = W E 8  B 8 [8  X &    & - ',( = D  -  &     G #  , - '( =      5 !   & !  * - 2 58 >?8FFF J CFF $ && L>Z
!  %!    !# #$( .%%'0 +%%'  ,$ #$%% ./$ %'0 "%- -  
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5 5 %#( %  8 8 2 /8  !    $     $    $ !!  2  G 2 .   !   & ! $  && 2 -    %(% %)   $  $   K8&  2&& M $  : 58 >?8FFF J CFF $ && LF
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6  1!  62 *   $ '  ( 2 6     8  !   ! !  !# : 6    K38 3  FEM 1!2   !    '& Q  ( : '%         ( 2 6  1!   !   2 +!!$ *  $  %+8   !  
 ,!  1  % 2 5!  G  <0 8 $      2 !!    ,    $ &&  2 -$ !8  ! !  1*  , K. O>M 2 +     !1G <0 2 !!  $    $  && 2 / 8   !    2 /!       8 !  &    # &    & !!!   
!!   ,!  ! 2  2 5  !2 -  !  : - !  : -$  
-$        %'$ ! &   , 
6 /!    ' (+.  , + ,  )' *( )' -*( *(
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-  . @  ? ! B   > EZ   EF?>AB >  L     [ 
%!   6 /! % /! K*!   FEM 2         !    !2 )   !   ! 2   ! $  !  $  
  6 /!   '&P   (           / / / /     !       !   # # /0  /0 . / 0 . /1/0 & /0 /0 . /1
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 6 /! / / / /   '( 3 4/5 / / / /  2 3  / / / /  2 3  2 3  2 3 
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3$    &$  !  !9 6 !   8 2 0   *8 +8 +& 6 - 6
$&# $   ,!  / 8  & * $    52 *!   !    4    !  2   &!  +!   & !    ! ! 4 2 /  8     $  
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 / ,       +  ! = B < G   !
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%!   /*/*-5 K   FFM - 4 = WE8 B8   X &   $#! %!    !  2   '8 \ (   1!  %!   ! ! ! 'S1T(   $#! 
-   4#! 4#! 4  E 8[8 44 & 8 8 4 ! /   !   /    $4   !  $   !  &   4 
& 2 , , 2 4#! 4  E 8[8 2  !     +  S  4 ',(  , !  $ 4 T      $ 4
+ / * $#! 4  E 8[8 - ,  Y ,' E (  Y [  Y ,' ( *  4 ',( !   -0$  ! 4 ',(  &    -  Y ,'( 2 ,    ! 0 -   G!
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/*/*-5  $ 4          '&        4 ' ( , (       /   '( $  $#! 48    ' ( 4 ',(     !  !  &   $ !   !       ! !  
/*/*-5,'(     , !  $  /  4 ',( ,!   ,  Y ,' E ( Y[[ Y ,' ( 2  !    # &   4 ',(   ,! 3 6   
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