Performance Tuning for Querieswith AggregatesASAP FOR BW ACCELERATORBUSINESS INFORMATION WAREHOUSE Documentation on using Aggregates in SAPsBWDocument Version 1.0 of June/2000AGGREGATE KEERTHITable of Contents1 INTRODUCTION.................................................................................................................................. 32 AGGREGATES..................................................................................................................................... 32.1 EXAMPLES.................................................................................................................................. 42.1.1 Aggregate grouped according to characteristic value.............................................................52.1.2 Aggregate filtered according to a fixed value.........................................................................52.1.3 Aggregate grouped according to navigation attribute value...................................................52.1.4 Aggregate grouped according to the nodes of a hierarchy level............................................63 MAINTAINING AGGREGATES............................................................................................................ 73.1 ACTIVATING AND FILLING.............................................................................................................. 73.2 ROLL-UP..................................................................................................................................... 83.3 CHANGE RUN.............................................................................................................................. 94 MAINTENANCE OTIMI!ATION....................................................................................................... 1"4.1 FILLING..................................................................................................................................... 14.2 CHANGE RUN............................................................................................................................ 1# $INDING E$$ICIENT AGGREGATES............................................................................................... 11!.1 RULES FOR EFFICIENT AGGREGATES........................................................................................... 11!.2 ESTIMATING THE SI"E OF AGGREGATES....................................................................................... 12!.3 EFFICIENT AGGREGATES FOR AN INFOCUBE................................................................................. 14% &UERIES AND AGGREGATES......................................................................................................... 1##.1 ANAL$"ING A %UER$ & A NAVIGATION STEP................................................................................. 1!#.2 TESTING THE EFFICIENC$ OF AGGREGATES.................................................................................. 1##.3 READ MODE OF A %UER$........................................................................................................... 17#.4 EFFECTS OF THE %UER$ DESIGN ON AGGREGATES......................................................................176.4.1 Query Definitions ith !articular "ffects on Aggregates......................................................1#6.4.2 $ecogni%ing !articular Query Definitions............................................................................. 1&7 AENDI'.......................................................................................................................................... 217.1 ROLL-UP AND CONSISTENC$....................................................................................................... 217.2 AGGREGATES AND MOST RECENT DATA FROM THE INFOCUBE.......................................................237.3 TRANSPORTING AGGREGATES..................................................................................................... 237.4 CHEC'TOOL FOR AGGREGATES................................................................................................... 247.! ADDITIONAL INFORMATION.......................................................................................................... 247.# OSS NOTES............................................................................................................................. 242""" SA AG 2AGGREGATE KEERTHI2""" SA AG 31 Int(o)*+t,onT()* +,-./012 34,5)+0* 61 ,5045)07 ,8 2(0 ,32),1 ,8 .*)19 699409620* )1 2(0 SAP B.*)10** I18,4/62),1 W640(,.*0. I2 +,0* 1,2 40804 2, 6 3642)-.:64 40:06*0; 00 )* 2(0 34)/64= .1)2 ,8 *2,4690 8,4 +626 8,4 403,42)19 3.43,*0*. T(0 40*.:2* ,>26)10+ >= 0.2 62 2(0 *6/0 2)/0 40*24)-2* 2(0 40*.:2)19 +626*02. A99409620* -61 >0 -40620+ 2, ,32)/)@0 2(0 3048,4/61-0 ,8 2(0*0 616:=*0*.A1 699409620 )* 6 /6204)6:)@0+; *.//64)@0+ 5)07 ,8 2(0 +626 )1 61 I18,C.>0. I2 *2,40* 6 *.>*02 ,8 I18,C.>0 +626 )1 6 40+.1+612 8,4/. W(01 61 6334,34)620 699409620 8,4 6 ?.04= 00 406+ +)40-2:= 84,/ 2(0 +626>6*0 +.4)19 ?.04= 00 406+ 84,/ 2(0 +626>6*0; *300+ .3 ?.04= 06*0.W(01 6 ?.04= )* 06*0 ?.04)0*1. T(0 *=*20/ 2(01 :,,A* 8,4 2(0 >0*2 3,**)>:0 699409620 8,4 06-( ,8 2(0 +626>6*0 ?.04)0*. A1 06*= 76= 2, -,1-032.6:)@0 61 699409620 )* 2, 2()1A ,8 2(0/ 6* 34,5)+)19 6 *)/):64 >0108)2 6* 6++)19 61 6++)2),16: )1+0< 2, 6 +626>6*0 26>:0. A99409620* 40?.)40 1, *30-)6: A1,7:0+90 >= 2(0 01+-.*04; 6* 2(0= 640 -,/3:020:= 2461*364012. T(0 ,1:= 76= 61 01+-.*04 /)9(2 40-,91)@0 2(0 0= 2(0 3048,4/61-0 96)1 2(62 )* ,>*0450+.$,. -61 ,1:= -40620 699409620* 8,4 B6*)-C.>0*2. B6*)-C.>0* 640 I18,C.>0* 2(62 (650 6 86-2 26>:0 61+ +)/01*),1 26>:0*. $,. +, 1,2 (650 2, -40620 699409620* 8,4 M.:2)C.>0* >0-6.*0 2(0 *=*20/ *3:)2* .3 6 M.:2)C.>0 ?.04= )12, *.>?.04)0* 8,4 2(0 )1+)5)+.6: *.>-I18,C.>0*. T(0*0 *.>?.04)0* -61 2(01 .*0 2(0 699409620 ,8 2(0 *.>-I18,C.>0*.2 A--(e-atesA99409620* *(,.:+ >0 >.):2 2, 01(61-0 2(0 3048,4/61-0 ,8 *30-)8)- ?.04)0* ,4 403,42*. W(01 >.):+)19 699409620*; -,1*)+04 2(0 *30-)8)- -(646-204)*2)-*; 165)962),1 6224)>.20*; ,4 ()0464-(= 1,+0* 2(62 2(0 ?.04= 40?.)40* 2, 8.:8):: 2(0 40?.0*2 )2 /6A0* ,8 2(0 +626>6*0. A99409620* -61 2(01 >0 26):,40+ 2, /0022(0 40?.)40/012* ,8 ?.04)0* ,4 *02* ,8 ?.04)0* )1 6 /,40 ,32)/6: /61104.A99409620* -61 >0 >.):2 84,/ 2(0 -(646-204)*2)-* 61+ 165)962),1 6224)>.20* ,8 61 I18,C.>0. T()* /061* 2(62 =,. -61 6:*, *2,40 2(0 56:.0* )1 2(0 ()0464-(= :050: ,8 61 0.20*; 7()-( =,. 7612 94,.30+ 6--,4+)19 2, 2(0)4 56:.0* )1 2(0 699409620; 640 )1+)-620+ >= 6 BCD. I8 =,. 7612 6 -(646-204)*2)- ,4 165)962),1 6224)>.20 2, >0 8):2040+ 6--,4+)19 2, 6 *)19:0; 8)0 *30-)8)0+. I8 =,. 7612 2(0 699409620 2, >0 94,.30+ 6--,4+)19 2, 2(0 1,+0* 2(62 640 ,1 ,10 :050: ,8 61 0,:)@0 2()*E 2(0 ()0464-(= 61+ 2(0 :050: /.*2 >0 *30-)8)0+.1 I1 2(0 1.2B S=*20/ 2(040 )* 1, /,40 2(61 ,10 +626>6*0 ?.04= 8,4 0504= 165)962),1 *203.2 S=*20/ 1.2B ,1:= (6* B6*)-C.>0*. R0/,20C.>0* 61+ M.:2)C.>0* 640 1,2 *.33,420+ (040.AGGREGATEKEERTHIC G4,.30+ 6--,4+)19 2, 2(0 56:.0* ,8 2(0 -(646-204)*2)- F 165)962),1 6224)>.20.H G4,.30+ 6--,4+)19 2, 2(0 1,+0* ,8 6 ()0464-(= :050:.F F):2040+ 6--,4+)19 2, 6 8)6*0. T()* 616:,9= 6:*, 9,0* 8,4 1,+0* 84,/ 6 ()0464-(=. I8 2(0 ?.04= 100+* 2(0 56:.0* 8,4 ()0464-(= 1,+0* 2(01 =,. -61 .*0 6:: 2(0 699409620* 2(62 640 94,.30+ 6--,4+)192, ()0464-(= 1,+0*; 7(,*0 :050: )* >0:,7 2(0 */6::0*2 :050: 100+0+. E0 +)*-.**0+ :6204.P:06*0 1,20 2(62 2)/0-+0301+012 165)962),1 6224)>.20* 61+ 2)/0-+0301+012 ()0464-(= *24.-2.40* -611,2 >0 .*0+ )1 61 699409620. I1 2(0*0 -6*0*; (,70504; =,. -61 94,.3 2(0 699409620 6--,4+)19 2, 2(0 56:.0* ,8 )2* -(646-204)*2)-*. I8 2(0 012)40 ()0464-(= )* 2)/0-+0301+012 )2 -61 >0 .*0+ )1 61 699409620; >.2 )8 2(0 ()0464-(= *24.-2.40 )* 2)/0-+0301+012 )2 -611,2 >0 .*0+. S00 2(0 40:05612 ASAP +,-./012 ,1 ()0464-()0* 8,4 +026):*.2.1 E/a0.lesT(0 8,::,7)19 06*0+ ,1 6 504= *)/3:)8)0+ I18,C.>0 7)2( 2(0 27, -(646-204)*2)-* GC,.124=G 61+ GC.*2,/04G 61+ 2(0 A0= 8)9.40 GS6:0*G. T(0 +626 )* 6* 8,::,7*HCountry Customer SalesUSA B.99= S,82 1G04/61= O-061 N027,4A* 1!USA F.11= D.+* !A.*24)6 O-061 N027,4A* 1A.*24)6 T(,4 I1+.*24)0* 1G04/61= F.11= D.+* 2USA B.99= S,82 2!E/a0.le InfoC*be2.1.1 A--(e-ate -(o*.e) a++o(),n- to +1a(a+te(,st,+ 2al*eA1 699409620 2(62 -,126)1* 2(0 -,.124= )18,4/62),1 61+ )* *.//64)@0+ 7)2( 2(0 -.*2,/04* :,,A* :)A0 2()*HCountry Sales2""" SA AG #AGGREGATEKEERTHIUSA 4G04/61= 3!A.*24)6 2A--(e-ate3 Co*nt(4 567T()* 00 .*0+ >= 6 ?.04= 2(62 403,42* 2(0 *6:0* >= -,.124= ,4 2,26: *6:0*. T(0 699409620 -,.:+ 6:*, >0 .*0+ 8,4 403,42* 6--,4+)19 2, 6 165)962),1 6224)>.20 8,4 2(0 -(646-204)*2)--,.124= ,4 6--,4+)19 2, 6 ()0464-(= -,126)1)19 2(0 -,.124)0*. I8 +.4)19 ?.04= 165)962),1 2(040 )* 6 +4)::+,71 ,4 6 *0:0-2),1 )* /6+0 8,4 6 I-.*2,/04J; 2()* 699409620 7,.:+ 1,2 >0 .*0+. T()* )* >0-6.*0 2()* 699409620 +,0* 1,2 -,126)1 61= +026):0+ )18,4/62),1 6>,.2 2(0 -.*2,/04*; ,1:= *.//64)@0+ -.*2,/04 +626. A99409620 8):2040+ 6--,4+)19 2, 6 8)0 .*0+ >= ?.04)0* 2(62 (650 2(0 *6/0 8):204. F):204 56:.0* 8,4 699409620* *(,.:+ ,1:= >0 .*0+ )8 =,. ,1:= 40?.)40 ,10 56:.0 8,4 6 *30-)8)- ?.04=; ,4 165)962),1 *203. T=3)-6: 0.20 ,8 2(0 )1+.*24= 7)2( 2(0 8,::,7)19 /6*204 +626 26>:0HCustomer IndustryB.99= S,82 T0-(1,:,9=O-061 N027,4A* T0-(1,:,9=F.11= D.+* C,1*./042""" SA AG %AGGREGATEKEERTHIT(,4 I1+.*24)0* C(0/)-6:*C*sto0e( Maste( Data TableA1 699409620 8,4 2(0 )1+.*24= -,126)1* 2(0 8,::,7)19 56:.0*HIndustry SalesT0-(1,:,9= #C,1*./04 2!C(0/)-6:* 1A--(e-ate3 In)*st(4 567I1 2()* )1+.*24= 69940962000.2):)@0+. H,70504; =,. -61 ,>26)1 2(0 2,26: *6:0* 6* 70:: 6* 1,+0 56:.0* )8 2(040 )* 6 ()0464-(= 6>,502(0 )1+.*24=.2.1.4 A--(e-ate -(o*.e) a++o(),n- to t1e no)es of a 1,e(a(+14 le2elA1 001-(4. T()* 34,-0** )* 6334,34)620 )8 2(0 +626 ,8 *05046: 36-A02* 8,4/ 6 :,9)-6: .1)2 61+ ,1:= /6A0 *01*0 )8 2(0= 640 40:06*0+ 2,902(04. A1 00 )8 +)8804012 3:612* +0:)504 2(0)4 +626 62 +)8804012 2)/0*; >.2 2(0 +626 *(,.:+ ,1:= >0 5)*)>:0 )8 6:: 3:612* (650 :,6+0+ 2(0)4 +626 )12, 2(0 I18,C.>0.2. $,. -61 6:*, *02 .3 2(0 I18,C.>0 *, 2(62 0504= +626 36-A02 )* 6.2,/62)-6::= 4,::0+ .3 )12, 2(0699409620 )8 )2 )* 20-(1)-6::= -,440-2 61+ 2(0 ?.6:)2= (6* >001 01*.40+. T, +, 2()*; )1 2(0 *-4001 7(040 =,. -61 *-(0+.:0 2(0 /61.6: 4,::-.3; -(,,*0 "nviron+ent ' $e,uest -andling. I1 2(0 100 26A01 )12, 6--,.12 8,4 2(0 -(6190 4.1. $,. -61 6:*, *-(0+.:0 2()* 34,946/ 304),+)-6::= ,4 6226-( )2 2, 05012 -(6)1*. $,. -61 6:*, *650 2(0 :)*2 ,8 -(646-204)*2)-* 61+ ()0464-()0* 6* 564)612* 61+ 24062 2(0/ 6* 564)612* 7(01 *-(0+.:)19. I8 =,. +, 1,2 01204 61=2()19; 6:: 2(,*0 -(646-204)*2)-* 640 26A01 )12, 6--,.12 7(,*0 /6*204 +626 =,. :,6+0+ ,4 -(6190+ /61.6::=; 61+ 6:: 2(0 ()0464-()0* 2(62 7040 /64A0+ 8,4 2(0 406:)91/012 4.1. I8 =,. -(6190+ 6 ()0464-(=; =,. /.*2 6-2)5620 2()* -(6190. W(01 =,. :,6+ ()0464-()0* =,. -61 *02 7(02(04 =,. 7612 2(0 ()0464-(= 2, >0 +)40-2:= 6-2)5620+ ,4 /64A0+. I8 2(040 640 1, 699409620* 2(62 -,126)1 2(0*0 ()0464-()0*; 2(0 ()0464-(= )* +)40-2:= 6-2)5620+. I8 2(040 640 699409620*; 6 3,3.3 633064* 6*A)19 =,. )8 =,. 7612 2, +0:020 2(0 699409620* )1 ?.0*2),1 61+ +)40-2:=6-2)5620 2(0 ()0464-()0*; ,4 7(02(04 2(0 -(6190* *(,.:+ M.*2 >0 /64A0+. W(01 =,. :,6+ 61+ 62 2(0 *6/0 2)/0 6-2)5620 2(0 ()0464-(=; )2 )* /64A0+ 8,4 2(0 -(6190 4.1 6* :,19 6* 699409620* 0.20* 61+ ()0464-(= :050:* 640 90104620+ 2(62 (650 6-2.6::= -(6190+#. T(0 40:05612 699409620* 2(62 640 2, >0 6+M.*20+ 640 90104620+ 84,/ 2()* :)*2.2. T(0 *=*20/ 6+M.*2* 2(0 699409620* 61+ -6:-.:620* 2(0 304-012690 ,8 -(6190 304 699409620. I8 2(0 304-012690 )* */6::; 2(0 -(6190* 640 -6:-.:620+ 0.):2 )1 6 20/3,464= 26>:0. I1 2.; =,. -61 *02 68204 7(62 -(6190 4620 2(0 699409620 *(,.:+ >0 -(6190+; )1 BW C.*2,/)@)19 K)ools ' 1usiness "ngineer ' 13 (usto+i%ingL K/A! $eference *45 ' 13 (usto+i%ing *+ple+entation 5uide' 1usiness *nfor+ation 3arehouse ' 5eneral 13 /ettings ' 4aintain Aggregate $ealign+ent $unL. P405),.* 20*2* (650 *(,71 2(62 2()* 56:.0 *(,.:+ >0 >027001 1 61+ 2 304-012. T(0 +0:26 34,-0** 76* )/3:0/0120+ :6204 )1 S=*20/ 1.2B. T, .*0 )2; *00 2(0 OSS 1,20 181944.3. M6*204 +626 61+ ()0464-()0* 640 6-2)5620+7.4. T(0 20/3,464= 699409620 26>:0* 640 4016/0+. W)2( +626>6*0* 2(62 +, 1,2 *.33,42 2(0 4016/)19 ,8 )1+)-0*; 2(0 )1+)-0* 640 40>.):2 62 2()* *2690. I1 2()* 504= *(,42 3(6*0; )8 2(0 )1+)-0* 640 1,2 40>.):2; =,. -611,2 06*0* 2(62 ,1:= (650 2(0 ID)42= R06+J /,+0; R03,42)19 )* 1,2 3,**)>:0 )1 2()* 3(6*0 ,8 2(0 -(6190 4.1.2""" SA AG 1"AGGREGATEKEERTHI4 Ma,ntenan+e O.t,0,=at,on $,. -61 /,1)2,4 2(0 3048,4/61-0 ,8 2(0 /6)120161-0 8.1-2),1* 7)2( BW *262)*2)-*. T(0 *262)*2)-6: +626 ,1 2(0 699409620* )* *2,40+ 20/3,464):= )1 2(0 26>:0 RSDDSTATAGGR; >08,40 )2 )* :,6+0+ )12, 2(0 BW *262)*2)-* I18,C.>0. $,. 6:*, :,,A )1 2()* 26>:0 K2461*6-2),1 /"16L )8 =,. 7612 6 ?.)-A 616:=*)*,8 (,7 6 3642)-.:64 4,::-.3 ,4 -(6190 4.1 (6* >0(650+. I8 3048,4/61-0 7,4*01* ,504 2)/0; )2 /6= >0 2(62 2(0 6/,.12 ,8 +626 (6* )1-406*0+; ,4 2(62 )1+)-0* (650 +090104620+. I1 2(0 :62204 -6*0; =,. /.*240,4961)@0 2(0 *0-,1+64= )1+)-0* ,8 2(0 699409620 86-2 26>:0 .*)19 +626>6*0*.4.1 $,ll,n-I8 =,.4 *=*20/ (6* 6+0?.620 40*,.4-0* K1./>04 ,8 34,-0**,4*; 1./>04 ,8 >6-A94,.1+ 34,-0**0*; 01,.9( 20/3,464= 26>:0 *36-0 PSAPTEMP; 01,.9( /6)1 /0/,4=L =,. -61 8):: *05046: 699409620* 622(0 *6/0 2)/0 )1 *05046: >6-A94,.1+ 34,-0**0*. T, +, 2()*; *0:0-2 3642 ,8 2(0 699409620 =,. 7612 2, 8)::; *-(0+.:0 )2 8,4 8)::)19; *0:0-2 61,2(04 3642; 61+ *-(0+.:0 2()* 8,4 8)::)19 2,,. R03062 2(0 34,-0**. A* 6 40*.:2; 2(0 *.>36-A02* 640 8)::0+ )1 3646::0:. T()1A 6>,.2 2(0 ()0464-()-6: *24.-2.40 ,8 2(0 699409620 >08,40(61+; 61+ *-(0+.:0 ,1:= -,/3:020 >461-(0*. T0*2 7(02(04 2(0 +626>6*0 ,32),1 IP646::0: %.04=J *300+* .3 2(0 8)::)19 34,-0**.4.2 C1an-e R*n$,. ,32)/)@0 6 -(6190 4.1 >= +08)1)19 >6*)- 699409620* 8,4 699409620* 2(62 -,126)1 ()0464-()0* ,4 165)962),1 6224)>.20* 2(62 6:204 840?.012:=. I1*206+ ,8 6224)>.20* ,4 ()0464-()0*; 2(0*0 >6*)- 699409620* -,126)1 2(0 40:05612 -(646-204)*2)- 94,.30+ 6--,4+)19 2, 56:.0*. T(0 6+5612690 )*; 2(62 2(0 -(6190 4.1 /.*2 1,2 6+M.*2 )2*0:8 2, 2(0 >6*)- 699409620*; >.2 2(0 +626 8,4 2(0 699409620 2(62 100+* 2, >0 6+M.*20+; -61 >0 406+ )1 61 6:406+= *.//64)@0+ 8,4/ 84,/ 2(0 >6*)- 699409620. I2 )* ,1:= .*08.: 2, .*0 6 >6*)- 699409620; (,70504; )8 )2 )* -,1*)+046>:= */6::04 2(61 2(0 I18,C.>0. $,. -61 6:*, .*0 ()0464-()0* 61+ 6224)>.20* 2(62 +, 1,2 6:204 840?.012:= )1 6 >6*)- 699409620. T()* -61; (,70504; /061 :,19 4.1 2)/0* 8,4 2(0 -(6190 4.1; )8 2(0*0 6224)>.20* ,4 ()0464-()0* +, 6-2.6::= -(6190 62 *,/0 3,)12.# $,n),n- Eff,+,ent A--(e-ates$,. -61 61+ *(,.:+ +08)10 6 :,2 ,8 699409620* 8,4 61 I18,C.>0. H,70504; 7(01 =,. -40620 699409620*; =,. /.*2 6:76=* /6)126)1 6 >6:61-0 >027001 -,*2 61+ .*0. O1 2(0 ,10 (61+; 699409620* )/34,50 ?.04= 3048,4/61-0; >.2 ,1 2(0 ,2(04 (61+; 2(0= (650 6 10962)50 0880-2 ,1 2(0 :,6+)19 2)/0* +.0 2, 4,::-.3 61+ -(6190 4.1*. O32)/6: 699409620 *24.-2.40 +0301+* ,1 (,7 ,8201 6 ?.04= )* 00 -,1*)*2* ,8 *05046: *203*. C40620 2(0 8)4*2 699409620* 68204 =,. (650 -40620+ 2(0 I18,C.>0 61+ 2(0 ?.04)0*; 2, 01*.40 6+0?.620 3048,4/61-0 8,4 2(0 8)4*2 20*2. C,12)1.0 2, -(0-A 7(02(04 6++)2),16: 699409620* 640 100+0+; ,4 7(02(04 699409620* 2(62 =,. (650 -40620+ 640 1, :,1904 .*0+ 62 6::. D0:020 699409620* 2(62 640 1, :,1904 .*0+ 2, /)1)/)@0 /6)120161-0 -,*2*.2""" SA AG 11AGGREGATEKEERTHI#.1 R*les fo( Eff,+,ent A--(e-atesF4,/ 2.; 2(0 IV6:.62),1J -,:./1 056:.620* 06-( 699409620 6* 0)2(04 9,,+ ,4 >6+. T(0 56:.62),1 *2642* 62 IOOOOOJ 8,4 504= .*08.:; 2, I-----J 8,4 +0:020. T()* 56:.62),1 )* ,1:= /0612 6* 6 4,.9( 9.)+0. F,4 6 /,40 +026):0+ 56:.62),1; 40804 2, 2(0 8,::,7)19 4.:0*H 1. A1 699409620 /.*2 >0 -,1*)+046>:= */6::04 2(61 )2* *,.4-0; /061)19 2(0 I18,C.>0 ,4 2(0 699409620 84,/ 7()-( )2 76* >.):2. A99409620* 2(62 640 1,2 ,8201 6880-20+ >= 6 -(6190 4.1 (650 2,>0 18 2)/0* */6::04 2(61 2(0)4 *,.4-0. O2(04 699409620* (650 2, >0 0501 */6::04. T(0 1./>04 ,8 40-,4+* -,126)10+ )1 6 8)::0+ 699409620 )* 8,.1+ )1 2(0 IR0-,4+*J -,:./1 )1 2(0 699409620* /6)120161-0. T(0 IS.//64)@0+ R0-,4+* KM061 V6:.0LJ -,:./1 20::* =,. (,7 /61= 40-,4+* ,1 6504690 (650 2, >0 406+ 84,/ 2(0 *,.4-0; 2, -40620 6 40-,4+ )1 2(0 699409620. S)1-0 2(0 699409620 *(,.:+ >0 201 2)/0* */6::04 2(61 )2* *,.4-0; 2()* 1./>04 *(,.:+ >0 9406204 2(61 201.2. D0:020 699409620* 2(62 640 1, :,1904 .*0+; ,4 2(62 (650 1,2 >001 .*0+ 8,4 6 :,19 2)/0. T(0 :6*2 2)/0 2(0 699409620 76* .*0+ )* )1 2(0 IL6*2 C6::J -,:./1; 61+ 2(0 840?.01-= ,8 2(0 -6::* )* )1 2(0 IN./>04 ,8 C6::*J -,:./1. D, 1,2 +0:020 2(0 >6*)- 699409620* 2(62 =,. -40620+ 2, *300+ .3 2(0 -(6190 4.1. D, 1,2 8,4902 2(62 3642)-.:64 699409620* /)9(2 ,1:= 1,2 >0 .*0+ 62 3642)-.:64 2)/0* K(,:)+6=*; 8,4 00 +04)50+ 84,/ 2(0*0 -(646-204)*2)-*. F,4 0:0 2, .*0 2()* 699409620. 4. D, 1,2 .*0 6 -(646-204)*2)- 61+ ,10 ,8 )2* 6224)>.20* 62 2(0 *6/0 2)/0 )1 61 699409620. S)1-0 /61= -(646-204)*2)- 56:.0* (650 2(0 *6/0 6224)>.20 56:.0; 2(0 699409620 7)2( 2(0 6224)>.20 )* -,1*)+046>:= */6::04 2(61 2(0 699409620 7)2( 2(0 -(646-204)*2)-. T(0 699409620 7)2( 2(0 -(646-204)*2)- 61+ 2(0 6224)>.20 (6* 2(0 *6/0 :050: ,8 +026): 61+ 2(0408,40 2(0 *6/0 *)@0 6* 2(0 699409620 7)2( 2(0 -(646-204)*2)-. I2 )* (,70504 6880-20+ >= 2(0 -(6190 4.1. T(0 6224)>.20 )18,4/62),1 )1 2(0 699409620 )* -,126)10+ )1 2(0 699409620 ,1:= 7)2( 2(0 -(646-204)*2)- .*)19 2(0 M,)1 7)2( 2(0 /6*204 26>:0. T(0 699409620 7)2( 2(0 -(646-204)*2)- 61+ 2(0 6224)>.20 *650* ,1:= 2(0 +626>6*0 & M,)1. F,4 2()* 406*,1; =,. -611,2 -40620 2()* A)1+ ,8 699409620. I8 2(0= 640 0504 9,)19 2, >0 .*08.:; *)1-0 ,2(047)*0 2(0 +626>6*0 ,32)/)@04 -40620* >6+ 0 D(,ll)o?n at1s2""" SA AG 14AGGREGATEKEERTHI#.3 Eff,+,ent A--(e-ates fo( an InfoC*beT(0 3405),.* *0-2),1 +0*-4)>0+ (,7 =,. .*0 A1,7:0+90 ,8 +626 +)*24)>.2),1 61+ 3,**)>:0 +4)::+,71 362(* 2, )+012)8= 088)-)012 699409620*. T(0 2,,: 6:*, 6-2* 6* 6 3,)1204 8,4 8)1+)19 699409620* 68204 =,. (650 -40620+ 2(0 I18,C.>0 61+ 2(0 ?.04)0*. I1 2(0 699409620 /6)120161-0 K-,1200 )1 2(0 A+/)1)*2462,4 W,4A>01-(L =,. 902 2(0 2,,: 2, 90104620 6 34,3,*6: 8,4 699409620* 84,/ 2(0 004; 2, 34,-0** 2(0 *2642 :)*2. T(0 *0-,1+ 699409620; 7)2( 2(0 16/0 IMAXJ 61+ 6 1./>04; )* +0*)910+ *, 2(62 2(0 +626 -61 >0 406+ 84,/ 2()* 699409620 8,4 0504= 165)962),1 *203. T(0 +61904 7)2( 2(0 IMAXJ 699409620* )* 2(62 2(0= 640 00. T()* )* 3642)-.:64:= 2(0 -6*0 )8 6 ?.04= -,126)1* 6 :,2 ,8 8400 -(646-204)*2)-*. I8 6 ?.04= +,0* 1,2 (650 61= 8400 -(646-204)*2)-*; 2(01 2(0 699409620* IMINJ 61+ IMAXJ 69400. T(0 *=*20/ )+012)8)0* *)/):64 699409620*; 61+ -,.12* (,7 ,8201 6 3642)-.:64 699409620 )* .*0+. T(0 1./>04 ,8 3,2012)6: -6::* 9)50* 61 )1)2)6: )1+)-62),1 ,8 (,7 )/3,42612 61 699409620 )*.I8 2(0 *=*20/ (6* >001 4.11)19 8,4 *,/0 2)/0 6:406+=; 616:=@0 7()-( 699409620* 640 406::= >0)19 .*0+; 61+ 7(040 0:0/*. D0:020 699409620* 2(62 640 1,2 >0)19 .*0+; >0-6.*0 2(0= -6.*0 61 .110-0**64= ,504:,6+ +.4)19 2(0 :,6+)19 34,-0**. T, ,32)/)@0 2(0 *=*20/; -40620 61= 00(65),4 ,8 2(0 01+ .*04 /6= -(6190. %.04)0* 2(62 640 )/3,42612 2,+6= /6= 1,2 >0 )12040*2)19 2,/,44,7. I8 =,. -,::0-2 BW *262)*2)-6: +6261 8,4 2(0 I18,C.>0; 2(0 2,,: -61 *.33,42 =,.7)2( 2()* 34,-0**. A99409620* -61 6:*, >0 34,3,*0+ 84,/ -,::0-20+ *262)*2)-6: +626.11 T(0*0 34,3,*6:* 640 6:: 9)501 6 16/0 2(62 *2642* 7)2( ISTATJ 61+ 6 1./>04.9 E0*. $,. /.*2 *0:0-2 2(0 IOLAPJ -,:./1 2, 4026)1 +626 ,1 2(0 0= ?.04)0*. A99409620* 2(62 640 *7)2-(0+ ,88; (,70504; 640 *2):: A032 -,1*)*2012. T(0= -61 2(.* >0 .*0+ 696)1 +)40-2:= 6* 61+ 7(01 2(0= 640 *7)2-(0+ >6-A ,1 696)1. T(0 6+5612690 ,504 +06-2)562)19 ,4 +0:02)19 )* 2(62 2(0 699409620 /.*2 1,2 >0 408)::0+ 696)1; 61+ *7)2-()19 ,88 )* 2(.* 3642)-.:64:= 70:: *.)20+ 2, *)/3:0 20*2)19. A* +0*-4)>0+ )1 2(0 3405),.* *0-2),1; =,. -61 1,7 0= 2(0 +626>6*0 2, 2(0 2)/0 2(62 )* 40?.)40+ >= 2(0 ?.04= .*)19 2(0 699409620. I8 2(0 ?.04= )* 1,2 -,1*)+046>:= *:,704 2(01 =,. -61 +06-2)5620 ,4 +0:020 2(0 699409620.13 T()* 8.1-2),1 +,0* 1,2 0