Chapter 14: Query Optimization

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Chopter 0: Query Optcotzdiva 

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+ Oleger UP: ‏یمن ببس‎ له )ملظ اه تساه و )۳ م3 مطدو() (Grotsticd dePorewaton Por Oust Bstcratiza Costbased opicrtzatics Opens Programing Por Okovstey (Evchritos Phacer Octertatzed views Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wo ©Sbervehnts, Cork ced Cnakershe 

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محا لح + بحصي ميف د لهج مرو فا ۲ سوه موه ۶ ‎OP Rene ckprthos Por pack operation (Ohare (9)‏ © مه بو و مه رم امه اج لو و ما سل بو ۲ موجه پم سا وی وا لا ۲ :امم ‎Porwatvd obou retoivas.‏ لس © ‎oF tuples,‏ ای ۱ اه معا سل خام اس ۱ ‎Cre.‏ > ‎esitvaiog Por terete resale‏ یه ۱ ‎of cowplex expressives‏ ۱ Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wo ©Sbervehnts, Cork ced Cnakershe 

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(0) ملس + ۲ ‏اد‎ qeuerded by two equided expressivas have the sue set oF utiibutes: ‎score set oF tuples:‏ تا مه لو ‎© though ther tuples/atrbues way be ordered dPPeredly. ‎1 ‎۹ ‎a ‎S bronch_city=Brooklyn 4 ‎branch account —_depdsitor ‎customer name ‎(b) Transformed expression tree ‎wee ‎TN customer name ‎S brsnch_cty-Brookdyn Da. branch 4 ‎account — depdsitor ‎(a) Initial expression tree ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‎ 

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(.20۰)) متسب (Geoeraica oF quer-evotuaicg phoos Por os expressiva wolves severd ‏وت‎ 0 Geueraioy byicdly equivdect expressive ‏صطفوجه رو‎ nies. 0) Ouuotatec ‏ماه اب وا موه تلو‎ query phic Choosiey the cheapest plo ‏اوه هی من لس‎ راون لوا پووی لا ممم مهو ‎“he‏ 4 Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wo ©Sbervehnts, Cork ced Cnakershe 

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+ ‏نموت میب‎ Rehiocd Cxpressive § ‏موه مارا اما ی‎ oe suid ty be equucedt P vo every leva ‏سنا | وله مرول‎ expressivas yrorrue the suxve set oP tuples © Ootet order of tuples is irrekevarat B10 GQ), tops ced napus ore wulicets oP tuples © Dion expresso ta he onset versiza of the rebtioad okebra ae said ‏ها‎ ‎be equivdedt Foc every lend docbase Retrace he buy expressive ‏مب‎ the rere crn deat of tahoe ‎Oc equidewe rib sae hol expressions of two Pores ore equiv‏ ال ‎vert‏ حصان سن ,صصص ‎Coc repr expressira of ret Pore by‏ © ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wo ©Sbervehnts, Cork ced Cnakershe 

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مس سم ها 0. Conuanive ‏جح و وا لول با موی شوه مشاه‎ of tordvicdual selertions. Oy 9,(B) =0,, (0, (2) ©. Gelevivn pperuioes ‏و وه‎ ‏رت‎ (0p,(B)) =0),(0;,(B) 9. Only ‏او ماو خن ویو و و تا‎ & ceeded, the vers cont be ‏ان‎ 11, (11, (..(1;,()...)) =, (B ‎Oates proxkarts orl theta ker.‏ رب لامرن سا مه وله ‎Go) = CM y‏ ,0,۵ ‏موی ‎OM‏ = )4 مرک امه ۲ ‎ ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wr ©Sbervehnts, Cork ced Cnakershe 

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+ Oqucdwr Rubs (Ova) 9: Dhetepa operations (aad ccturd pie) are cori. Mi, , ‏6د ي©‎ © هه موه موز ‎Ocird‏ )9( .© (ه با شره ۵9 ف (b) Dheta pres ore cseoctive ta the ‏ی مسا‎ CB, WPS ‏ره‎ WB, orn (Bs Bs) بر لو ره ره مس اه ‎where 0, tucker‏ Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wo 

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Rule 7a 1f 8 only has attributes from El Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wo ©Sbervehnts, Cork ced Cnakershe 

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(0) () دج ۵, (۲ ‏رهاط موه ماه‎ the theta pis operctiva vender ‏سا‎ ‏او رو‎ (0) Okeu dl ke inbutes ۰ 0 ‏اه ات بط را سامت‎ ocr oP the expressions (@,) beter ped. ‎Bs) = (CmOM Co‏ , مه ‎(b) Whew 0 ywobes oy he airbates of B, ond 0, tucker he aber Ce ‎Opa" 02 Be < ۵ 11 ٠, ‏يره)‎ )©0(( ‎ ‎ ‎4 ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‏سا0 لح 0 لا سواه 1 هه‎ 

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+ ۳ ‏ست ط‎ Cbs (Ora) تسس موه ‎theta pis‏ ون تا موه موم .0 ‎Le!‏ ذا ينا ما صطف ره امه 1 ۸ (0) Tun (BoB) = (Th, (B)) XU, (B)) (b) ‏اه سین‎ B, 9 Ba. © bet yaad b, be ‏لو ما اه‎ Ba, respectively. © Let L, be ctirbntes of, trot are evolved is pis cndtion 8, but cre ort ta, U Uy sx © bet lg be cirbutes oF Brot ore volved ia pia corndion 8, but are oot ia Ly U ie Thon (A 9 B) = Thy ux, (Tl, x, Mo Th, uz, (BD) Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. 00 1 ‏سا0 لح 0 لا سواه‎ 

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+ ۳ ‏ست ط‎ Cbs (Ora) ۳ ‏وی و اتسوا وه موی اوه اد‎ ‏لا و6 < م8 دا,6‎ ۵ 6,0 ‏و© 2 م8‎ 6 © BO eee teed eee teens (0. Get unica gad totersenica are ‏چیه‎ ‎(@ UV @,) U @, = & UV (@, U By) (@,. 9 8( 0 ‏و8‎ - 0 (@z 0 Ez) (0. Dke selection ‏ممصم‎ distributes over U, 0 od — O% (E, — @) = 0,۸ - %(E,) cand sirtady Por U od 9 ta place ‏خام‎ - ben: Oy (@, - ©0( - ‏-0©)ره‎ Ce vac sievkody Por 0 ict ‏ارم‎ oP —, but oot Por U (0. Vke proecics ppercica detributes over vir T(@, U @) = (1(@,)) V (1 (,)) ha Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‏سا0 لح 0 لا سواه 1 موه‎ 

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+ TresPorwdea Oxenply 18 Qher: Pied the oonves oP ol custowers why hove oo orem of sre broads located ta Brocka. ‎(acc! deposior)))‏ مب ‎wok nde Pa.‏ ممق ناص 2110 ل 1 ‎(racic gui (ore ‎(wer depositor) ۲ ‏رو‎ the seleiiog we por) oe poseble reduces the ste of the rettiza to ‏اس سا‎ ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‏سا0 لح 0 لا سواه 1 مهو‎ 

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+ ‏لیس‎ wit Ouiple TrawPorwdiows B Qe: Cred he coves oP ol cstowers wit ‏رطس( وه مسجت و‎ break whose uno bose is ner $IDOO. ‎Tirana = Uren” fe > DD‏ سس أ ‎11 ‎(break ‏((سسکطه مسل‎ ۱ ‏و ما‎ fort woorktively (Rue Ox): ‎ ‎| ‏اس )سین یی‎ = roca *Iedewe COX ‎) ‏11 ‏(مسستد سسج) ‎۱ to apply the “perPorw seleviivas ead” ‏(ح) ونوا سین 6 ‎to the subexpression‏ بانج رابص ‏)وه سا0 ‏خی سا من موجه موه و سا ۲ ‏وه ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. 

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+ ‏بش‎ TrixePoruxtiow (Ovu.) Tl eustomer_nare Tl customer_name | ۳ ۳۹ branch_city=Brooklyn A balance < 1000 a ™ ۳ depositor 4 4 Tia 70 © branch_city-Brooklyn 9; branch ۳۹4 ty-Brooklyn Obalance < 1000 account depositor branch account (a) Initial expression tree (b) Tree after multiple transformations Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‏سا0 لح 0 لا سواه 1 موه‎ 

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+ @rvjpvivd Operon Cxawple ‎cvbrttor)‏ — ۳ ۳ موی ویس نکاس سا ‏یی سس انا ۲ ‎ured) ۳‏ (اصصط) بييية ييه ‎we ‏وا وله وا و و ان‎ (brouck_onre, brouh_niy, assets, uorvuat_aurber, bua) © ch ‏افو ری ات‎ nuler Ou od Ob; elcpicdie ‏ات وی‎ Proow totermedtte remus to cet! 11 ‎Late ( (Groening (broek) ‏الا‎ ‎ ‎werk) ‎© PerPorwiey the projeviva os ead) ws possible reduces he stze of the rehation to be joie ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. 

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+ tid Getrag execs ۱ ‏سا‎ ry Mt, DA) ‏لا مایت‎ rs) mw PN ye qe tare ody, De sod, we choose Mh, Py ne oo thot we cowie ond ‏روموت ارو و و‎ retatioc. Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‏جوهه‎ 

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‎Biceps (Ov)‏ م0 ول ‏ی ‎(brexarh)‏ و0 )عت سس 11 ((سسسسط ال ا ‎resub wits‏ مر لمت بوذا سك مه مج نون الا ‎(Prema)‏ سوسه مس ما ماه جا صا بالا ص تلا مه بط ‏اجه جوا ۲ راما و وی وا ‎of‏ مه لو ه رین 7 ‎broockes located ta Brocka‏ ‏و ‎te beter‏ و ‎ ‎(a) ee ‎0 ‎First. ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‏سا0 لح 0 لا سواه 1 مهو‎ 

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+ ‏و یه‎ Oqurded Oxpressow © Quy openers we equivdeuse rules to systewotcdly ‏ی‎ expressive ‏تفج‎ ip he ‏موه مهف‎ مساو ‎exevutay‏ رل روا موه تقو آه وی امن ۲ لو( ‎step vail oo sore expressions oot be‏ © Por euck expression Pound sv Por, use oll opplodble equicdeue rues ١ add ceil) yeuercied expressives ty the set of expressicos Pourd sv Por BO OVhe hove wero & very expeweive fo space ued tke ۲ poe ‏وه وله موی موه روا ال نو‎ ۱ wendy ody the top level oP the two ore dPPered, subtrees below oe the sexee ood coo be shared رس ‎appl icy joi‏ ات .6 ۱ وه اه رو و را اد و و ‎BOD‏ ‎Dore dette shorty‏ © Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‏سا0 لح 0 لا سواه 1 موجه‎ 

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+ Ove ‏سوه‎ ۲ ‏ین‎ oP eurk opercior copter us deserted i: Obupter (2, © Deed statsics oF ‏اه نو‎ ١ ‏ام بر‎ of tuples, sizes oF tuples: ۲ ‏ما‎ con be results of sub-expressioes © ‏طلجت و‎ © Do de oy, we require obhiced statistics * Coy. cunvber oP detent udues Por ‏اه من‎ © ere v0 ost ‏وا مت‎ Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. 9 

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مان ملس + مسج له مه اه ‎ts used‏ مود نوات رام ی بل مره وه ۳ لسرا ‎be re‏ ممصو جهو نجل لأ ‎he rete nen‏ TT customer_name (60tt to remove duplicates) ‎(hash join)‏ هم ‎Dd (merge join) depositor‏ ‎pipeline pipeline‏ ‎balance < 1000 (use linear scan) ‎ ‎account ‎woe ‎9 branch_city = Brooklyn (use index 1) ‎ ‎branch ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‎ 

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+ Oboe oP @uchntioa Phare ماه واه ما مومت مره تاه ‎BL Ox et coceider he fntererioa‏ د ی و مس ای روط بو مس بل رما یر ‎ux.‏ سود امه با لاس ۱ ‏جاتشعابب و‎ reduces the ost Por co cuter level ‏وروی‎ © ce stedyop jet way provide opportuntiy Por pipettes © Creted gery opikeizers tworporde eleweuts oP the ‏مد ماو‎ brood ‏اسر‎ ‎4. ‏ی اجه ام ۳ اه سم‎ the best plas io ‏او( لاه‎ 8 ‏ام و واه وا یج و()‎ Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‏سا0 لح 0 لا سواه 1 66م‎ 

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+ Ovet- Bed Optica BE ‏مین‎ Pdr he best preorder Porn, re. Mr, Bl Vhere a (O(o- ‏-م)/ا()‎ 0)! dPPered jor orders Por chove expressiza. Otk =, he ‏امه‎ QOOCOO, wik 0 = 00, he ‏تا طلسم‎ rruier tro 19 ‏اسطا‎ BE ‏ی وا له و‎ di he pra orders. ‏رومام مد روا‎ te best ost ‏مج جر‎ Por cay subset oP ‏و رات ام ...رت تا‎ ed stored Por Pukire wer. Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‏سا0 لح 0 لا سواه 1 هه‎ 

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د ست يعاس نام 0) ‎Opcenmc Pronrecowiny ia‏ + ان ل لا © Do Pred best ph Por a set G oP arektions, ooasiter dll possible pkre Pike Porn: G, (G-G,) whit ©) te ‏سم بو‎ subset of C. © Recursive) co pue ovsts Por pte subsets oF G to Prod the ‏ومن‎ of eowk pk. Choose the cheupest oP the O° — ( ohercaives. © ‏ددا(‎ pha Por coy subset & copied, store tired reuse ihghen tie regnined oysia, testeud of ‏مومس‎ tt © Opsenvic progr Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. woe ©Sbervehnts, Cork ced Cnakershe 

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ملاح ردو ۳ ومیل + )8 ساسا یسم ‎B (bevipkm| G].cvet # 00)‏ ‎renara bevipkn | @]‏ Mebee besipkr| O) ‏وه ,وه اجه جوا هچ‎ I cE (مصسام )0 باد صمح 6( ‎B‏ ‎ou the bent way‏ تما اس ]انا لجی تاموتا ‎] apvessteny GO ‎vb Por pack are mbort Ol of G suck tt OU # G (P= Prbevipkra( O11) (POs Penbesipke(G - Gi) ‏ی و‎ eee 1 ‏م‎ ‎root = oot‏ .)6 هم ‎CG) pk = “execate (PU phat, ‏سح‎ 6 pha ‎pit remus of (PU od PO ‏ری‎ B” ‎ ‎bmg ‏اس موم‎ ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. 

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+ belt (Deep deta Trew Babee pia treee, fe righthoud-side fara Ror park jek i a rekon, ‏بحسم سوج سمج صو ب خم لمجو موا مج‎ 00 ‏(ب0 بسط‎ wee ©Sbervehnts, Cork ced Cnakershe 

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Cost oP ‏مدومن‎ Bik doonnir progrewiny we cowpleniy oP ppicotzaiod wits bushy trees te 06 © ل(زج ‏سم جا ,000 حب‎ ip GOOOO ‏لمصطاط 186 خاح تمجصم‎ («©)0 حا بصا سر ل ب ا ل لا © ‏لحت ذجوا جلمد لمحل عار جد وصتمامب صمج لت مهن ون‎ the pier ‏مار‎ os lePtHsced side ‏.نحو‎ 5 ‏باس سمحصه) مدا‎ coepuied aad stored) leustovet pis order Por mack ‏هط و ما و الط و رم‎ ۱ ‎O(a")‏ & 069 ه عم بجاوح سر ۰ ‎but workuckte Por queries va hace‏ ,وج و و0 لا (10 > را ‎queries kare sad a,‏ لس سید ‎ ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wor ©Sbervehnts, Cork ced Cnakershe 

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+ 7| ‏ود عله‎ Orders in Ouet-Bosed Opicoinion 9 ‏حلصت‎ the expressions (r, mx BM) (4 4 Bl ‏وه بجاو و‎ order & u partouker sort order of tuples trot pou be ved Por ‏وه با و‎ © everctin he result ok, RL leorted va the utrbues corre wih: rp or ry be we, but ‏پم‎ fl sorted po ‏مین ما‎ oxy ryswnd rat set woe x x ‏رد رت وا موه و‎ way be oostter, bul way provide ‏رود‎ rit sorted ‏مس مه دا‎ order © Oot suP Picea to Prod the best pic order Por eack subset oP the set oP orgies rehticgs; cust Pod the best ips order Por ack subset, Por pack ‏او رس‎ order © Grople exteusiva oP eater dvecnnic progrowwiey okprikeos: © Osudly, accber of ‏تسه‎ orders is quite su7dl ord doesat oPPect ‏رتاو موی سوام‎ Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‏سا0 لح 0 لا سواه 1 موه‎ 

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+ Wewsir Opivizdiva © Costbused opitoizutivg fs expeusive, eved uty dyoanic programy. © Gystews way use heurstics to reduce the oxeober of choices trot west be wore feo costbased Poshion. ‎oP nudes trot‏ اس و رس روا رو سا موم و محا ل طسو (مه ‎(but ce ta dl‏ اسر ‎Perforw seleviva rary (reduces the cnnober of tint)‏ © ‎of uirbvter)‏ اه ‎Perfor propvion coy (rehices‏ © ‎© Cerforn wost resinoive selection oad jpit opercivas bePore ‏ات ان‎ per oho. ‎© Cows ‏ها وی اه ها زان ی رو‎ wit portal ‏رن لامرن‎ ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. 9 1 ‏سا0 لح 0 لا سواه‎ 

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+ ‏سب‎ 1a Typed “Leweto Opkotrtioa | nmiKeLe sekrine hi 6 seqee 5 (Cqw. nie (.). ©. ‏مرو موه موه مه(‎ he query trey Por te ratest presble ‏برفجظ) مج‎ ries ©, Pa, Pb, Ad). اه ما مس نت فا سین مزلم ماه ما نس سح :9 ‎rehaiocs (Bou. rue (۰‏ مه ماه و ‎fro oe Pobiued by‏ بهذم مه بل .@ ‎(Bq. nie Pa).‏ وه و و ©. ‏لجی سم‎ wove os Par dow he tee os posable ‏منم اه تا‎ ‏,حاف‎ creukn SEW propuivws where weded (Bquv. nies 9, Ou, Ob, ae). 0: (dew) hose subtrees whose operons canbe preted, ond exert woke ‏ماس‎ Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. woo ©Sbervehnts, Cork ced Cnakershe 

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+ 9 ‏دی و‎ Chmey Opies © Ve Gpstew ‏ون ماو‎ ovusiders vay lePedeep pia orders. Mhis reduces ‏ماه‎ rowpiediy ood yeourrates phos arecable to pipetoed ‏سار‎ ‎Gystew /Gtorburst dev wees heuristics to push selevives oad proevives dow the query tree. ۲ Weursic opieizatog vsed to sowe versives oP Orurte: © Repediedy pick “best” relation ty jot ext * ‏موه‎ Prow eark oF a startey poivis. Pick best ocoeny hese. © Cor seus wsiey sevoudery indices, swe ppikeizers tobe fay occu the probubliiy thot the poge mrotototry the tuple ts to the buPPer. ۲ ‏مت‎ of OGD complicate ‏من توص‎ © Cy, vested subqueries: Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‏سا0 لح 0 لا سواه 1 مهمه‎ 

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+ Grishre ob Chewy Opkotare (Oot) ۲ Gowe query opikotzers ‏ها مر‎ selection oad ‏مجو موسر وا‎ of ‏همم‎ poor. © Gpstew R od Gtarburst use 9 hierorchicd provedure based a the ‏هن یرالیه‎ (SQL: heurtstic revoritesy ‏لاو روا انوا‎ ‏راون لصو‎ © ‏و موه ری او ها جاه ی با رت مر‎ substocttal pverkecd. ۲ Dh expewe ‏ماه ما وت را‎ by soviep of query-exevutivg toe, ‏وت ال ناو اه ای با رل بو تالا‎ Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. woo ©Sbervehnts, Cork ced Cnakershe 

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+ Oratetod “Porwatod Por us! eva بل ‎oP tuples irs rekon‏ وی نو ‎oF‏ وه وی وا اه میم نبا سر حك جاده خم ماد :ا م 0 O, 1): Kober oP distiadt voles thot uppeur tar Por otdrute B; sume ‏جد‎ the size oF T(r). ۲ 1 ‏یا‎ oP roe stored together physicdly tao Pie, theo! ay Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. woo ©Sbervehnts, Cork ced Cnakershe 

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Wewqaws 4 © Wistograe vo ‏اه‎ oye oF ‏موم ما‎ 610 11-15 16-20 21-25 value wor 50 1-5 موس 0 لما مسا او ۲ Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. 

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+ Ocbutra One Betartia Boe.) ١ ‏سجاريصي : 000 / ب‎ oP record thet wl outePY) the ‏ادن‎ ‎١ Davey coedio ow a hey othe! otze eoitrute = ( ‏للا‎ pzclr) (owe oP Gy. fr) ® sere) © Leto dewte ‏رای سوه بط‎ oP Kp out ary her vox, 00 xed crxax(D yr) are ‏و امه‎ > DEO Ru < amy) v- min@r) “max@7)- ming 7) 8 AP heteernee avakble, cou rePie above eter ۵ ‏واه هه لصا تاه مسا وا‎ wemneed ty be «, /2. Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. woo 

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+ Cue Ovtadioa oP Oowpex Orkviow Bh solve, of a ooention 0,6 the proboblly ato hile ‏ایس مارب‎ 0 © Rg, & he cxneber oP sushi Apes ir, he seleca ay oP 0, wea by &, ha. BM ‏وه لمح( بو م6 تون‎ of tole abe ede: 5 5 ‏...ری ی‎ 5 ‏اال ار‎ تا ‎of‏ یه هه رن ی نصا ۵ | 207 جرت كل درت 1 زا« 2 رید نمی لاه « - <)0( Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. woo ©Sbervehnts, Cork ced Cnakershe 

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+ tbat porta Candy Breage | ‏هوك‎ ١ ‏مهد‎ ‏و با مس ی‎ Bim 240,000. BP. = CG, whick trophies trot <00000/66 = FOO. م .00( = 60000/060 < بط ۲ ‏اس 06000 < (س سم‎ Kepler ho, or werne, cok ‏اوه مسا جمصصی‎ ۱ ia deposior is a Poreky hey va msinwer. * Ofesiwer_onve, netroer) = IDDOO (pricey key!) Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wor ©Sbervehnts, Cork ced Cnakershe 

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+ @vtertioa oP te Otze oP oko Phe Ooreotes produit rx es ovotciee 0-0, fuples pack tule oooupies & + =, bytes. BERN C=O, beak ste he cae wr xe BP RN Gtr akey Por ®, hea a hele of sud pic wis of const oe hee Pro © erePore, the ouncber oP tuples fe eis a eter trom ‏امه‎ of hues a =. x BERN Cn 6a Pore bey i © ‏يواسم وتاي‎ R, ‏اه امه عم‎ tinker ‎the sue oe the oanvber of tuples ts:‏ عبط ‎9 eer Por RO G bern 0 Poretes hey rePerearicy Gis ‏ورد ‏اس ماع هه امه ‎١‏ یط هو ار 3 ‎Foren hey of rst x‏ ‎© hewe, the result hos excl Ui jcen Apes, whick t& GOOD ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‏سا0 لح 0 لا سواه 1 موه‎ 

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+ Cstantiog oP the Gre oP vies (Onc) BERN )© - )0(( ‏بوط د اس حا‎ hor Por C. AB we weave tot every tiple fia R prockices tuples in RG, tk cncober of Apes RO extend bbe: ako, 662 AP he reverse nw, the eotcodte ‏تا لس لاه‎ رت 0063 (he lower of ‏سا وی میا جوا‎ probably the wore ‏و عمجت‎ © Cog topreve 00 oboe ۲ ‏ره و مموستا‎ © Ose Porta sober ‏صا‎ cbove, Por each cell oP histogreres oo the to ‏اسر‎ Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wee ©Sbervehnts, Cork ced Cnakershe 

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+ @vtaraiva oP the Otze oP ote (Ova) Bl Owner the size esiedtes Bor deprntior ebper wahout vein kPoreatira ‏فص‎ Pores keys © Ofer etxrer_cnve, ‏دمي‎ ‎Ofretrrer_ ance, netewer) > 0 له 60,0۵0 - 10۵0۵/660 ۲ 6000 مه مه مس ‎Dhe‏ © ‎SOOO * 0۵6۵/۵۵۵0 - 00‏ © Oe chovee the bwer poke, whick in this care, tr he sae os our coder ‏ری موه‎ Pores Key. Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wen ©Sbervehnts, Cork ced Cnakershe 

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© Get operctioces © Cor wairsloiersevive oP selevioes va the sve retiva! rewrite oad use ste estate Por selevticos ۱ Exp Oy) U Oyo (7) ea be ‏(ص) مرت يرت جه صعميص‎ © Cor operctioes va dPPered rebtioas: > eoitrated size oP Us = size oP r+ otze ‏بج اه‎ ( ‏سوه مک 0 هه او‎ oP rund sie ‏بد خام‎ ۱ ‏با كان صو ای‎ « ‏و سا نوت مه سا با(‎ truscurde, bul provide upper vothe stes. Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‏سا0 لح 0 لا سواه 1 مهو‎ 

صفحه 42:
+ 6 ‏سم‎ (Ovu.) ترصن 9 رو + ‎oP Mb = ste oP DM‏ و لبق ۶ و وم و ور ‎Case oP‏ » خا مياد خم خم مواد + 4< ‎ste Pr Xe = ste Pr‏ 1۱ Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wee ©Sbervehnts, Cork ced Cnakershe 

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اه مت و این( ان مشیم + شا ره :ده .4 = (۵) ,00,6 تس لو هس ‎io‏ و 0 ‎BP‏ ‏60-8 روم ‎١‏ :ساس خم اد للج اسرد د خم صم صم جام جز 09 م۵ ۲ .علس لجتاعصمد خانم ‎O(®,.0, (7) = suncber‏ » (ex, (P=10 = 9 0 62 (( ‎vetevivs ocnttivg 6 is oP the Pow @ opr‏ لا ‎votcrted O(P,6, (r)) = (Pr) * =‏ ‎where ste he seleviviy oP the oelevion. ‎emirate oF‏ سوت و ‎cher owes!‏ با ‎wi Pr), %6 (3)‏ ‎© Dore wounnte estate con be yet stay probably theory, but this vor works Proe ‏بای‎ ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wee ©Sbervehnts, Cork ced Cnakershe 

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+ Ostantioa oP Owtat Ockes (Ovu.) eee ۲ ۱ ‏ات اه‎ tt Owe ‏ما‎ ‏ف ,« ,)1,7( مب < هلا ,010 لسع‎ ۲ 1 ۵ ‏اه ی‎ )2 Prow rund GC Prow », theo estevoted O@,™ ‏و‎ ‎000۳06۵ - 00,۵, ۵۵-۵۸۵۳۵۵8۵ 9.) ۶ Dore wow ‏رت اب سا مت سرت‎ probably theory, but tis oe works Pie gecercthy Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wee ©Sbervehnts, Cork ced Cnakershe 

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+ Ostantioa oP Owtat Ockes (Ovu.) ۴ ‏مه‎ of dora ‏نالف سیف تا‎ Bor propane. © Dhey ore te exer ts Ts 4) 9 RF BE Dhe sae hkl Por group ‏سويت خا وجا‎ ای وی و ۲ حت اجه سا موه ملس مه اه بط ‎Corer ®) ord wax((P),‏ © اه موی مس ۵ ‎where‏ (6) ,)اه © ‏مج سوه و و‎ dh uckes or detect, od vee O(B,r) Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wee ©Sbervehnts, Cork ced Cnakershe 

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+ Optootziy ested Oubqures"* ۲ GQL cowephnlly treats vested subqueries ia he where ‏ماه‎ os Puarticas tot ‏اه‎ ‎ponnveters ond retura o stage vohue or set oP udkes © Coraweters we vortbles Prow puter level query trot ore weed to he ‏اس‎ ‏حون موی لا بت لت سوه همطل‎ 9۵" جات مره لیر © Coweptudly, vested subquery is executed vure Por euck tuple to the orvss-product yesertted by the cuter level Prow chase مه اوه سای ها مره بلق و © ‏مرن مان :ج0000‎ is where vkuse way be used ty orp 3 fos (ketewd of pross-produes) bePore exert ihe cevied bnery Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wero ©Sbervehnts, Cork ced Cnakershe 

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0 ‏دادج 0م‎ Dested Gubqueries (Ovd.) وه ماه حشي ججا بوجه مه لهوامون ‎ahi wober of ols way be wade to he vested query‏ © ‎a recut‏ جه ‎here wy be wovevessury reedow VO‏ © (GQD opioiers ‏لو متام صا اومجاه‎ subqueries to iptos where possible, مج موز ای ‎use of‏ باروج جه ‎query coc be rewrites‏ له وی نو سنجمه تسود Prow borawer, depositor ‎acer 2-5-2-2‏ برس ای ‎© Dote: obove query desu! vorreniy ded ui: duplicates, vad be wodPied to de 55 55 we will see ‎4 geverd, itis ont possibte/strahPor werd to wove the eutire ‏ترجه لو‎ Prow ‎douse foto the cuter level query Pro ckruse ‎© ۵ ‏روموت‎ reltiod is oredied keteud, god wed fo body oP outer level query ‎ ‎4 ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‏سا0 لح 0 لا سواه 1 موه‎ 

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‎Obqurvn (Ove)‏ سس سس ز ‎4a yecerd, GGL queries of the Pore below co be rewrites we shows ‏با بح ‎ukere P,)‏ ‎pres tbl fo‏ 9 ‎eke ‏ماطف‎ ‎row by, ‎kere P,° ‎voles... ‎Pro ‏انا‎ ‎where P, od PP © Pf cockice predates ta ‏جا يفل‎ de ‏ای امه رون امه مه‎ © P28 ‏,بو سوه ام طلسم ولمم‎ wil ‏امه لمیر ما‎ ۱ ainbuies wed is predzaies wil correo vores Eg ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. 

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+ ‏اس( بسن‎ Oubqusries (Ooct.) BE dome menor, the orkid costed query unakl be ‏ها مامتا‎ rede tbl (we ‏تسه سم سیر‎ ‏سرت مها‎ 5000-5 Prow borrower, | 1۱ ١ ‏مسد _سخصمصسص ور صجوما > بجون_ممجصت.‎ ‏لا‎ Phe process of nephrin ‏ب جلاب باماعصدم) جاجز د خلت نو و با وضو له و‎ 0 ‏اا‎ ‎Bh Qecorrckion & wore cowpioded whoo © he ceed subnery wes exnrewntiva, oF © he the reo oP ‏یج موه اجه با‎ i est Por ecco © ken the ‏تاها سلجم‎ he costed subcery to the ober ‏حا تبي‎ wo ‏عاج‎ © ad ovo. Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. 

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+ Octertczed Oswe"* 11 cootertcteed Yew & 0 view whose codes oe oocpuied onl stored. ۴ ‏با لین‎ ew ‏و( اه اا‎ ‏ردنا واد‎ sano rout) Brow bar ‏ممم سحا باجحو‎ ۳ ‏سا له‎ view would be very ‏جا مسجم وجا امنا جا خا مخ‎ required Prequeciy © Gaves ‏ونان جملا‎ of ‏عولی بل‎ tuples: ood oddiog, up their cera Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. woo ©Sbervehnts, Cork ced Cnakershe 

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و( بل [ س دب زا + © Dhe tosh of ‏لس ری لا و ریا‎ wit the vader io date te ‏أده حادب وه منم‎ ew wotdeurae § Odertdized views coo be woiutcced by ‏من ولمم‎ every upd BO beter option is to ‏مجه حصت‎ view ‏ومدمحامادجه‎ اس و ‎to commie chames‏ لو همطل با بو ‎Yew, whick trea usted‏ © Ow wotdtecsue van be door by © Door) deRcioy iriqgers co fesert, delete, cod update oP ‏و ما ای‎ the ‏ماو ند‎ ۱ wheaever dotobase rebiiocs are ‏ال‎ © Gupponted direviy by the dotcbuse Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. ‏سا0 لح 0 لا سواه 1 مهمه‎ 

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پر 0 + ۱ ۱ ‏لو سم و‎ deletes) to ot rektion or expressions or ‏اس‎ to oe fo dPPerectd © Get oP ‏من و لس لو‎ deleted Brow rare ‏اس‎ § oo BV stop iPy our description, we oly ‏اعد اجه ی ی‎ © We repre updies tou tuple by deletion oP the tuple Polloued by iesertica of the update tuple 19 We desorbe how to copie the chooge to the resul oP rack ‏ام‎ operon, yeu cheney 7 is tts ‏ا‎ Qe teu vue how te hoode rebaiccd dyebra expressivas Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. woo ©Sbervehnts, Cork ced Cnakershe 

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iota Opsrciva ‎he wrteridied ew 7 = r=) Mad oo updhte to‏ ون لا ل ‎BE bet Mood deur the ob ood sew tes oP rekitioa‏ ‎he ose oP oa keer ir‏ ییون ۴ ‎© Decanter ee (U1) ‏4ج‎ ‎© Ocdreure te bos (PU, =X ‎ ‎۰ ‏حا إل سر ین‎ erry er ohh che of tr erst ‏وجو‎ 2 ‏ع عوط ندب صطا جا صحصاء احص ‎BPs, Poker ‏لاس‎ 5) Grok Por debs = (do) ‎Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. woo 

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+ Gebota ci! Propotod percha ۴ ‏تسیل‎ Orconter 3 view 1 = 0,(r). © ‏(إ)يىنا الس سر‎ 9 ‏(اری - برع سر‎ Bo ‏مس مه سس و‎ * © - )00۵( ۱ ( ‏(فه) ب(فع)) ع‎ #9 ۱1 ‏.ك) عاج طيجاد د‎ 0 1P we delete the tuple (0,2) Brow we shod ot delete the ture (0) Pow Tlo(r), but P we thea debe (0,9) a7 wel, we should delete the tuple © or cock pe too preevion [],(r) , we wil keep a covet oP how woop ves tuo ‏ال‎ © Oc eert oP a ture tr B tke resukod tuple ts drewdy ts [g(r) we taorewet te ‏جحت ,سجن‎ wwe kd a eu tuple wk cont = (1 © On dekte of 0 tue Brow 1, we deorewent the count of the correspoadn tuple i Tol) » Be count becowes , we delete the tuple Prow [,4(r) bs Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. woe ©Sbervehnts, Cork ced Cnakershe 

صفحه 55:
+ ®qyeqdioa ‏يمن"‎ سگم ای سوه اه سوه ان © ‎٠١ or rack pkey at Phe comreepoenken (roy ty dbase presirct fv,‏ ‎eerewed ty Dent, ee we onkl a oe phe wh: ovr =‏ اما وه ساره خن ‎Dhow a oe‏ © ‎Bor marks Ripe tr wee books Por the ory LD 1, ond brant (| Prox her oot‏ > Por he wep. AP thee cout becowes (D, we debts Brow v the phe ‏مس سا و‎ 00 B aciv= ‏امس گ9ه‎ ٩ ‏او () سا اند لللی س ام روت با نادجو هط تمه سا موب‎ ‏بمستع ساد ليمطلي ١ن لمسهصر‎ ) Por tae cant © ck) we etc he ov i ode eter rope ‏عالت‎ Keke. Ourk ares ore debe Brow v < ‏اج راد ون‎ sunny = D (why?) Bo hen he came oP ag, ive atstta the pu orn! Poet coger: Vokes separately, ‏لمن‎ vides of hor er Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. woo 

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expeveive. De hove to bok ‏ان لب‎ tuples oP rikot ore ta the seve yu to Pred ‏مج تن صا‎ Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. woo ©Sbervehnts, Cork ced Cnakershe 

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+ Oter ‏سم‎ جر نموه بت ۲ ۱ toy. © 1P the tuple ‏جز‎ deleted Prow 1, we delete it Prow the tntersevtiza ‏.سوسم صا ذا خأ‎ © Opdites to sre ‏مرو‎ او و و الما و وله له موی ‎Dhe ober set opperuives,‏ © ما۳ اجب هی ویو لت لها عم چه رورت ‎wurk the suze‏ و متا بت ین ۲ ‎we tewe dete ty you.‏ © Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. wor ©Sbervehnts, Cork ced Cnakershe 

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Nbealay Gupresspu § Ve koode oo eutre expressiva, we derive expressivas Por ‏شوه‎ the fore edd chooge te the result oP ack sub-expressives, stortay Pro the ‏وه موم یله مور‎ یه و ‎G@.y. cowry &, MG, where cack of @, ond Cy ww be‏ نا ‎expresses‏ ‎Oppose the set oP tipkes ty be teserted tir Bis sien by D,‏ © ‎Comrie poder, shoe srdder sb-expressions ore handed Prot‏ > © Dhow ter ort oP ‏سا‎ be ‏اس‎ 0, Days tors ly Dro 7 Dhis te just the vsudl way of ‏و ری‎ Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. woo ©Sbervehnts, Cork ced Cnakershe 

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۲ ed Drtorictard Owe ۱ Rewriters queries ‏صا‎ wee uteri views! لاه 4 رس نی ۵ © © ۵ ‏وه له ی‎ r pe Dl 4 مجه و تا سم و بط © ها مس ‎Por‏ ماه امه مه تلو بو و با ی( او تنج ‎view by the‏ لو و ‎of‏ اه ما ۲ © OD crterned vew y= Gb wobble, bu wihout cay trex oot سوت هو و وله و0 ۶ © Guppose dbo thot & hos on index oo the coon utiribute B, ced r kos oc ice ‏دم‎ trie )۰ © Dhe best pha Por his query way be to repkee vbr; Pk ror brad ty the ‏لاوييت كمام نحصو‎ 5 x © Qeey opiwizer should be extruded to crosider ol obove ‏ام امه ما ها وه له مهم‎ ha Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. woo ©Sbervehnts, Cork ced Cnakershe 

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QOctevidized Otew Gelevioa ۱ view selvion: “What is the best set of views to wotertaize?”, © Dhis devisioa wet be wade vo the busis oP the systew ‏مروت‎ ۲ dodves ore pet the wotertaized views, problew of ‏یاه ها ماه و‎ relied, to that oP wotertdtzed view selection, uous itis stopler. © ‏لول تن‎ systews, provide tools to help the dotcbose ‏ات ول‎ todex ood wolertatzed view selection. Ocsdrer Gyre Oncewpe -O* Crim, Ooi ?, OOOO. woo ©Sbervehnts, Cork ced Cnakershe 

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Gad oP Okaper 

Chapter 14: Query Optimization Database System Concepts 5th Ed. ©Silberschatz, Korth and Sudarshan See www.db-book.com for conditions on re-use Chapter 14: Query Optimization  Introduction  Transformation of Relational Expressions  Catalog Information for Cost Estimation  Statistical Information for Cost Estimation  Cost-based optimization  Dynamic Programming for Choosing Evaluation Plans  Materialized views Database System Concepts - 5th Edition, Aug 27, 2005. 14.2 ©Silberschatz, Korth and Sudarshan Introduction  Alternative ways of evaluating a given query  Equivalent expressions  Different algorithms for each operation (Chapter 13)  Cost difference between a good and a bad way of evaluating a query can be enormous  Need to estimate the cost of operations   Statistical information about relations. Examples:  number of tuples,  number of distinct values for an attributes,  Etc. Statistics estimation for intermediate results  to compute cost of complex expressions Database System Concepts - 5th Edition, Aug 27, 2005. 14.3 ©Silberschatz, Korth and Sudarshan Introduction (Cont.)  Relations generated by two equivalent expressions have the same set of attributes and contain the same set of tuples  although their tuples/attributes may be ordered differently. Database System Concepts - 5th Edition, Aug 27, 2005. 14.4 ©Silberschatz, Korth and Sudarshan Introduction (Cont.)   Generation of query-evaluation plans for an expression involves several steps: 1. Generating logically equivalent expressions using equivalence rules. 2. Annotating resultant expressions to get alternative query plans 3. Choosing the cheapest plan based on estimated cost The overall process is called cost based optimization. Database System Concepts - 5th Edition, Aug 27, 2005. 14.5 ©Silberschatz, Korth and Sudarshan Transformation of Relational Expressions  Two relational algebra expressions are said to be equivalent if on every legal database instance the two expressions generate the same set of tuples   In SQL, inputs and outputs are multisets of tuples   Note: order of tuples is irrelevant Two expressions in the multiset version of the relational algebra are said to be equivalent if on every legal database instance the two expressions generate the same multiset of tuples An equivalence rule says that expressions of two forms are equivalent  Can replace expression of first form by second, or vice versa Database System Concepts - 5th Edition, Aug 27, 2005. 14.6 ©Silberschatz, Korth and Sudarshan Equivalence Rules 1. Conjunctive selection operations can be deconstructed into a sequence of individual selections.  1  2 (E)  1 (  2 (E)) 2. Selection operations are commutative.  1 (  2 (E))   2 ( 1 (E)) 3. Only the last in a sequence of projection operations is needed, the others can be omitted.  L1 ( L2 ( ( Ln(E))))  L1 (E) 4. Selections can be combined with Cartesian products and theta joins. a. (E1 X E2) = E1 b. 1(E1 2  E2 E2 ) = E 1 Database System Concepts - 5th Edition, Aug 27, 2005. 1 2 E2 14.7 ©Silberschatz, Korth and Sudarshan Equivalence Rules (Cont.) 5. Theta-join operations (and natural joins) are commutative. E1  E2 = E2  E1 6. (a) Natural join operations are associative: (E1 E2) E3 = E1 (E2 E3 ) (b) Theta joins are associative in the following manner: (E1 1 E2) 2 3 E3 = E1 2 3 (E 2 2 E 3) where 2 involves attributes from only E2 and E3. Database System Concepts - 5th Edition, Aug 27, 2005. 14.8 ©Silberschatz, Korth and Sudarshan Pictorial Depiction of Equivalence Rules Database System Concepts - 5th Edition, Aug 27, 2005. 14.9 ©Silberschatz, Korth and Sudarshan Equivalence Rules (Cont.) 7. The selection operation distributes over the theta join operation under the following two conditions: (a) When all the attributes in 0 involve only the attributes of one of the expressions (E1) being joined. 0E1  E2) = (0(E1))  E2 (b) When  1 involves only the attributes of E1 and 2 involves only the attributes of E2. 1 E1 Database System Concepts - 5th Edition, Aug 27, 2005.  E2) = (1(E1)) 14.10  ( (E2)) ©Silberschatz, Korth and Sudarshan Equivalence Rules (Cont.) 8. The projections operation distributes over the theta join operation as follows: (a) if  involves only attributes from L1  L2: L1L2 (E1 (b) Consider a join E1    E2)  (L (E1))  1 E2. (L2 (E2)) Let L1 and L2 be sets of attributes from E1 and E2, respectively.  Let L3 be attributes of E1 that are involved in join condition , but are not in L1  L2, and  let L4 be attributes of E2 that are involved in join condition , but are not in L1  L2. L L (E1 1 2 Database System Concepts - 5th Edition, Aug 27, 2005.  E2 )  L L (( L L (E1 )) 1 2 14.11 1 3  ( L 2 L4 (E2 ))) ©Silberschatz, Korth and Sudarshan Equivalence Rules (Cont.) 9. The set operations union and intersection are commutative E1  E2 = E2  E 1 E1  E2 = E2  E 1  (set difference is not commutative). 10. Set union and intersection are associative. (E1  E2)  E3 = E1  (E2  E3) (E1  E2)  E3 = E1  (E2  E3) 11. The selection operation distributes over ,  and –.  (E1 – E2) =  (E1) – (E2) and similarly for  and  in place of – Also:   (E 1 – E2) = (E1) – E2 and similarly for  in place of –, but not for  12. The projection operation distributes over union L(E1  E2) = (L(E1))  (L(E2)) Database System Concepts - 5th Edition, Aug 27, 2005. 14.12 ©Silberschatz, Korth and Sudarshan Transformation Example  Query: Find the names of all customers who have an account at some branch located in Brooklyn. customer_name(branch_city = “Brooklyn” (branch (account depositor)))  Transformation using rule 7a. customer_name ((branch_city =“Brooklyn” (branch)) (account depositor))  Performing the selection as early as possible reduces the size of the relation to be joined. Database System Concepts - 5th Edition, Aug 27, 2005. 14.13 ©Silberschatz, Korth and Sudarshan Example with Multiple Transformations  Query: Find the names of all customers with an account at a Brooklyn branch whose account balance is over $1000. customer_name((branch_city = “Brooklyn”  balance > 1000 (branch  account)) depositor) Second form provides an opportunity to apply the “perform selections early” rule, resulting in the subexpression branch_city = “Brooklyn” (branch)  depositor))) Transformation using join associatively (Rule 6a): customer_name((branch_city = “Brooklyn”  balance > 1000 (branch  (account  balance > 1000 (account) Thus a sequence of transformations can be useful Database System Concepts - 5th Edition, Aug 27, 2005. 14.14 ©Silberschatz, Korth and Sudarshan Multiple Transformations (Cont.) Database System Concepts - 5th Edition, Aug 27, 2005. 14.15 ©Silberschatz, Korth and Sudarshan Projection Operation Example customer_name((branch_city = “Brooklyn” (branch)  account) depositor) When we compute (branch_city = “Brooklyn” (branch) account ) we obtain a relation whose schema is: (branch_name, branch_city, assets, account_number, balance)  Push projections using equivalence rules 8a and 8b; eliminate unneeded attributes from intermediate results to get: customer_name (( account_number ( (branch_city = “Brooklyn” (branch) account )) depositor )  Performing the projection as early as possible reduces the size of the relation to be joined Database System Concepts - 5th Edition, Aug 27, 2005. 14.16 ©Silberschatz, Korth and Sudarshan Join Ordering Example  For all relations r1, r2, and r3, (r1  If r2 r2) r3 is quite large and r1 (r1 r2) r3 = r1 (r2 r3 ) r2 is small, we choose r3 so that we compute and store a smaller temporary relation. Database System Concepts - 5th Edition, Aug 27, 2005. 14.17 ©Silberschatz, Korth and Sudarshan Join Ordering Example (Cont.)  Consider the expression customer_name ((branch_city = “Brooklyn” (branch)) ( account depositor))  Could compute account depositor first, and join result with branch_city = “Brooklyn” (branch) but account depositor is likely to be a large relation.  Only a small fraction of the bank’s customers are likely to have accounts in branches located in Brooklyn  it is better to compute branch_city = “Brooklyn” (branch) account first. Database System Concepts - 5th Edition, Aug 27, 2005. 14.18 ©Silberschatz, Korth and Sudarshan Enumeration of Equivalent Expressions  Query optimizers use equivalence rules to systematically generate expressions equivalent to the given expression  Conceptually, generate all equivalent expressions by repeatedly executing the following step until no more expressions can be found:  for each expression found so far, use all applicable equivalence rules  add newly generated expressions to the set of expressions found so far  The above approach is very expensive in space and time  Space requirements reduced by sharing common subexpressions:  when E1 is generated from E2 by an equivalence rule, usually only the top level of the two are different, subtrees below are the same and can be shared   E.g. when applying join associativity Time requirements are reduced by not generating all expressions  More details shortly Database System Concepts - 5th Edition, Aug 27, 2005. 14.19 ©Silberschatz, Korth and Sudarshan Cost Estimation  Cost of each operator computer as described in Chapter 13  Need statistics of input relations   Inputs can be results of sub-expressions  Need to estimate statistics of expression results  To do so, we require additional statistics   E.g. number of tuples, sizes of tuples E.g. number of distinct values for an attribute More on cost estimation later Database System Concepts - 5th Edition, Aug 27, 2005. 14.20 ©Silberschatz, Korth and Sudarshan Evaluation Plan  An evaluation plan defines exactly what algorithm is used for each operation, and how the execution of the operations is coordinated. Database System Concepts - 5th Edition, Aug 27, 2005. 14.21 ©Silberschatz, Korth and Sudarshan Choice of Evaluation Plans   Must consider the interaction of evaluation techniques when choosing evaluation plans: choosing the cheapest algorithm for each operation independently may not yield best overall algorithm. E.g.  merge-join may be costlier than hash-join, but may provide a sorted output which reduces the cost for an outer level aggregation.  nested-loop join may provide opportunity for pipelining Practical query optimizers incorporate elements of the following two broad approaches: 1. Search all the plans and choose the best plan in a cost-based fashion. 2. Uses heuristics to choose a plan. Database System Concepts - 5th Edition, Aug 27, 2005. 14.22 ©Silberschatz, Korth and Sudarshan Cost-Based Optimization  Consider finding the best join-order for r1  There are (2(n – 1))!/(n – 1)! different join orders for above expression. With n = 7, the number is 665280, with n = 10, the number is greater than 176 billion!  No need to generate all the join orders. Using dynamic programming, the leastcost join order for any subset of {r1, r2, . . . rn} is computed only once and stored for future use. Database System Concepts - 5th Edition, Aug 27, 2005. 14.23 r2 . . . rn. ©Silberschatz, Korth and Sudarshan Dynamic Programming in Optimization  To find best join tree for a set of n relations:  To find best plan for a set S of n relations, consider all possible plans of the form: S1 (S – S1) where S1 is any non-empty subset of S.  Recursively compute costs for joining subsets of S to find the cost of each plan. Choose the cheapest of the 2n – 1 alternatives.  When plan for any subset is computed, store it and reuse it when it is required again, instead of recomputing it  Dynamic programming Database System Concepts - 5th Edition, Aug 27, 2005. 14.24 ©Silberschatz, Korth and Sudarshan Join Order Optimization Algorithm procedure findbestplan(S) if (bestplan[S].cost  ) return bestplan[S] // else bestplan[S] has not been computed earlier, compute it now if (S contains only 1 relation) set bestplan[S].plan and bestplan[S].cost based on the best way of accessing S else for each non-empty subset S1 of S such that S1  S P1= findbestplan(S1) P2= findbestplan(S - S1) A = best algorithm for joining results of P1 and P2 cost = P1.cost + P2.cost + cost of A if cost < bestplan[S].cost bestplan[S].cost = cost bestplan[S].plan = “execute P1.plan; execute P2.plan; join results of P1 and P2 using A” return bestplan[S] Database System Concepts - 5th Edition, Aug 27, 2005. 14.25 ©Silberschatz, Korth and Sudarshan Left Deep Join Trees  In left-deep join trees, the right-hand-side input for each join is a relation, not the result of an intermediate join. Database System Concepts - 5th Edition, Aug 27, 2005. 14.26 ©Silberschatz, Korth and Sudarshan Cost of Optimization  With dynamic programming time complexity of optimization with bushy trees is O(3n).  With n = 10, this number is 59000 instead of 176 billion!  Space complexity is O(2n)  To find best left-deep join tree for a set of n relations:   Consider n alternatives with one relation as right-hand side input and the other relations as left-hand side input.  Using (recursively computed and stored) least-cost join order for each alternative on left-hand-side, choose the cheapest of the n alternatives. If only left-deep trees are considered, time complexity of finding best join order is O(n 2n)   Space complexity remains at O(2n) Cost-based optimization is expensive, but worthwhile for queries on large datasets (typical queries have small n, generally < 10) Database System Concepts - 5th Edition, Aug 27, 2005. 14.27 ©Silberschatz, Korth and Sudarshan Interesting Orders in Cost-Based Optimization  Consider the expression (r1  An interesting sort order is a particular sort order of tuples that could be useful for a later operation.  r2 r3) r4 r5  Generating the result of r1 r2 r3 sorted on the attributes common with r4 or r5 may be useful, but generating it sorted on the attributes common only r1 and r2 is not useful.  Using merge-join to compute r1 r2 r3 may be costlier, but may provide an output sorted in an interesting order. Not sufficient to find the best join order for each subset of the set of n given relations; must find the best join order for each subset, for each interesting sort order  Simple extension of earlier dynamic programming algorithms  Usually, number of interesting orders is quite small and doesn’t affect time/space complexity significantly Database System Concepts - 5th Edition, Aug 27, 2005. 14.28 ©Silberschatz, Korth and Sudarshan Heuristic Optimization  Cost-based optimization is expensive, even with dynamic programming.  Systems may use heuristics to reduce the number of choices that must be made in a cost-based fashion.  Heuristic optimization transforms the query-tree by using a set of rules that typically (but not in all cases) improve execution performance:  Perform selection early (reduces the number of tuples)  Perform projection early (reduces the number of attributes)  Perform most restrictive selection and join operations before other similar operations.  Some systems use only heuristics, others combine heuristics with partial cost-based optimization. Database System Concepts - 5th Edition, Aug 27, 2005. 14.29 ©Silberschatz, Korth and Sudarshan Steps in Typical Heuristic Optimization 1. Deconstruct conjunctive selections into a sequence of single selection operations (Equiv. rule 1.). 2. Move selection operations down the query tree for the earliest possible execution (Equiv. rules 2, 7a, 7b, 11). 3. Execute first those selection and join operations that will produce the smallest relations (Equiv. rule 6). 4. Replace Cartesian product operations that are followed by a selection condition by join operations (Equiv. rule 4a). 5. Deconstruct and move as far down the tree as possible lists of projection attributes, creating new projections where needed (Equiv. rules 3, 8a, 8b, 12). 6. Identify those subtrees whose operations can be pipelined, and execute them using pipelining). Database System Concepts - 5th Edition, Aug 27, 2005. 14.30 ©Silberschatz, Korth and Sudarshan Structure of Query Optimizers  The System R/Starburst optimizer considers only left-deep join orders. This reduces optimization complexity and generates plans amenable to pipelined evaluation. System R/Starburst also uses heuristics to push selections and projections down the query tree.  Heuristic optimization used in some versions of Oracle:  Repeatedly pick “best” relation to join next  Starting from each of n starting points. Pick best among these.  For scans using secondary indices, some optimizers take into account the probability that the page containing the tuple is in the buffer.  Intricacies of SQL complicate query optimization  E.g. nested subqueries Database System Concepts - 5th Edition, Aug 27, 2005. 14.31 ©Silberschatz, Korth and Sudarshan Structure of Query Optimizers (Cont.)  Some query optimizers integrate heuristic selection and the generation of alternative access plans.  System R and Starburst use a hierarchical procedure based on the nested-block concept of SQL: heuristic rewriting followed by cost-based join-order optimization.  Even with the use of heuristics, cost-based query optimization imposes a substantial overhead.  This expense is usually more than offset by savings at query-execution time, particularly by reducing the number of slow disk accesses. Database System Concepts - 5th Edition, Aug 27, 2005. 14.32 ©Silberschatz, Korth and Sudarshan Statistical Information for Cost Estimation  nr: number of tuples in a relation r.  br: number of blocks containing tuples of r.  lr: size of a tuple of r.  fr: blocking factor of r — i.e., the number of tuples of r that fit into one block.  V(A, r): number of distinct values that appear in r for attribute A; same as the size of A(r).  If tuples of r are stored together physically in a file, then: nr  br   fr      Database System Concepts - 5th Edition, Aug 27, 2005. 14.33 ©Silberschatz, Korth and Sudarshan Histograms  Histogram on attribute age of relation person  Equi-width histograms  Equi-depth histograms Database System Concepts - 5th Edition, Aug 27, 2005. 14.34 ©Silberschatz, Korth and Sudarshan Selection Size Estimation   A=v(r)  nr / V(A,r) : number of records that will satisfy the selection  Equality condition on a key attribute: size estimate = 1 AV(r) (case of A  V(r) is symmetric)  Let c denote the estimated number of tuples satisfying the condition.  If min(A,r) and max(A,r) are available in catalog     c = 0 if v < min(A,r) c= nr . v  min(A, r) max(A, r)  min(A, r) If histograms available, can refine above estimate In absence of statistical information c is assumed to be nr / 2. Database System Concepts - 5th Edition, Aug 27, 2005. 14.35 ©Silberschatz, Korth and Sudarshan Size Estimation of Complex Selections  The selectivity of a condition i is the probability that a tuple in the relation r satisfies i .   If si is the number of satisfying tuples in r, the selectivity of i is given by si /nr. Conjunction: 1 2. . .  n (r). Assuming indepdence, estimate of tuples in the result is:   s1  s2  ... sn nr  nrn Disjunction:1 2 . . .  n (r). Estimated number of tuples: Negation:  s  s s nr   1 (1 1 )  (1 2 )  ... (1 n ) nr of tuples:nr nr  (r). Estimated number  nr – size((r)) Database System Concepts - 5th Edition, Aug 27, 2005. 14.36 ©Silberschatz, Korth and Sudarshan Join Operation: Running Example Running example: depositor customer Catalog information for join examples:  ncustomer = 10,000.  fcustomer = 25, which implies that bcustomer =10000/25 = 400.  ndepositor = 5000.  fdepositor = 50, which implies that bdepositor = 5000/50 = 100.  V(customer_name, depositor) = 2500, which implies that , on average, each customer has two accounts.  Also assume that customer_name in depositor is a foreign key on customer.  V(customer_name, customer) = 10000 (primary key!) Database System Concepts - 5th Edition, Aug 27, 2005. 14.37 ©Silberschatz, Korth and Sudarshan Estimation of the Size of Joins  The Cartesian product r x s contains nr .ns tuples; each tuple occupies sr + ss bytes.  If R  S = , then r  If R  S is a key for R, then a tuple of s will join with at most one tuple from r   therefore, the number of tuples in r tuples in s. s is no greater than the number of If R  S in S is a foreign key in S referencing R, then the number of tuples in r s is exactly the same as the number of tuples in s.   s is the same as r x s. The case for R  S being a foreign key referencing S is symmetric. In the example query depositor foreign key of customer  customer, customer_name in depositor is a hence, the result has exactly ndepositor tuples, which is 5000 Database System Concepts - 5th Edition, Aug 27, 2005. 14.38 ©Silberschatz, Korth and Sudarshan Estimation of the Size of Joins (Cont.)  If R  S = {A} is not a key for R or S. If we assume that every tuple t in R produces tuples in R tuples in R S is estimated to be: S, the number of nr  ns V( A, s ) If the reverse is true, the estimate obtained will be: nr  ns V( A, r ) The lower of these two estimates is probably the more accurate one.  Can improve on above if histograms are available  Use formula similar to above, for each cell of histograms on the two relations Database System Concepts - 5th Edition, Aug 27, 2005. 14.39 ©Silberschatz, Korth and Sudarshan Estimation of the Size of Joins (Cont.)  Compute the size estimates for depositor about foreign keys: customer without using information  V(customer_name, depositor) = 2500, and V(customer_name, customer) = 10000  The two estimates are 5000 * 10000/2500 - 20,000 and 5000 * 10000/10000 = 5000  We choose the lower estimate, which in this case, is the same as our earlier computation using foreign keys. Database System Concepts - 5th Edition, Aug 27, 2005. 14.40 ©Silberschatz, Korth and Sudarshan Size Estimation for Other Operations  Projection: estimated size of A(r) = V(A,r)  Aggregation : estimated size of AgF(r) = V(A,r)  Set operations  For unions/intersections of selections on the same relation: rewrite and use size estimate for selections   E.g. 1 (r)  2 (r) can be rewritten as 1 2 (r) For operations on different relations:  estimated size of r  s = size of r + size of s.  estimated size of r  s = minimum size of r and size of s.  estimated size of r – s = r.  All the three estimates may be quite inaccurate, but provide upper bounds on the sizes. Database System Concepts - 5th Edition, Aug 27, 2005. 14.41 ©Silberschatz, Korth and Sudarshan Size Estimation (Cont.)  Outer join:  Estimated size of r   s = size of r s + size of r Case of right outer join is symmetric Estimated size of r Database System Concepts - 5th Edition, Aug 27, 2005. s = size of r 14.42 s + size of r + size of s ©Silberschatz, Korth and Sudarshan Estimation of Number of Distinct Values Selections:  (r)  If  forces A to take a specified value: V(A, (r)) = 1.   If  forces A to take on one of a specified set of values: V(A, (r)) = number of specified values.   (e.g., (A = 1 V A = 3 V A = 4 )), If the selection condition  is of the form A op r estimated V(A, (r)) = V(A.r) * s   e.g., A = 3 where s is the selectivity of the selection. In all the other cases: use approximate estimate of min(V(A,r), n (r) )  More accurate estimate can be got using probability theory, but this one works fine generally Database System Concepts - 5th Edition, Aug 27, 2005. 14.43 ©Silberschatz, Korth and Sudarshan Estimation of Distinct Values (Cont.) Joins: r   s If all attributes in A are from r estimated V(A, r s) = min (V(A,r), n r s) If A contains attributes A1 from r and A2 from s, then estimated V(A,r s) = min(V(A1,r)*V(A2 – A1,s), V(A1 – A2,r)*V(A2,s), nr  s) More accurate estimate can be got using probability theory, but this one works fine generally Database System Concepts - 5th Edition, Aug 27, 2005. 14.44 ©Silberschatz, Korth and Sudarshan Estimation of Distinct Values (Cont.)  Estimation of distinct values are straightforward for projections.  They are the same in A (r) as in r.  The same holds for grouping attributes of aggregation.  For aggregated values  For min(A) and max(A), the number of distinct values can be estimated as min(V(A,r), V(G,r)) where G denotes grouping attributes  For other aggregates, assume all values are distinct, and use V(G,r) Database System Concepts - 5th Edition, Aug 27, 2005. 14.45 ©Silberschatz, Korth and Sudarshan Optimizing Nested Subqueries**  SQL conceptually treats nested subqueries in the where clause as functions that take parameters and return a single value or set of values  Parameters are variables from outer level query that are used in the nested subquery; such variables are called correlation variables  E.g. select customer_name from borrower where exists (select * from depositor where depositor.customer_name = borrower.customer_name )  Conceptually, nested subquery is executed once for each tuple in the cross-product generated by the outer level from clause  Such evaluation is called correlated evaluation  Note: other conditions in where clause may be used to compute a join (instead of a cross-product) before executing the nested subquery Database System Concepts - 5th Edition, Aug 27, 2005. 14.46 ©Silberschatz, Korth and Sudarshan Optimizing Nested Subqueries (Cont.)  Correlated evaluation may be quite inefficient since  a large number of calls may be made to the nested query  there may be unnecessary random I/O as a result  SQL optimizers attempt to transform nested subqueries to joins where possible, enabling use of efficient join techniques  E.g.: earlier nested query can be rewritten as select customer_name from borrower, depositor where depositor.customer_name = borrower.customer_name   Note: above query doesn’t correctly deal with duplicates, can be modified to do so as we will see In general, it is not possible/straightforward to move the entire nested subquery from clause into the outer level query from clause  A temporary relation is created instead, and used in body of outer level query Database System Concepts - 5th Edition, Aug 27, 2005. 14.47 ©Silberschatz, Korth and Sudarshan Optimizing Nested Subqueries (Cont.) In general, SQL queries of the form below can be rewritten as shown   Rewrite: select … from L1 where P1 and exists (select * To: from L2 where P2) create table t1 as select distinct V from L2 where P21 select … from L1, t1 where P1 and P22  P21 contains predicates in P2 that do not involve any correlation variables  P22 reintroduces predicates involving correlation variables, with relations renamed appropriately V contains all attributes used in predicates with correlation variables  Database System Concepts - 5th Edition, Aug 27, 2005. 14.48 ©Silberschatz, Korth and Sudarshan Optimizing Nested Subqueries (Cont.)  In our example, the original nested query would be transformed to create table t1 as select distinct customer_name from depositor select customer_name from borrower, t1 where t1.customer_name = borrower.customer_name  The process of replacing a nested query by a query with a join (possibly with a temporary relation) is called decorrelation.  Decorrelation is more complicated when  the nested subquery uses aggregation, or  when the result of the nested subquery is used to test for equality, or  when the condition linking the nested subquery to the other query is not exists,  and so on. Database System Concepts - 5th Edition, Aug 27, 2005. 14.49 ©Silberschatz, Korth and Sudarshan Materialized Views**  A materialized view is a view whose contents are computed and stored.  Consider the view create view branch_total_loan(branch_name, total_loan) as select branch_name, sum(amount) from loan groupby branch_name  Materializing the above view would be very useful if the total loan amount is required frequently  Saves the effort of finding multiple tuples and adding up their amounts Database System Concepts - 5th Edition, Aug 27, 2005. 14.50 ©Silberschatz, Korth and Sudarshan Materialized View Maintenance  The task of keeping a materialized view up-to-date with the underlying data is known as materialized view maintenance  Materialized views can be maintained by recomputation on every update  A better option is to use incremental view maintenance   Changes to database relations are used to compute changes to materialized view, which is then updated View maintenance can be done by  Manually defining triggers on insert, delete, and update of each relation in the view definition  Manually written code to update the view whenever database relations are updated  Supported directly by the database Database System Concepts - 5th Edition, Aug 27, 2005. 14.51 ©Silberschatz, Korth and Sudarshan Incremental View Maintenance  The changes (inserts and deletes) to a relation or expressions are referred to as its differential   Set of tuples inserted to and deleted from r are denoted ir and dr To simplify our description, we only consider inserts and deletes  We replace updates to a tuple by deletion of the tuple followed by insertion of the update tuple  We describe how to compute the change to the result of each relational operation, given changes to its inputs  We then outline how to handle relational algebra expressions Database System Concepts - 5th Edition, Aug 27, 2005. 14.52 ©Silberschatz, Korth and Sudarshan Join Operation  Consider the materialized view v = r s and an update to r  Let rold and rnew denote the old and new states of relation r  Consider the case of an insert to r:  We can write rnew  And rewrite the above to (rold  But (rold s) is simply the old value of the materialized view, so the incremental change to the view is just ir s  Thus, for inserts  Similarly for deletes s as (rold  ir) s)  (ir vnew = vold (ir Database System Concepts - 5th Edition, Aug 27, 2005. s s) s) vnew = vold – (dr 14.53 s) ©Silberschatz, Korth and Sudarshan Selection and Projection Operations  Selection: Consider a view v = (r).  vnew = vold (ir) vnew = vold - (dr)  Projection is a more difficult operation  R = (A,B), and r(R) = { (a,2), (a,3)}     A(r) has a single tuple (a). If we delete the tuple (a,2) from r, we should not delete the tuple (a) from A(r), but if we then delete (a,3) as well, we should delete the tuple For each tuple in a projection A(r) , we will keep a count of how many times it was derived  On insert of a tuple to r, if the resultant tuple is already in A(r) we increment its count, else we add a new tuple with count = 1  On delete of a tuple from r, we decrement the count of the corresponding tuple in A(r)  if the count becomes 0, we delete the tuple from A(r) Database System Concepts - 5th Edition, Aug 27, 2005. 14.54 ©Silberschatz, Korth and Sudarshan Aggregation Operations  count : v = Agcount(B)(r).  When a set of tuples ir is inserted   For each tuple r in ir, if the corresponding group is already present in v, we increment its count, else we add a new tuple with count = 1 When a set of tuples dr is deleted  for each tuple t in ir.we look for the group t.A in v, and subtract 1 from the count for the group. – If the count becomes 0, we delete from v the tuple for the group t.A  sum: v = Agsum (B)(r)  We maintain the sum in a manner similar to count, except we add/subtract the B value instead of adding/subtracting 1 for the count  Additionally we maintain the count in order to detect groups with no tuples. Such groups are deleted from v   Cannot simply test for sum = 0 (why?) To handle the case of avg, we maintain the sum and count aggregate values separately, and divide at the end Database System Concepts - 5th Edition, Aug 27, 2005. 14.55 ©Silberschatz, Korth and Sudarshan Aggregate Operations (Cont.)  min, max: v = Agmin (B) (r).  Handling insertions on r is straightforward.  Maintaining the aggregate values min and max on deletions may be more expensive. We have to look at the other tuples of r that are in the same group to find the new minimum Database System Concepts - 5th Edition, Aug 27, 2005. 14.56 ©Silberschatz, Korth and Sudarshan Other Operations   Set intersection: v = r  s  when a tuple is inserted in r we check if it is present in s, and if so we add it to v.  If the tuple is deleted from r, we delete it from the intersection if it is present.  Updates to s are symmetric  The other set operations, union and set difference are handled in a similar fashion. Outer joins are handled in much the same way as joins but with some extra work  we leave details to you. Database System Concepts - 5th Edition, Aug 27, 2005. 14.57 ©Silberschatz, Korth and Sudarshan Handling Expressions  To handle an entire expression, we derive expressions for computing the incremental change to the result of each sub-expressions, starting from the smallest sub-expressions.  E.g. consider E1 expression  Suppose the set of tuples to be inserted into E1 is given by D1   E2 where each of E1 and E2 may be a complex Computed earlier, since smaller sub-expressions are handled first Then the set of tuples to be inserted into E1 D1 E2  E2 is given by This is just the usual way of maintaining joins Database System Concepts - 5th Edition, Aug 27, 2005. 14.58 ©Silberschatz, Korth and Sudarshan Query Optimization and Materialized Views  Rewriting queries to use materialized views:  A materialized view v = r  A user submits a query  We can rewrite the query as v    s is available r s t t Whether to do so depends on cost estimates for the two alternative Replacing a use of a materialized view by the view definition:  A materialized view v = r s is available, but without any index on it  User submits a query A=10(v).  Suppose also that s has an index on the common attribute B, and r has an index on attribute A.  The best plan for this query may be to replace v by r query plan A=10(r) s s, which can lead to the Query optimizer should be extended to consider all above alternatives and choose the best overall plan Database System Concepts - 5th Edition, Aug 27, 2005. 14.59 ©Silberschatz, Korth and Sudarshan Materialized View Selection  Materialized view selection: “What is the best set of views to materialize?”.  This decision must be made on the basis of the system workload  Indices are just like materialized views, problem of index selection is closely related, to that of materialized view selection, although it is simpler.  Some database systems, provide tools to help the database administrator with index and materialized view selection. Database System Concepts - 5th Edition, Aug 27, 2005. 14.60 ©Silberschatz, Korth and Sudarshan End of Chapter Database System Concepts 5th Ed. ©Silberschatz, Korth and Sudarshan See www.db-book.com for conditions on re-use