Exact Minimization of # of Joins

Transcription

1 A Quer Rewriing Algorihm: Ec Minimizion of # of Joins Emple (movie bse) selec.irecor from movie, movie, movie m3, scheule, scheule s2 where.irecor =.irecor n.cor = m3.cor n.ile =.ile n m3.ile = s2.ile Noe: number of joins in corresponing lgebr epression is (number of uples in FROM cluse) 1 Gol: minimize he number of uples in he FROM cluse k join minimizion Ec Minimizion of # of Joins Emple (movie bse) selec.irecor from movie, movie, movie m3, scheule, scheule s2 where.irecor =.irecor n.cor = m3.cor n.ile =.ile n m3.ile = s2.ile Cn his be simplifie? 1

2 Ec Minimizion of # of Joins Emple (movie bse) selec.irecor from movie, movie, movie m3, scheule, scheule s2 where.irecor =.irecor n.cor = m3.cor n.ile =.ile n m3.ile = s2.ile More inuiive represenion: movie ile irecor cor scheule heer ile m3 s2 71 Ec Minimizion of # of Joins Emple (movie bse) Cn his be simplifie? Clim: i is enough o keep n in he pern Reson:.cor cn pl he role of cn pl he role of movie ile irecor cor scheule heer ile m3 s2 72 2

3 Ec Minimizion of # of Joins Emple (movie bse) Cn his be simplifie? Clim: i is enough o keep n in he pern Reson:.cor cn pl he role of cn pl he role of movie ile irecor cor scheule heer ile 73 Ec Minimizion of # of Joins Emple (movie bse) Simplifie SQL quer: selec.irecor from movie, scheule where.ile =.ile movie ile irecor cor scheule heer ile 74 3

4 Ec Minimizion of # of Joins 4 joins selec.irecor from movie, movie, movie m3, scheule, scheule s2 where.irecor =.irecor n.cor = m3.cor n.ile =.ile n m3.ile = s2.ile 1 join selec.irecor from movie, scheule where.ile =.ile 75 Ec Minimizion of # of Joins Anoher emple: using consrins (k semnic opimizion) Fin heers showing ile b Bero n ile in which Winger cs selec.heer from scheule, scheule s2, movie, movie where.heer = s2.heer n.ile =.ile n.irecor = Bero n s2.ile =.ile n.cor = Winger movie ile irecor cor scheule heer ile Bero Winger s2 76 4

5 Ec Minimizion of # of Joins Anoher emple: using consrins Fin heers showing ile b Bero n ile in which Winger cs Suppose ech ile hs onl one irecor n ech heer shows onl one ile Then = n.irecor = Bero movie ile irecor cor scheule heer ile Bero Winger s2 77 Ec Minimizion of # of Joins Anoher emple: using consrins Fin heers showing ile b Bero n ile in which Winger cs Suppose ech ile hs onl one irecor n ech heer shows onl one ile Then = n.irecor = Bero movie ile irecor cor scheule heer ile Bero Bero Winger s2 78 5

6 Ec Minimizion of # of Joins Anoher emple: using consrins Fin heers showing ile b Bero n ile in which Winger cs Suppose ech ile hs onl one irecor n ech heer shows onl one ile Then = n.irecor = Bero movie ile irecor cor scheule heer ile Bero Winger 79 Ec Minimizion of # of Joins Anoher emple: using consrins Fin heers showing ile b Bero n ile in which Winger cs selec.heer from scheule, movie where.ile =.ile n.irecor = Bero n.cor = Winger movie ile irecor cor scheule heer ile Bero Winger 80 6

7 Ec Minimizion of # of Joins 3 joins selec.heer from scheule, scheule s2, movie, movie where.heer = s2.heer n.ile =.ile n.irecor = Bero n s2.ile =.ile n.cor = Winger 1 join selec.heer from scheule, movie where.ile =.ile n.irecor = Bero n.cor = Winger 81 Ec Minimizion of # of Joins How o reunn joins rise? Comple queries wrien b humns especill on lrge schems wih consrins Queries resuling from view unfoling see ne emple Ver comple SQL queries genere b ools 82 7

8 Dbse: Emple: Join reunncies from view unfoling Pien pi hospil oci Docor oci ocnme View (Scripps ocors): cree view ScrippsDoc s selec 1.* from Docor 1, Pien p1 where p1.hospil = Scripps n p1.oci = 1.oci View (Scripps piens): cree view ScrippsPien s selec p2.* from Pien p2 where p2.hospil = Scripps Scripps quer (using views): selec p.pi,.ocnme from ScrippsPien p, ScrippsDoc where p.oci =.oci 83 Quer on bse obine b view unfoling quer using view view1 view2 selec p.pi,.ocnme from ScrippsPien p, ScrippsDoc where p.oci =.oci cree view ScrippsDoc s selec 1.* from Docor 1, Pien p1 where p1.hospil = Scripps n p1.oci = 1.oci cree view ScrippsPien s selec p2.* from Pien p2 where p2.hospil = Scripps resul of view unfoling selec p.pi,.ocnme from Pien p, Docor, Pien p1 where p.oci =.oci n p.hospil = Scripps n p1.hospil = Scripps n p1.oci =.oci 84 8

9 Resuling quer hs reunn join selec p.pi,.ocnme from Pien p, Docor, Pien p1 where p.oci =.oci n p.hospil = Scripps n p1.hospil = Scripps n p1.oci =.oci Pien pi hospil oci Docor oci ocnme p j Scripps i i n p1 Scripps i reunn nswer pi ocnme j n 85 Pien pi hospil oci Docor oci ocnme p j Scripps i i n nswer pi ocnme j n Minimize SQL quer hs one join: Selec p.pi,.ocnme From Pien p, Docor Where p.hospil = Scripps n p.oci =.oci 86 9

10 Ec Minimizion of # of Joins Minimizion lgorihm for conjuncive SQL queries: SQL quer whose where cluse is conjuncion of equliies Bsic ie: SQL quer simplifie SQL quer QBE pern minimize QBE pern 87 QBE perns Sme s QBE, ecep (for beer rebili): no unerscore o mrk vribles wilcrs re eplicil enoe b inse of blnk no inser I. in he nswer relion movie ile irecor cor scheule heer ile nswer irecor 88 10

11 From SQL conjuncive queries o QBE perns 1. Rewrie he SQL quer using uple vribles 2. For ech uple vrible in he from cluse lising relion R inser corresponing QBE row in R 3. Use repee vribles n consns o epress he equliies in he where cluse if conricion rises (wo ifferen consns re me equl) hen oupu 4. The QBE nswer relion conins row whose vribles occur in he coorines specifie in he selec cluse 5. Coorines no involve in n equli n no in he nswer re wilcrs 89 From SQL conjuncive queries o QBE perns Emple selec.irecor from movie, movie, movie m3, scheule, scheule s2 where.irecor =.irecor n.cor = m3.cor n.ile =.ile n m3.ile = s2.ile movie ile irecor cor scheule heer ile m3 nswer irecor s

12 From SQL conjuncive queries o QBE perns Emple selec.irecor from movie, movie, movie m3, scheule, scheule s2 where.irecor =.irecor n.cor = m3.cor n.ile =.ile n m3.ile = s2.ile movie ile irecor cor scheule heer ile nswer irecor 91 From SQL conjuncive queries o QBE perns Anoher emple selec.heer from scheule, scheule s2, movie, movie where.heer = s2.heer n.ile =.ile n.irecor = Bero n s2.ile =.ile n.cor = Winger movie ile irecor cor scheule heer ile Bero Winger s2 nswer heer 92 12

13 From SQL conjuncive queries o QBE perns Anoher emple selec.heer from scheule, scheule s2, movie, movie where.heer = s2.heer n.ile =.ile n.irecor = Bero n s2.ile =.ile n.cor = Winger movie ile irecor cor scheule heer ile Bero Winger nswer heer 93 Quer efine b pern: ll nswers obine b mching he pern ino he bse (jus like QBE) scheule heer ile scheule heer ile Hillcres Tngo Plom Gofher. movie ile irecor cor movie ile irecor cor Tngo Bero Brno Gofher Coppol Brno nswer irecor nswer irecor Bero 94 13

14 Quer efine b pern: ll nswers obine b mching he pern ino he bse (jus like QBE) scheule heer ile scheule heer ile Hillcres Tngo Plom Gofher. movie ile irecor cor movie ile irecor cor Tngo Bero Brno Gofher Coppol Brno nswer irecor nswer irecor Coppol 95 Bck o emple: Pern Minimizion movie ile irecor cor scheule heer ile m3 s2 nswer irecor Inuiion: rows, m3, s2 re reunn Wh: if n re presen, hen he enire pern is sisfie 96 14

15 Bck o emple: Pern Minimizion movie ile irecor cor scheule heer ile m3 nswer irecor s2 Inuiion: rows, m3, s2 re reunn More precisel:, m3 cn be mppe o, n s2 o.cor 97 Pern Minimizion Formll: pern foling (k homomorphism) mpping f on vribles, consns n wilcrs of pern P such h f() = for nswer vribles n consns ever row of P is mppe o n eising row of P in he sme relion movie ile irecor cor scheule heer ile m3 s2 nswer irecor 98 f() =.cor = f(.ile) = ; f() = f(m3.irecor) = f(s2.heer) =.heer = f() = 15

16 Pern Minimizion Formll: pern foling (k homomorphism) mpping f on vribles, consns n wilcrs of pern P such h f() = for nswer vribles n consns ever row of P is mppe o n eising row of P in he sme relion Theorem: if P is pern n f is foling of P hen f(p) efines he sme quer s P 99 Theorem: P n f(p) efine he sme quer. Proof ie bse R P f(p) : nswer Mus show h nswer of P on R = nswer of f(p) on R

17 Theorem: P n f(p) efine he sme quer. Proof ie bse R h P f(p) h() h : nswer nswer of P on R nswer of f(p) on R Since f(p) P, n mching h of P in bse R is lso mching of f(p) 101 Theorem: P n f(p) efine he sme quer. Proof ie bse R P h f(p) h() h nswer of f(p) on R nswer of P on R

18 Theorem: P n f(p) efine he sme quer. Proof ie bse R h f P f(p) (h f) () h f nswer of f(p) on R nswer of P on R If h is mching of f(p) in R hen h f is mching of P in R n (h f) () = h (f()) = h(). 103 Pern minimizion lgorihm Repeel elimine reunn rows is reunn if here is foling f of P such h f(p) movie ile irecor cor scheule heer ile reunn reunn reunn nswer irecor

19 Pern minimizion lgorihm Repeel elimine reunn rows is reunn if here is foling f of P such h f(p) movie ile irecor cor scheule heer ile nswer irecor Miniml pern 105 Anoher emple R nswer A B C b c A B C b 1 c 1 -- b c 1 b b 2 c 2 b 1 c B ril n error, we cn elimine rows 3 n 4 using he foling mpping b 2 o b 1 n leving ll oher vribles unchnge. R A B C b 1 c 1 -- b c 1 2 b 1 c nswer A B C b c minimize pern 19

20 From minimize pern bck o SQL quer Emple: R A B C b 1 c 1 -- b c 1 2 b 1 c nswer A B C b c selec 1.A, 2.B, 3.C from R 1, R 2, R 3 where 1.B = 3.B n 1.C = 2.C 107 A complee emple R: ABC SQL conjuncive quer: Pern: c Minimize pern: selec 1.A, 2.B, 3.C from R 1, R 2, R 3 where 2.A = 3.A n 1.B = 5 n 2.B = 3.B n 2.B = 1.B R A B C nswer A B C R A B C nswer A B C c c 5 c Minimize SQL quer: selec 1.A, 5 s B, 3.C from R 1, R 3 where 1.B = 5 n 3.B = 5 20

21 Theorem: he minimizion lgorihm prouces n SQL quer wih minimum number of joins mong ll conjuncive SQL queries equivlen o he originl one on ll bses. Bu we cn o even beer: ke ino ccoun consrins (semnic quer opimizion). To see how his works, we een he lgorihm wih funcionl epenencies. 109 D Depenencies (k consrins) Semens bou vli Kes SSN uniquel eermines ll ribues of emploee Referenil inegri Ever suen is person Funcionl epenencies: eension of kes Ech emploee works in no more hn one eprmen NAME DEPARTMENT Use of epenencies: check inegri quer opimizion schem esign norml forms

22 Funcionl Depenencies Generlizion of ke consrins emploee ssn nme ci zip-coe se primr ke: ssn ``ssn eermines ll oher ribues`` ssn nme ci zip-coe se more generll: some ribues m eermine oher ribues wihou being kes: zip-coe se 111 Funcionl Depenencies Funcionl epenenc on R: epression X Y where X, Y (R) An insnce of R sisfies X Y iff whenever wo uples gree on X, he lso gree on Y e.g. SCHEDULE THEATER TITLE l joll killer omoes hillcres ngo Sisfies THEATER TITLE SCHEDULE THEATER TITLE l joll killer omoes hillcres ngo hillcres splenor Violes THEATER TITLE sisfies TITLE THEATER

23 Using FDs in quer opimizion Emple revisie: suppose ile irecor, heer ile Fin heers showing ile b Bero n ile in which Winger cs selec.heer from scheule, scheule s2, movie, movie where.heer = s2.heer n.ile =.ile n.irecor = Bero n s2.ile =.ile n.cor = Winger movie ile irecor cor scheule heer ile Bero Winger s2 nswer heer 113 movie ile irecor cor scheule heer ile Bero Winger s2 nswer heer This pern is miniml. However, we know h ile irecor, heer ile. Since he bse sisfies heer ile, = in ever mching. Ne, since ile irecor n =,.irecor =.irecor = Bero. We obin he following pern: movie ile irecor cor scheule heer ile Bero Bero Winger 114 nswer heer 23

24 movie ile irecor cor scheule heer ile Bero Bero Winger nswer heer Minimize pern: movie ile irecor cor scheule heer ile Bero Winger nswer heer 115 In generl: cn simplif pern P if he bse sisfies se F of FDs. Algorihm: The Chse Inpu: pern P, se F of FDs Oupu: bleu CHASE F (P) equivlen o P on ll relions sisfing F Inuiion: he chse moifies P so h i sisfies ll FDs in F Noe: ssume wihou loss of generli h FDs in F re of he form X A where A is one ribue

25 Bsic chse sep wih X A If pern conins wo rows h gree on X n isgree on A, chnge hem so h he lso gree on A X X A A 117 The Chse in eil Repe unil no chnge For ech X A in F o For ll rows 1, 2 in P such h 1 (X) = 2 (X), 1 (A) 2 (A) o if 1 (A), 2 (A) re non-nswer vribles hen replce one b he oher everwhere in P if 1 (A) is non-nswer vrible n 2 (A) is wilcr, hen replce 2 (A) b 1 (A) everwhere in P If 1 (A), 2 (A) re wilcrs, replce boh wih new vrible if 1 (A) is n nswer vrible n 2 (A) is vrible or wilcr, hen replce 2 (A) b 1 (A) everwhere in P if 1 (A) is consn, 2 (A) is vrible or wilcr, hen replce 2 (A) b 1 (A) everwhere in P if 1 (A) is consn, 2 (A) is consn hen STOP n oupu

26 Opimizion of SQL conjuncive queries wih FDs Inpu: SQL conjuncive quer Q, se of FDs F buil he pern P of Q compue CHASE F (P) minimize CHASE F (P) consruc he SQL quer corresponing o he miniml pern Clim: he bove prouces n SQL quer equivlen o Q on ll bses sisfing F, h hs he minimum possible number of joins 119 Emple selec 1.A, 1.B, 2.C from R 1, R 2 where 1.A = 5 n 1.B = 2.B R:ABC sisfies B A 1. Pern: R A B C nswer A B C 1 5 b -- 5 b c 2 -- b c 2. Chse wih B A: R A B C nswer A B C 1 5 b -- 5 b c 2 5 b c 3. Minimize: R A B C nswer A B C 5 b c 5 b c selec * from R where A =

27 Emple selec 2.A, 2.B, 1.C from R 1, R 2 where 1.A = 5 n 2.A = 6 n 1.B = 2.B R: ABC sisfies B A 1. Pern: R A B C nswer A B C 1 5 b c 6 b c 2 6 b Chse wih B A: 5 6 so he resul is emp 3. Minimize quer: 121 Emple selec 1.A, 3.B from R 1, R 2, R 3, R 4 where 1.A = 2.A n 2.A = 4.A n 1.B = 3.B n 4.B = 5 n 2.C = 3.C R: ABC sisfies A B 1. Pern: R A B C nswer A B 1 b -- b 2 -- c 3 -- b c Chse wih A B: R A B C nswer A B 5 c c 3. Minimize: R A B C 5 c 122 selec A, 5 s B from R where B = 5 27