Database System Concepts, 5 th Ed. Silberschatz, Korth and Sudarshan See for conditions on re-use

Transcription

1 Chpter 2: Reltionl Model Dtbse System Concepts, 5 th Ed. See for conditions on re-use

2 Bnking Exmple brnch (brnch_nme, brnch_city, ssets) customer (customer_nme, customer_street, customer_city) ccount (ccount_number, brnch_nme, blnce) lon (lon_number, brnch_nme, mount) depositor (customer_nme, ccount_number) borrower (customer_nme, lon_number) 2.2

3 Exmple of Reltion Account Reltion brnch_nme ccount_no blnce College rod A 0000 C.G. Rod A M.G. Rod A Ashrm Rod A City Sttion A Centrl City A Ring rod A Depositor Reltion Customer_nme ccount_no Amit Amir 2 Leen 235 Himnshu 425 Azhr 42 Schin 752 Priynk 524 Brnch Reltion brnch_nme brnch_city ssets College rod Ndid CG C.G. Rod Ahmedbd dbd M.G. Rod Surt Ashrm Rod Vdodr City Sttion Vpi Centrl City Gndhingr Mningr Jmngr Ring rod Ahmedbd Mnsrovr Ahmedbd

4 Exmple of Reltion Customer Reltion Borrower Reltion customer_nme customer_streetstreet customer_citycity Amit Min Ndid customer_nme lon_no Suresh North Ahmedbd Amit L Leen Prk Surt Amir L 23 Amit Putnm Vdodr d Leen L 5 Azhr Nssu Vpi Himnshu L 4 Schin Sentor Gndhingr Azhr L 93 Yuvrj Snd Hill Jmngr Schin L Amir North Ahmedbd Priynk L 6 Priynk North Ahmedbd Sulekh Sentor Gndhingr Himnshu Putnm Vdodr Lon Reltion Anjum Min Ndid brnch_nme lon_no blnce College rod L 0000 C.G. Rod L M.G. Rod L Ashrm Rod L City Sttion L Centrl City L Ring rod L

5 Bsic Structure Tble, Attributes, Domin (permitted vlues) D. Formlly, given sets D, D 2,. D n reltion r is subset of D x D 2 x x D n Thus, reltion is set of n-tuples (, 2,, n ) where ech i Exmple: If customer_nme = {Jones, Smith, Curry, Lindsy, } /* Set of ll customer nmes */ D i customer_street = {Min, North, Prk, } /* set of ll street nmes*/ customer_city = {Hrrison, Rye, Pittsfield, } /* set of ll city nmes */ Then r = { (Jones, Min, Hrrison), is reltion over (Smith, North, Rye), (Curry, North, Rye), (Lindsy, Prk, Pittsfield) } customer_nme x customer_street x customer_city 2.5

6 Attribute Types Ech ttribute of reltion hs nme The set of llowed vlues for ech ttribute is clled the domin of the ttribute t Attribute vlues re (normlly) required to be tomic; tht is, indivisible E.g. the vlue of n ttribute cn be n ccount number, but cnnot be set of ccount numbers Domin is sid to be tomic if ll its members re tomic The specil vlue null is member of every domin The null vlue cuses complictions in the definition of mny opertions We shll ignore the effect of null vlues in our min presenttion nd consider their effect lter 2.6

7 Reltion (Dtbse) Schem A, A 2,, A n re ttributes R = (A, A 2,, A n )i is reltion schem Exmple: Customer_ schem = (customer _ nme, customer_ street, customer_ city) r(r) denotes reltion r on the reltion schem R Exmple: customer (Customer_schem) 2.7

8 Reltion Instnce The current vlues (reltion instnce) of reltion re specified by tble An element t of r is tuple, represented by row intble customer_nme customer_street customer_city ttributes (or columns) Jones Smith Curry Li d Min North North P k Hrrison Rye Rye Pitt fi ld Lindsy Prk Pittsfield tuples (or rows) customer 2.8

9 Reltions re Unordered Order of tuples is irrelevnt (tuples my be stored in n rbitrry order) Exmple: ccount reltion with unordered tuples 2.9

10 Dtbse A dtbse consists of multiple reltions Informtion bout n enterprise is broken up into prts, with ech reltion storing one prt of the informtion ccount : stores informtion bout ccounts depositor : stores informtion bout which customer owns which ccount customer : stores informtion bout customers Storing ll informtion s single reltion such s bnk(ccount_number, blnce, customer_nme,..) results in repetition of informtion e.g.,if two customers own n ccount (Wht gets repeted?) the need for null vlues e.g., to represent customer without n ccount 2.0

11 The customer Reltion 2.

12 The depositor Reltion 2.2

13 Keys Let K R K is superkey of R if vlues for K re sufficient to identify unique tuple of ech possible reltion r(r) K is cndidte key if K is miniml Exmple: {customer_nme} is cndidte key for Customer, since it is superkey nd no subset of it is superkey. Primry key: cndidte key chosen s the principl mens of identifying tuples within reltion Should choose n ttribute whose vlue never, or very rrely, chnges. E.g. emil ddress is unique, but my chnge 2.3

14 Foreign Keys A reltion schem my hve n ttribute tht corresponds to the primry key of nother reltion. The ttribute is clled foreign key. E.g. customer_nme nd ccount_number ttributes of depositor re foreign keys to customer nd ccount respectively. Only vlues occurring in the primry key ttribute of the referenced reltion my occur in the foreign key ttribute of the referencing reltion. Schem digrm 2.4

15 Query Lnguges Lnguge in which user requests informtion from the dtbse. Ctegories of lnguges Procedurl Non-procedurl, or declrtive Pure lnguges: Reltionl lgebr Tuple reltionl clculus Domin reltionl clculus Pure lnguges form underlying bsis of query lnguges tht people use. 2.5

16 Reltionl Algebr It is Procedurl Query Lnguge Six bsic opertors select: σ (unry opertor) project: (unry opertor) union: (binry opertor) set difference: (binry opertor) Crtesin product: x (binry opertor) renme: ρ (unry opertor) Other Opertions: set intersection, nturl join, division nd ssignment The opertors tke one or two reltions s inputs nd produce new reltion s result. 2.6

17 Select Opertion Exmple Reltion r A B C D σ A=B ^ D > 5 (r) A B C D

18 Select Opertion Nottion: σ p (r) p is clled the selection predicte Defined s: σ p (r) = {t t r nd p(t)} Where p is formul in propositionl clculus l consisting of terms connected by : (nd), (or), (not) Ech term is one of: <ttribute> where op is one of: =,, >,. <. Exmple of selection: op <ttribute> or <constnt> σ brnch_nme= Perryridge (ccount) 2.8

19 Select Opertion Exmple 2.9

20 Project Opertion Exmple Reltion r: A B C A,C (r) A C A C A C =

21 Project Opertion Nottion: A,, ( A2, K A k r where A, A 2 re ttribute nmes nd r is reltion nme. The result is defined s the reltion of k columns obtined by ersing the columns tht re not listed Duplicte rows removed from result, since reltions re sets Exmple: To eliminte the brnch_nme ttribute of ccount ) ccount_number, blnce (ccount) 2.2

22 Project Opertion Exmple 2.22

23 Union Opertion Exmple Reltions r, s: A B A B 2 r 2 3 s A r s: B

24 Union Opertion Nottion: r s Defined s: For r s to be vlid. r s = {t t r or t s} }. r, s must hve the sme rity (sme number of ttributes) 2. The ttribute domins must be comptible (exmple: 2 nd column of r dels with the sme type of vlues s does the 2 nd column of s) Exmple: to find ll customers with either n ccount or lon customer_nme (depositor) customer_nme (borrower) 2.24

25 Set Difference Opertion Exmple Reltions r, s: A B A B 2 r 2 3 s r s: A B 2.25

26 Set Difference Opertion Nottion r s Defined s: r s = {t t r nd t s} } Set differences must be tken between comptible reltions. r nd s must hve the sme rity ttribute domins of r nd s must be comptible 2.26

27 Crtesin-Product Opertion Exmple Reltions r, s: A B C D E r x s: r 2 A B C D E γ γ 0 b b b 2 γ 0 b s b b 2.27

28 Crtesin-Product Opertion Nottion r x s Defined s: r x s = {t q t r nd q s} } Assume tht ttributes of r(r) nd s(s) re disjoint. (Tht is, R S = ). If ttributes of r(r) nd s(s) re not disjoint, then renming must be used. 2.28

29 Crtesin-Product Opertion Exmple 2.29

30 Composition of Opertions Cn build expressions using multiple opertions Exmple: σ A=C (r x s) r x s A B C D E γ γ b b b b σ A=C (r x s) A B C D E b 2.30

31 Renme Opertion Allows us to nme, nd therefore to refer to, the results of reltionllgebr expressions. Allows us to refer to reltion by more thn one nme. Exmple: ρ x (E) returns the expression E under the nme X If reltionl-lgebr expression E hs rity n, then ρ x,,..., ) ( E A A n ( A 2 ) returns the result of expression E under the nme X, nd with the ttributes renmed to A, A 2,., A n. 2.3

32 Exmple Queries Find ll lons of over $200 σ mount > 200 (lon) Find dthe lon number for ech hlon of n mount greter thn $200 lon number (σ mount > 200 (lon)) Find the nmes of ll customers who hve lon, n ccount, or both, from the bnk customer_nme (borrower) customer_nme (depositor) 2.32

33 Exmple Queries Find the nmes of ll customers who hve lon t the Perryridge brnch. customer_nme (σ brnch_nme= Perryridge (σ borrower.lon_number = lon.lon_number (borrower x lon))) Find the nmes of ll customers who hve lon t the Perryridge brnch but do not hve n ccount t ny brnch of the bnk. customer_nme (σ brnch_nme = Perryridge (σ borrower.lon_number = lon.lon_number (borrower x lon))) customer_nme (depositor) 2.33

34 Exmple Queries Find the nmes of ll customers who hve lon t the Perryridge brnch. Query customer_nme (σ brnch_nme = Perryridge ( σ borrower.lon_number = lon.lon_number (borrower x lon))) Query 2 customer_nme (σ lon.lon_number = borrower.lon_number ( (σ brnch_nme = Perryridge (lon)) x borrower)) 2.34

35 Exmple Queries Find the lrgest ccount blnce Strtegy: Find those blnces tht re not the lrgest Renme ccount reltion s d so tht we cn compre ech ccount blnce with ll others Use set difference to find those ccount blnces tht were not found in the erlier step. The query is: blnce (ccount) - ccount.blnce (σ ccount.blnce < d.blnce (ccount x ρ d (ccount))) 2.35

36 Forml Definition A bsic expression in the reltionl lgebr consists of either one of the following: A reltion in the dtbse A constnt reltion Let E nd E 2 be reltionl-lgebr expressions; the following re ll reltionl-lgebr expressions: E E 2 E E 2 E x E 2 σ p (E ), P is predicte on ttributes in E s (E ), S is list consisting of some of the ttributes in E ρ x (E ), x is the new nme for the result of E 2.36

37 Additionl Opertions We define dditionl opertions tht do not dd ny power to the reltionl lgebr, but tht simplify common queries. Set intersection Nturl join Division Assignment 2.37

38 Set-Intersection Opertion Nottion: r s Defined s: r s = { t t r nd t s } Assume: r, s hve the sme rity ttributes of r nd s re comptible Note: r s = r (r s) 2.38

39 Set-Intersection Opertion Exmple Reltion r, s: r s A B 2 r A B 2 A B 2 3 s 2.39

40 Nturl-Join Opertion Nottion: r s Nturl join is binry opertor tht is written s (R S)whereR nd S re reltions. The result of the nturl join is the set of ll combintions of tuples in R nd S tht re equl on their common ttribute nmes. Exmple: R = (A, B, C, D) S = (E, B, D) Result schem = (A, B, C, D, E) r s is defined s: r.a, r.b, r.c, r.d, s.e (σ r.b = s.b r.d = s.d (r x s)) 2.40

41 Nturl Join Opertion Nturl Join Opertion Exmple Exmple Reltions r, s: A B C D B D E A B 2 4 C D γ b 3 γ γ δ 4 2 γ b b 2 3 b b γ δ r s r A B C D E s r s γ γ γ γ 2.4 δ 2 γ b γ δ

42 Nturl Join Opertion Exmple For n exmple consider the tbles Employee nd Dept nd their nturl join: 2.42

43 2.43

44 Thet Join Opertion Exmple Consider tbles Cr nd Bot which list models of crs nd bots nd their respective prices. Suppose customer wnts to buy cr nd bot, but she doesn't wnt to spend more money for the bot thn for the cr. The θ-joinj i on the reltion CrPrice BotPrice produces tble with ll the possible options. 2.44

45 Equi Join Opertion In cse the opertor θ is the equlity opertor (=) then this join is lso clled n equijoin. Exmple: Given the two smple reltionl instnces S nd R The opertor S R.sid=Ssid R yields 2.45

46 Division Opertion Nottion: r s Suited to queries tht include the phrse for ll. Let r nd s be reltions on schems R nd S respectively where R = (A,, A m, B,, B n ) S = (B,, B n ) The result of r s is reltion on schem R S = (A,, A m ) r s = { t t R-S (r) u s ( tu r ) } Where tu mens the conctention of tuples t nd u to produce single tuple 2.46

47 Division Opertion Exmple Reltions r, s: r s: A A γ δ δ δ r B B s

48 Another Division Exmple Another Division Exmple A B C D E Reltions r, s: D E γ γ γ b b s γ γ γ γ γ γ b b 3 γ b r s: r r s: A B γ C γ γ 2.48 γ γ

49 Division Opertion (Cont.) Property Let q = r s Then q is the lrgest reltion stisfying q x s r Definition in terms of the bsic lgebr opertion Let r(r) nd s(s) be reltions, nd let S R r s = R-S (r ) R-S ( ( R-S (r ) x s ) R-S,S (r )) To see why R-S,S (r) simply reorders ttributes of r R-S ( R-S (r ) x s ) R-S,S (r) ) gives those tuples t in, R-S (r ) such tht for some tuple u s, tu r. 2.49

50 Assignment Opertion The ssignment opertion ( ) provides convenient wy to express complex queries. Write query s sequentil progrm consisting of series of ssignments followed by n expression whose vlue is displyed s result of the query. Assignment must lwys be mde to temporry reltion vrible. Exmple: Write r s s temp R-S (r ) temp2 R-S ((temp x s ) R-S,S (r )) result = temp temp2 The result to the right of the is ssigned to the reltion vrible on the left of the. My use vrible in subsequent expressions. 2.50

51 Bnk Exmple Queries Find the nmes of ll customers who hve lon nd n ccount t bnk. customer_nme (borrower) customer_nme (depositor) Find the nme of ll customers who hve lon t the bnk nd the lon mount customer_nme, lon_number, mount (borrower lon) 2.5

52 Bnk Exmple Queries Find ll customers who hve n ccount from t lest the Downtown nd the Uptown brnches. Query customer_nme (σ brnch_nme = Downtown (depositor ccount )) Query 2 customer_nme (σ brnch_nme nme = Uptown (depositor o ccount)) customer_nme, brnch_nme (depositor ccount) ρ temp(brnch_nme ) ({( Downtown ), ( Uptown )}) Note tht Query 2 uses constnt reltion. 2.52

53 Bnk Exmple Queries Find ll customers who hve n ccount t ll brnches locted in Brooklyn city. customer_nme, brnch_nme (depositor ccount) brnch_nme (σ brnch_city = Brooklyn (brnch)) 2.53

54 Extended Reltionl-Algebr-Opertions Generlized Projection Aggregte Functions Outer Join 2.54

55 Generlized Projection Extends the projection opertion by llowing rithmetic functions to be used in the projection list. F, F 2,..., F n ( E) E is ny reltionl-lgebr expression Ech of F, F 2,, F n re re rithmetic expressions involving constnts nd ttributes in the schem of E. Given reltion credit_info(customer_nme, info(customer nme, limit, credit_blnce), find how much more ech person cn spend: customer_nme, limit credit_blnce (credit_info) 2.55

56 Aggregte Functions nd Opertions Aggregtion function tkes collection of vlues nd returns single vlue s result. vg: verge vlue min: minimum vlue mx: mximum vlue sum: sum of vlues count: number of vlues Aggregte opertion in reltionl lgebr G,,, ϑ ( ), (,, ( )( E G2 KGn F A F2 A2 K Fn An E is ny reltionl-lgebr expression G, G 2, G n is list of ttributes on which to group (cn be empty) 2 n Ech F i is n ggregte function Ech A i is n ttribute nme ) 2.56

57 Aggregte Opertion Exmple Reltion r: A B C g sum(c) (r) sum(c )

58 Aggregte Opertion Exmple Reltion ccount grouped by brnch-nme: brnch_nmenme ccount_numbernumber Perryridge Perryridge Brighton Brighton Redwood A-02 A-20 A-27 A-25 A-222 blnce brnch_nme g sum(blnce) (ccount) brnch_nme Perryridge Brighton Redwood sum(blnce)

59 Aggregte Functions (Cont.) Result of ggregtion does not hve nme Cn use renme opertion to give it nme For convenience, we permit renming s prt of ggregte opertion g brnch_nme g sum(blnce) s sum_blnce (ccount) 2.59

60 Outer Join An extension of the join opertion tht voids loss of informtion. Computes the join nd then dds tuples form one reltion tht does not mtch tuples in the other reltion to the result of the join. Uses null vlues: null signifies tht the vlue is unknown or does not exist All comprisons involving null re (roughly speking) flse by definition. We shll study precise mening of comprisons with nulls lter 2.60

61 Outer Join Exmple Reltion lon lon_number brnch_nme L-70 Downtown L-230 Redwood L-260 Perryridge mount Reltion borrower customer_nme lon_number Jones L-70 Smith L-230 Hyes L

62 Outer Join Exmple Join lon borrower lon_number brnch_nme mount customer_nme L-70 Downtown 3000 Jones L-230 Redwood 4000 Smith Left Outer Join lon borrower lon_number brnch_nme mount L-70 Downtown 3000 L-230 Redwood 4000 L-260 Perryridge 700 customer_nme Jones Smith null 2.62

63 Outer Join Exmple Right Outer Join lon borrower lon_number brnch_nme mount customer_nme L-70 L-230 L-55 Downtown Redwood null null Jones Smith Hyes Full Outer Join lon borrower lon_number brnch_nme mount L-70 Downtown o 3000 L-230 Redwood 4000 L-260 Perryridge 700 L-55 null null customer_nme Jones Smith null Hyes 2.63

64 Null Vlues It is possible for tuples to hve null vlue, denoted by null, for some of their ttributes null signifies ifi n unknown vlue or tht t vlue does not exist. The result of ny rithmetic expression involving null is null. Aggregte functions simply ignore null vlues (s in SQL) For duplicte elimintion nd grouping, null is treted like ny other vlue, nd two nulls re ssumed to be the sme (s in SQL) 2.64

65 Null Vlues Comprisons with null vlues return the specil truth vlue: unknown If flse ws used insted of unknown, then not (A < 5) would not be equivlent to A>=5 Three-vlued logic using the truth vlue unknown: OR: (unknown or true) = true, (unknown or flse) = unknown (unknown or unknown) = unknown AND: (true nd unknown) = unknown, (flse nd unknown) = flse, (unknown nd unknown) = unknown NOT: (not unknown) = unknown In SQL PP is unknown evlutes to true if predicte P evlutes to unknown Result of select predicte is treted s flse if it evlutes to unknown 2.65

66 Modifiction of the Dtbse The content of the dtbse my be modified using the following opertions: Deletion Insertion Updting All these opertions re expressed using the ssignment opertor. 2.66

67 Deletion A delete request is expressed similrly to query, except insted of displying tuples to the user, the selected tuples re removed from the dtbse. Cn delete only whole tuples; cnnot delete vlues on only prticulr ttributes A deletion is expressed in reltionl lgebr by: r r E where r is reltion nd E is reltionl lgebr query. 2.67

68 Deletion Exmples Delete ll ccount records in the Perryridge brnch. ccount ccount σ brnch_nme = Perryridge (ccount ) Delete ll lon records with mount in the rnge of 0 to 50 lon lon σ mount 0 nd mount 50 (lon) Delete ll ccounts t brnches locted in Needhm. r σ brnch_city = Needhm (ccount brnch ) r 2 ccount_number, brnch_nme, blnce (r ) r 3 customer_nme, ccount_number (r 2 depositor) ccount ccount r 2 depositor depositor r

69 Insertion To insert dt into reltion, we either: specify tuple to be inserted write query whose result is set of tuples to be inserted in reltionl lgebr, n insertion is expressed by: r r E where r is reltion nd E is reltionl lgebr expression. The insertion of single tuple is expressed by letting E be constnt reltion contining one tuple. 2.69

70 Insertion Exmples Insert informtion in the dtbse specifying tht Smith hs $200 in ccount A-973 t the Perryridge brnch. ccount ccount {( A-973, Perryridge, 200)} depositor depositor {( Smith, A-973 )} Provide s gift for ll lon customers in the Perryridge brnch, $200 svings ccount. Let the lon number serve s the ccount number for the new svings ccount. r (σ brnch_nme = Perryridge (borrower lon)) ccount ccount lon_number, brnch_nme, 200 (r ) depositor depositor customer_nme, lon_number (r ) 2.70

71 Updting A mechnism to chnge vlue in tuple without chrging ll vlues in the tuple Use the generlized projection opertor to do this tsk r Ech F i is either F K (, 2 r F,, Fl, ) the I th ttribute of r, if the I th ttribute is not updted, or, if the ttribute is to be updted F i is n expression, involving only constnts nd the ttributes of r, which gives the new vlue for the ttribute 2.7

72 Updte Exmples Mke interest pyments by incresing ll blnces by 5 percent. ccount ccount_number, number brnch_nme, nme blnce * (ccount) Py ll ccounts with blnces over $0,000 6 percent interest nd py ll others 5 percent ccount ccount_number, brnch_nme, blnce *.06 (σ BAL > 0000 (ccount )) ccount_number, brnch_nme, blnce *.05 (σ BAL 0000 (ccount)) 2.72