Một số vấn đề đối với phụ thuộc kết nối. potx

Tro g bai bao nay se chtrng minh mot so tinh cMt ve S \ O suy d.1n cac JD tu: mot t~ phu thuoc cho tr uo'c v a trlnh bay tinh chfit d~c tru'n cua hro'cdo quan h cr d ang chua'n ch ieu-ke

Ti p chi Tin h9c va Di'eu khi€ tioc, T 17, S. 1 (2001), 89 - 96

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PRAM Q ANG TRUNG

Abstract Join depen ency (JD) and further n rmal forms play an important role in the theory of normalize

In this paper we prove new properties on JD implication from a given set of dependencies and presen t special

property of a relational scheme is in proje t-join n rmal form (PJNF

Tom t~t Ph u thuoc ket noi (join dependency - JD) va dang chuan b~c cao co vai tro quan tro g tro g

ly t huye t chuin h6a Tro g bai bao nay se chtrng minh mot so tinh cMt ve S \ O suy d.1n cac JD tu: mot t~

phu thuoc cho tr uo'c v a trlnh bay tinh chfit d~c tru'n cua hro'cdo quan h cr d ang chua'n ch ieu-ket noi (project-join normal form -PJNF)

1 MO'DAU Cac ky hi~u: Quan h~ R tr en t~p thuoc tinh U diro'c ki hieu la R(U), h91> cua hai t~p thuoc tfnh

Phan nay chi neu mi?t so kh ai niern va ket qua lien quan,ban d9C quan tam chi tiet hcm de nghi xem [ 2-5 ].

D!nh nghia 1 Cho R(Al , A2, ,An) la mot hro'c do quan h~, cho X va Y la cac t~p con cua

{Ai, A2, , An} · Chung ta noi X -+ Y (d9Cla "X xtic i1.inh ham Y" hay " Y ph.u thuqc ham va o X")

neu vo'i moi quan h~r la the' hien cua R, thl tron r khong the' co hai bi?tr ung nhau ten cac thanh

p an ciia moi thuoc tinh tro g t~p X m a lai khcng tr img nhau tren mdt hay nhicu hem cac thanh phan cua c c thuoc tinh cua t~p ho-p Y

- Quan h~ r th6a ph", thuoc ham (functional dependency - FD) X -+ Y , neu vo'i moi c~p bi?1-'-,v

tro g r sao cho I-'- [ X ] = v[ X ] thll-'-[Y] = v [ Y ] cling dung Neu r khcng tho a X - + Y , thl r vi ph am

phu thuoc do

- Ch F la t~p ph", thuoc ham cu a hroc do quan h~ R v a cho X -+ Y la mot ph", thuoc ham Chung ta noi F s uy dt e n l o gic ra X -+ Y , viet la F FX -+ Y , neu voi moi quan h~ r cua R ma thoa

cac ph", thuoc ham trong F thl cling thoa man X -+ Y

D!nh nghia 2 Bao do g cuat~p ph", thuoc ham F , ky hieu la F + , la t~p cac ph", thuoc ham dtroc suy dien logic ti F , n hia la: F = {X -+ YI F F X - + V}

D!nh nghia 3 Cho hro'c do quan h~ R voi t~p ph", th uoc ham F, ch X la m<?t t~p con cua R,

t~p X dU'9"Cgoi la kh6 a (key) cu a hro'c do quan h~ R neu: 1) X - + R E F +; 2) Vo'i \l Y c X thl

Y =r » R Tap X neu chi thoa man dieu kien 1) neu tren d o'c goi la mot sieu kh6a (superkey) Cac

k oa (hay sieu kho a] diroc li~t ke ro r ang cling vo'i hro'c do quan h~ du'oc goi la cac kh 6a duo c c h i

ilinh (designated key)

D!nh nghia 4 Hai t~p ph", thuoc ham F va G tren hroc d R la tu a r u ; d ua n q (equivalent), k h ieu

la F == G, neu F + = G + Neu F == G thi F la m9t phd (cover) cu a G

Ph", thuoc ham X -+ Y E F la du o thu:a neu F - {X - + Y} FX - + Y

Dirih nghia 5 Hai t~p thuoc tinh X va Y la iu ru; d o tu; vo inhau tr en t~p ph", thuoc ham F,

neu F F X - + Y va F FY - + X (ky hi~u litX < > V)

Dlrih nghia 6 Phs; ih uo c ham phsic hop (compound functonal dependency - CFD) co dang

(Xl , X2, , X k ) -+ Y , trong do X l X2 " X k va Y la cac t~p con khac nhau cua hro c do R.

Quan h~ r(R ) tho a phu thuoc ham ph u'c hop ( X l X 2, , X k ) Y neu n thoa cac phu thuoc ham

X i + XJ v a Xi + Y , v i 1 ::; i , J ::; k Trong phu thuoc ham plnrc hop nay, ( X I ,X 2, ,X k) du'o c

g i la ve t.i ,X l, X 2 , , X k la cac tap t ai, Y la ve ph ai

CFD la cach viet rut g9n hori t%p cac pliu thuoc ham co cac ve trai tuong du'o'ng Trong 'tru'o'ng

h p neu Y = 0, co d ang d~c biet cu a CF D la (Xl , X 2, ,Xd

Dirih nghia 7 Tfip F duo cgoi la ph d ct aG IH:UF : = G, trong do F v a G bao gom hoac la tap cac

p h u th uoc ham, t%p cac ph u th uoc ham ph uc hop, hoac la t~p hop chi gom mot lo ai phu th uoc D~nh nghia 8 Tfip ph u thuoc ham F d o'c g i la t ¢ a c i rut iq (characteristic set) doi voi phu

th oc ham ph ire h 1J (X I, X 2, , X k) + Y , ne u F := {(Xj, X2, , Xd + Y} Neu m6it%p ho'p tr ai

cu a phu thuoc ham phirc hop dU'9'Csuodung V01tu' each la ve tr ai cua phu thuoc ham dung mot ran (nghia la F co dan {X l + Y j, X2 + Y 2, , X k + Yd ) th] F dtro'c goi la tiip di i c truru ; t l! nh ve n

(natural characteristic set) doi V01 hu thucc ham plnrc h 1J da cho

Dirih nghia 9 Tap phu t.hudc ham ph trc hap F duoc goi la da i iq va n (annular)' neu kho g co cac tap t ai X v a Z trong cac ve tr ai khac nhau, ma X +-+ Z tr en F

D~nh nghia 10 Ch hro c do quan he R V01 tap ph u thuoc ham F Cho tap th uoc tinh: X ~ R,

thucc tin h A E R Ta n i th uoc tfnh A ph u th uoc bd c ciiu ( ansiively dependent vao X tr en R neu ton tai Y ~ R sao cho X + Y v a Y + A nlurng Y = r + X voi A r/: XY

Djnh n hia 11 M9t hroc do quan h~ R voitap phu thuoc ham F du'oc goi la o ·d ng chu a' n thu ' b

(third normal form - 3NF) neu kho g co thuoc tfnh kho g kho a phu thuoc bic cau vao khoa cu a R

M9t hro'c do C O" so' dii"li~ R la o·d ang chuin thir ba neu rnoi luoc do quan h~ tron R la o·3N F

Cho luo c do R v a t~p phu thuoc ham F Phep uich mot lu oc ao quan h~ la viec thay the mot IU'q'Cdo R bang t%p cac lu'o:c do con p= {RI' R2, R d [c ac R ; kho g nhfit thiet phai r01 nhau) sao

cho: a) R; ~ R, i = 1,2, ,k ; b) R = R 1 R2 · Rk.

- Cho hro'c do quan he R Phep tach p la ph.ep uic t co k t noi k h ong mat th o g tin (lossless join decomposition) neu voimoi q an he r tr en R m a tho a F , ta co: r = 7rR , ( * 7rR2( * * 7rRk (r).

Tire la quan h~ r Ia ket noi tu:nhien cu a cac hinh chieu cu a r t en c c R i

- Phep tach p = { RI ' R 2, , Rd d oc goi la phep tac h bdo to an ( pr e e ve) u ip phs : thu qc F , neu:

p = 7 r R , (F) U7rR2 (F) U Ur » , (F) suy dan ra F ( o g do: =«. = {X + Y E F IX, Y ~ R;}).

Co hai ky thuat chinh M chuiin hoa hroc do q an he b~ g viec tach (decomposition) la ph ep ph.iin Lich (analysis) va p ep t5ng ho p (synthesis)

• Chuiin hoa b ng phep phan tfch

Voi di,ctrung chinh d am bao tieu chuin tin h ket n i khorig mat th ng tin cua cac hroc do thanh

ph an la ky th uat thong dung d chdn ho a lu'oc do quan he V0 c c dang chufin khac nhau Neu mot hroc do quan h~ khong tho a dang ch ufn mo g muon VImot phu thuoc n ao do thl no du'o'c tach

th anh hai hoac mot so cac hroc do quan h~ can cir v ao phu th uoc nay Meii mot IU"<?,cdo du'o'ctach Lhua huong cac rang buoc thich hop Viec tach du'o'cl~p lai cho den khi tat d cac ltro'c do da d u'o'c chuiin hoa

• Chuiin hoa 3NF bKng phep t&ng h01> (normalization throu h synthesis)

Ph an nay chi giai t.hieu p ep t&n hop suodung ph u dang vanh

Quy uoc: Ky h ieu R = { R I' R 2, R d la t%phroc do quan h~ nhan dtroc bo-imot thuat toan chuS:n hoa

'I'h uat t.oan TH-3NF

MOT SO AN DE DO! PHU THU C Klh NO! DANG CHUAN CRIEU - Klh NO!

RA: T~p hroc do quan h~0' dang chuitn ba, bao toan F , c6 Ht noi khong mat thOng tin, c6 so hro'ng

hro'c do Ii it nhfit

PHU'O'NG PHAp:

1) B5 sung th uoc ham U + @ VaG t~p ph u thuoc ham F (trong d @ la ten "th uoc tinh gia"

khorig th uoc U ) , Rut gon ve trai cua cac phu thuoc ham, LO,!-ibo cac phu th uoc ham dtr thira Ket

qu a cua burrc nay n hfin d o c t~p F ' ,

2) Tao tap phu d ang vanh G doi voiF',

3) Tuo q.p ph u thuoc ham di.c trung tv.'nhien G1 tu'o g dtro'ng voi t~p G, G9i G2 Ii t~p G1

dil duo c rut g<;lI1ve phd.i

tong G 3 , xfiy dU11ghroc do qu an he co tap thuoc tinh la tat d c c thuoc tinh xuft hi~ tong m5i

phu thuoc ham plurc 11O'p,tap cac khoa chi din h cuam6i hro'c do tu ' cn irng la bao gom c ac t%ptr ai

cua m6i phu thuoc ham ph ire hQ1>,

5) Ket qua lit t%p hro c do duo c xay dung & buoc 4), Thuoc tinli gi.i @ duoc IO,!-ikhoi hro'c do clnra @ ,

D1nh ly 1 1 ] L uo:c ao CO' sd - du; L i~u R = (R l R 2, " Rk) d oc to' n g h op bl £ g T h u i t o t n : TH- !JN F

t u ' t a cac ph1f th uq c ham F th6a man cdc iinh chat s a u aa y:

1) Doi VO'2 moi LtCO'cao bat kif R, thuqc R , moi kh6 a c hi a inh c d a R, La mot kho a

2) Luo: c a C O ' s d - du ; Li e u R b o to an u i p i h uo c ha m F ,

3 ) L uo : c ao CO ' s d du; L ieu R bao g m c ac lu o : c ao t h an h : p a La d' dq,ng c hu ii' n b a.

5) NgOa2 ra , khong ton toi luo: c a o CO ' sd - dil: li e u nao klu i c co s olu ' O ' ng lu o c a o c on it h o n tlui a

Djnh nghia 12, Cho R la mot hro'c doqu an h~, cho X vi Y la cac tap can cu a R , vaZ = R - (X Y) ,

Quan he r (R) tho a p h t h qc i a ir i [mu rtivalued dependency - MVD) X + - t Y neu vo'i hai b bat

t 3 (Z) =t 2(Z),

Dirrh ly 2, 1 ] Cho r la mot quan he t r in l u oc ao R , va cho X , Y v a Z Ld cdc u ip co n c i i a R ma

Z = R - (X Y) Q uan he r t ho a phu t iuo c da t r i X - + - + Y n eu v a c h i n e u r t ac h co k et k h ng mat

th o ng tin tl ui nh ca e luo: c ao qu an h e R1= X Y va R 2 = X Z

D1nh ly 3, IS] Cho R La mot lu o:c ao q an he va p = (R 1' R2) L a p h e p tac h R C h o L; La tqp ph u

Dirrh nghia 13, Cho R = { R1' R 2, R , } la mdt t~p IU'Q'cdo quan h~ ten U , M9t quan h~ r(R)

th a phu t h uo c k t no i (JD) * I R 1 ' R 2, " R,, ] neu r duoc tach co Ht noi kho g mat thOng tin thanh

R1 , R 2, " RI " Tu'c la: r = 7rR, (r) *7rR2 ( r ) * , *7rR" ( r ) ,

Ta cling viet * I R1 ' R - 2, " Rl']la * I R ],

Dieu kien can de' mot quan h~ r( ) thoa JD * I R 1 ' R 2, "Rp]a U = R1 R 2 , R ", MVD la mot tru'on h p rieng cu a JD, Mot qnan h r(R) thoa MV X - + - + Y neu v a chi neu r du'o'c tach co

Mot JD * I R 1 ' R 2 , "R,,]la tam t ii u o r u; neu moiq an he r ( R ) deu tho a no, Mot JD * I R 1' R2 , " R, , ]

I tip durcq i iuo c vao hro cd quan h~R neu R = R 1 R2 , R" ,

ket noi tren R Lu'oc do quan h~ R la ( y dang churin c h ieu - kt t no i (P JNF) neu doi voi moi JD

* [ R1, R 2 , , RI '] su din tu:L; v ap d ung diroc vao R , thl JD do la tam th iro g hoac moi R, la mdt

sieu khoa doi voi R M9t hro'c do CO" so dir lieu R la 6' P JNF doi vo'i L; neu moi hro'c do quan h~ R

thuoc R la d P JNF doi voiL;.

B cl ng (tableau)

M9t bdng la mot ma tr~ gom t~p cac dong Moi cot tro g bin t,U'011gtrng v i mot thucc tfrih

trong R Moi dong gom cac bien duoc viet ra ti tap V , la h -p phan bi~t cua hai t~p Vd v a Vn: a)

Vd la t~p cac bi e n iluoc dtinh dau (distinguished variable - dv)' mot bien irng voi moi th uoc tinh:

neu A Ia mot thuoc tinh diro'c xet , thi V la mot dv tU'011g irng b) Vn la t~p cac bien kh oru ; duo : « aanh dau (nondistinguished variable - ndv): ky hi~u la n1 , n 2, n k,

M9t bien bat ky bi h an che x at hien n hieu nhfit tro g mot C9t, rnot bien duo c danh dau phai xufit hien tro g moi cot, va tro g m9t C9t chi co th€ co mot bien d arih dau

to g d m(A) , trong do A la C9t ma bien xufit hie n trong do Day la S ·mo: rorig ham tir bing

T t&i mot quan h~ tren R nhu sau, neu w = ( V1 , V 2, , V r ) la rnct dong cti a T, thl p ( w ) la b9

(p ( v t p ( V2 ) , , p (v,,) ) v a p (T) = {p ( w ) Iw la mot dong trong T}

Cho L ; la t~p cac MVD va FD [rnot, MVD bat ky duoc th~ hien nhu mot JD) Sa n au o' i (hay

theo doi - chase) la ket qui cd a viec ap clung cac phep bien d5i sau day v ao bin T ch den khi

khong co th lam bien d5i them:

• F-qui tic (F-rule): VO'i moi FD - >A trong L; ,c6 mot F- qui tiic bien d5i bang n h u sau Gii sti:

bang T co c ac dong W1 va W2, tro g d6 w d X ) = W2 [ X ] va ch Vj = wd A ] va / 12= w2 [ A ] Neu

V 1 ho ac V 2 la bien duoc d anh dfiu va cai kia thl kho g , thi bien khorig du'oc danh dau du'cc d i

th anh bien diroc dan h dau Neu d hai la cac bien khorig du'cc danh dau, thl bien c6 chi so

diroi lon h011 duoc thay bhg bien co chi so d u'oi n ho h 11

• lqui tiic (l-rule): Cho * [ R j , R 2, , R p ) la mot 1D to g L;. Neu co mot d ng w sao cho

W [ R1 ) E T [ R 1 ] , , w [ R p ] E T [ R I'] , w dtro'c b5 sung vao T

K y hieu chasedT) la bang ket qua nhan dtro'c tir viec ap dung F-qui tic v a l-qui tiic doi voi

moi phu thuoc trong L; cho den khi khOng co thg thay d5i them bing duoc niia Co th~ chirng t6

r~n [ 3 ) chase luon ket th uc va bin ket qui la duy nhat, kho g phu thuoc vao th ir tl).·ap dung cac qui ute d€ d t lai ten cho cac bien khorig dtro'c d an h d au

c d a U, vO'i U j U2 " ,U m = U C h T La mot bdng tren U , uoi r r i do ng S S2 "", S r n, t ron g ao vO' i moi

k h ong mat th o g t n i O i v 6 - i U1, U2, U m khi va chi khi bdng ch ase F(T) co mot dong g o m toan bq

cac dv.

2 MQT SO VAN DE DOl VOl JD vA PJNF

Luu y la 6' day khong xet truong h p cac hroc do quan h~chi c6cac phu thuoc ham tam thU'011g

v a cac phu thuoc da tri, ;va 6'muc nay kh ai niern khoa chi dinh co cling mot Y nghia nhir doi voi

cac hrcc d CO " s6' dir li~u 6'3 N F

2.1 Mot van de d t ra la: co ph irong ph ap n ao d~ suy d5.n cac ph u thuoc ket noi tir t~p cac phu

t.huoc cho tru 'c hay khong? Duo g nh ien la co thg b5.ng each ap dung H~ tien de cho t~p cac phI)

thu9C [ 3, 5 ] n hia la pHi tfnh toan bao dong ctia tap phI) thu9c di.cho Ly thuyet ve Bing va Chase

MOT SO VAN D E D o r VO l PH { ,TT H UOC K l h No r vA DANG CH AN CHIEU - K l h Nor 9

d u'oc dung lam cong C\ ! de' kiifm tra m9t phan tach la co ket noi khOng mat thon tin hay khOng,

cling de' kiifm tra tin h dung dan cu a cac dan xufit ph u thuoc tir m9t t~p phu thuoc cho truo'c, nhirng

cling chi dioc st'dung dif kiifm tra clnr khcng phai la corig C\! dif du'a ra cac dan xuat

Nh u dii thay, viec nghien cU'Uvan de phan tach IU'<?,doc quan h~ dong vai tr quan tron tro g

de 1va B5 de 2sau day trlnh bay phiron ph ap tao phu thuoc ket n i tir ket qua ciiacac thuat toan chuiin h a

Merih de 1 Cho luo:c a D quan h~ R vO'i t4p ph ' l!- th uo c L:, Gt ' d s J: R = {R 1 , R2, " Rd 10,l u o: c aD

tw Thi phu th uo c kE t noi : * i Rl , R 2, , Rk) la tip d ' l!-ng iluo c vao luo:c aD R.

Ghu ' ng minh, Voi R la hro c do CO' so' d irIieu ket qua cua t.huat to an chuin ho a c6 t.inh chat ket noi

ciia cac hroc do quan h~ thanh phan (Rl *R2 * , *R d la khong mat thong tin va R = R 1 R2 Ri:

Do do phu th uoc ket noi *i Rj, R2, " Rk) la ap dung dtroc VaG R , 0

Thi du 1 Ch hroc do quan h~ R = A B GD E H I va t~p ph u th uoc I: = { A + B GH , B CH +

A , B CHI + E , E - > B H , EB + C},

Thu'c h ien tllU~t toan t5ng ho'p doi voi cac phu th oc ham cu a L: , truo'ng hop Sl\: dung ph u dang

vanh: G= { ( A , B CH) , (B CH 1) + E , (E ) + B H} , va ket ho'p vo'i hro:c do th anh ph an k 6a de'

dam bao t.inhchfit ket n i khorig mat thong tin: neu su'd ung hro'c do kh6a A D I , thl nhan dtro'c IU'<!c

doCO 'so'dirleu ket qua la R = { A B CH , B CE H I , BE H , AD I}, Theo Menh de 1p u thudc ket noi * ! A B C H , B CE HI , BE H , A D I ) la ap d ung dtro'c vao R ; co neu ket hop vo ilu'o'c do khoa

C D E I , thl n han duoc luoc do CO's& d irlieu ket qu a la R = {A B C H , B C E H I , BE H, CDEI} ,

vi theo Merih de 1 c6 phu thuoc ket noi * i A B CH , B CE HI , BE H, C D E I la ap dung duo'c

v ao R

Truo ng hops11'dung ph u dang vanh: G' = { (A, B C H) , (A 1) + E , (E ) + B H} va ket hC!P

v 'i hro'c d th anh phan khoa d€ darn bao t inh chat ket noi k orig mat thong tn thl cac phu th ucc

ket noi * i A B C H , B GE HI , BE H , A D I va * i A B C H, B GE H I , B H , GDEI ) 111ap dung

d uo c VaG R

Co th bing cac phep ph an tich-ket noi khong mat thOng tin lien tiep doi VOlt~p I: gom c ac

ph u thuoc him va p u thuoc da tri d~ nhan duo c cac ph u thuoc ket n i, nhung khOng luon lucn

nhfin d 'cc moi p u thucc ket noi co the' co doi voi luoc do quan h R bat ky,co nhirng truong hC!P

mot quan he co the' c6 phep tach- ket noi khcn mat th ng tin khorig tam th tro'n [khcng c6 hro'c do

chieu tr ung voi R ) thanh ba hro'c do, m a khorig co phep tach nhir v~y thanh chi mdt cap cac hro'c

do Thid 2 111m.9t minh ho a cv th€ cho dieu khin din h nay, phu thucc ket noi * i A B, AC, BC]

khorig thif n an duoc bing cach ap dung phep phan t.ich lien tiep tren hroc do quan h~r(A B C)

Thi du 2 Quan he r( A B G) tong Hinh 1 duo'c tach co ket noi khcng mat thong tin thanh c ac

luoc do quan h~ A B, A G va BG. Cac hinh chieu d uo'c th€ hi~n trong Hlnh 2

Quan he r nay khong tho a cac ph u th uoc da tri khorig tam thu'o g ,nen khong co phep tach-kdt

n i kho g mat th ng tin r thanh chi mot c~p cac hro'c do quan h~ R l va R 2 m a R j = f ABC va

R2 = f A B G

a" b " c"

PHAM QUANG TRUNG

'TrA I J ( r) A B ' Tr A!; (r) = ~A~~C ' TrI J d r) = ~ B ~~C

H i nh 2

n8 de 2 C ho lu o:c a qu an h R V O 'j tap p hu th uo c 2 N e u t p d ng t h u i it io t r i to - Jng h op sJ:

du ng ph s l d ng u anh VaG R v a n l uin i l uo: c lu o c ao CO' s d - d ii L ieu R c i c d y nh mot lu o :c ao

quan h~ tlu i r h phi i : ( k h i~ u R = { R ~} du o:c hinh i u i nh tv: p h thuqc ham p hu c hop duy n l ui t ( X I , X2, "Xk ) + Y Thi tuo r u ; u : n vo i phu th uo c ha m phuc hop n ay, cdc p hu t h uqc k t n o i co

dan g * I R I , R 2 , " R k l L a t p d ' l!ng d uo : c V aG R , t r o ng ao : u:n g vO ' mot chi so t (vo ' 1 <S;t <S;k ) , t h i

n; = x , x , ( VO 'j 1 <S;I <S;k - 1, J i = t , 1 <S;) < ;k) va s ; =x , v.

C hs i r u ; m i n Theo cach tao ph u thuoc ket n i rieu to g Bc5de 2: irng v i mot chi so t (1 <S;t < ;k ) ,

thi R, = X t X ] [v i 1 <S; i <S;k - 1,) i = t, 1 <S; <S;k ) va R k = X t Y , va co R = R I R 2 Ri ; B6i vi

X t, X , la khoa cua R , va ciing la khoa cua cac R ; [vo'i moi i, moi J ) ' moi R; la.mot sieu khoa, thi

tat cd.cac hinh chieu cua qu an h~ r(R) t en cac R ; se co cling so hro'rg cac bo nlnr r , Them nil-ala,

ca R , gion nhau tre kho a X , uen neu ap dung F-qui tic VaG ban T d 'oc xfiy dung theo Dinh

ly 4, se co mot d n gom to an bo d v, do do ket noi: r = ' Tr n l (r) * 'Tr n 2 (r) * *'Trn k (r) la.khOn mat

th ng tin,

Vi vay ket luan d oc r5.n , cac ph u thuoc ket nai co dang *I RI , R 2, " R k l the e ch xay d u'n

tron Bc5 e 2 Ia.ap dung d uo c VaGR, D

Thi du 3 Ch IU'<?,cdo qu an he gom ti).p cac th uoc tinh R = AI A 2 A 3 A 4 A " A G va ti).p phu thuoc

F = {AI + A 2 A 3 A G, A 2 + A 3 A 4, A 3 + A 4 A " , A " + A l A 4 } ,

Luo c do CO ' so' diiIieu ket qui cua vie ap dung thufit to an t6 g h 'p stl: dung phu d ang vanh la

R = { AI A 2 A 3 A 4 A " Ad , hinh thanh tu: phu th uoc ham phtrc ho'p: (AI , A 2 , A 3 , A ,, ) + A 4 A G ,

Can cu VaG Be)de 2, cac phu thuoc Ht noi ap dung d uoc VaGRia: *[AI A 2 , Al A 3 , Al A " ,

Al A 4 A G ) * I A I A 2 , A 2 A 3 , A 2 A " , A 2 A 4 A G ) , * I AI A 3 , A 2 A 3 , A 3 A A 3 A 4 A G i v a * I A I A " , A 2 A " ,

A 3 A " , A 4 A " AG I

Han che c a viec suy dan phu th uoc ket nai ban tep can phfintich - ket n i mat th n tin da

du'oc minh hoa boi Thi du 2 tren day, Can tiep can t6ng hop cling khorig cho phep trong truo'ng

ho'p t6ng quat co the' suy din ra moi p hu th uoc Ht nai, vi n hu dii biet, phep t6ng hop chi rip dung

tren cac ph u t.huoc ham,

Tuy yay, v i Men de 1 va Bc5de 2 ta co phiro-n p ap dan x fit cac phu t.h oc ket nai tir ket

qua cii a viec ap dung th uat toan chu5n hoa, la van de khac voi Be)de 1 va Dinh ly 4 chi cho phep

kie'm tr a tinh dung din ciia cac din xufit

2.2 Khac v 'i cac dang chu5n: 3NF, BCNF va 4NF, kho g ph a i moi hroc do quan h~ bat ky R v i

ti).p ph thuoc 2:deu co the' churn ho a than h PJNF,

Thi du 4 Ch hroc d quan h R = A B I B 2 CI C2 DE I 1 1 J va ti).p2::

{ A + BIB2C I C 2 DEI I 2 hJ ,

B I B 2 C I A C2 DEI I 2 hJ , B I B 2C2 A CI DEI I 2 hJ ,

E + I h h, CI D + J , C2 D + J ,

1 1 + 1 , 1 t , + I , I h + 1 2, BI B 2 1 - + CI C2 D},

Ap dung t.huf toan t6ng hop su dung ph u dang van h , n h an dtroc hroc do CO' so' duoli~u ket qua

la R = {RI , R R 3 , R Rd , tro g do:

M(lT SO VAN DE DO! VOl PHU THU C KET NO! VA DANG CIIUAN CHIEU-KET N ! 95

R I = A B I B 2 C I C2 D E ; v 'i cac kh6a chi dinh KI = {A , B I B 2CI, B I B 2 C 2 }

R 2 =E 1 1 1 ; voi kh6a chi dirih K 2 = {E}

R 3 = CI D J ; voi kh6a chi dinh K 3= { C J D }

R 4 = C2 D J ; v i kh6a chi dinh K4= { C 2 D}

R " = [ Iz 13 ; v ic ac kh6a chi dinh K " = {II 12, Iz h ,I h }

Luo'c d R khorig Ii a P JNF VI theo Men de 1thl phu th oc ket n i

* [ A e,B 2 Cl C2 D E , E II Iz, Cl D J , C2 D J , 111 2h I Ii ap d u ng du'o c vao R , tro g d c6 hro c d

than h p an A B , B 2Cl C2 DEl i sieu kh6a ctia R , nhirng cc luo'c do thanh phfin E I J 1 2, CI D J ,

C2D J va I Iz 1 k hong ph ai Ia cac sieu kh6a cu a R,

V6-i tep can ph irong phap t6n h p, Cl!the' Ia phep t6n h p su dung phu dang vanh ta phat

hien mot tin h chat dic trung cua 1 -phro c d quan he 0' PJNF,

nO'de 3 C h Iuoc ao quan h e R v o 'i tap ph u thuoc B, N e u lu o :c ao qu an he R l a d PJN F t h i kh i

ap dung th iu i to dn to'ng hop s : d,!!ng phJ dq,ng »anh vao R va nlu i n d wo : c lu o:c ao CO' s 6 ' d ii: l ~ R thi: R c hi c o duy nhat mot lu o : c ao q an h e iluinh phan (k y ht e u R = {R~} duo:c hinh h ta nh t u : p u

th uo c h am p u;e h op duy nh a t (X l, X2 , " X k ) - + Y

Ch iin q min h, Cd, su 1110'cd C ' so' dir lieu R c6 h n rnot luo'c do quan he than h phen, ttrc R = {R' l R ~, " R : /} , v i q 2 ' 2,

1~ ] ~ q ) th uoc R = {R~ , R ~ , " R:J c6 the' d uo'c ky h ieu nhu' sau:

- Lu'oc do than h phfin R : = K l K ; " , K ;' i v- , v i c ac kh6a chi dinh K i = { K ~ , K " , K ; J , va

- Lu'O'Cd than h phfin R ~= K i K ~ " , K :'J y J; v 'i cac kh6a chi dirih K J = {K i, K ~, " K :;J } ,va

y la ve trai cua phu th uoc ham ph ire ho'p th ir J ,

VI cac R ; v a R ~ la hai luo'c d than h phan d o c huih than h tir viec p an hoach tap B, nen

k ho g the' c6 su: tuo'n d uo g giiia cac luoc do than h phfin: R : + - R ~ [voi moi i moi ], Boi VI neu

c6 su tu n d 'o g n hu vay, thl d K : la kh6a ct a R : [voi moi i moi t) c6 K ; + - R : con K I, la

kh6a cua R ~[v i moi l ,moi h) c6 K I + - R ~,se c6 su tu 'ng du'o g giiia c c t~p trai K : + - K I, [v i

ham ph ire 11O'p, Tuc la c ac R; v a R ; kho g la h ai luoc do th anh p an duoc hinh th anh tir viec phan

ho ach tap B,

Nh ung neu k hong c6 S1:l ' tu'o'ng d cn g iira c ac hro c do th anh phfin: R: + - R~ [vo'i rnoi i moi

J ) ' thi c ac R: va R~k hong the' cling Ii sieu khoa cii a R, Nghia la phu thuoc Ht n i * [R~ , R ~, " R~1

B6 de 3 neu tin h chat di).c trung cua luo'c do quan h~ 0'PJNF vi la dieu k ien can, Nhu dil p an

t ch, uoc d R tron Th i du 4 vi pham dieu k ien n eu trong B6 de 3va k ho g la 0' PJNF,

B = {AI - + A 2 A 3 A G , A 2 - + A 3 A 4, A 3 - + A 4 A ", A " - + Al A4, *[Al A2, Al A 3, Al A ", Al A 4 AGj

* [ A j A 2 , A 2 A 3 , A 2 A ", A 2 A 4 A G) *[Al A 3 , A 2 A 3 , A 3 A ", A 3 A4 A G ) *[AI A ", A 2 A " , A 3 A ", A 4 A "

Thf d1 , 1 5 sau day,

Thf du 5 Ch hroc do quan h R = A BC D E v a tap phu th oc B = {A - + B C E , B C E + AD ,

Mac du hroc d CO' so' d ir lieu Ht q a cua viec ap dung thuat toan t6n h p su' dung ph u dan

v an h la R = {A BC D E } , hin h than h tli' phu thuoc ham plurc h p duy n St: ( A , B C E ) D , theo

Nluin b(iing a y 12 - 7- 2 000 Ntuin Lai s au khi s da ngay 19 - 2- 2 001

B5 d 2, cac phu thuoc kte;t noi a dung dtro'c vao RIa: * [ A B e E , A D ] v * [ A BeE, B C D E ]

Nhung ro rang hro'c d R dii c o khorig la o' PJNF

[1] Atzeni P., De Anton llis V R e l atio n l D a t a ba se Th eo r , The Benjamin/Cummings Publishing

Company, 1993

[3] Maier D Medelzon A.O and Sagiv Y., Testing implicatio s of data d p nde cies, A C M

[4] Pham Quang Trung, Nguyen Xua Hu , Thuat toin t5n h 'p jU" < !C do CO" so' dir lieu qua h~ dang chuiln ba, T ap chi T in ho c va D ieu k hi e "' n hoc 16 (2) (2000) 4 -5

[5] Ullman J.D., Pnnciple s o f Databa s S y t e m s, 2nd edition, Computer Science Press, 1982

V~ e n K i e "' m s at n ii n d i n t oi cao