Slide chương 6 PTTKGT
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Transcript of Slide chương 6 PTTKGT
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7/25/2019 Slide chng 6 PTTKGT
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Chng 6
Nhng bi tan NP-y
1. Gii thut thi gian a thc tt nh v khngtt nh
2. Vn NP-y
!. "nh #$ %&&k'. ()t *+ ,i t&n NP-y
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Tn ti hay khng tn ti gii thut hu hiu
"+i vi nhiu ,i t&n ch/ng ta c0 nhng gii thuthu hiu 3 gii.
4uy nhi5n6 c0 7t nhiu ,i t&n khc khng c0 gii
thut hu hiu 3 gii. V +i vi 8)t #9 kh #n ca nhng ,i t&n nh:
vy6 ch/ng ta khng th3 n0i c0 t;n t
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Nhng bi t!n kh " nhng bi t!n #$
Nhiu nghi5n cu = :>c th?c hin v c0 nhng c@ chA 39hBn #&
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%& 'ii thut th(i gian a th)* t+t ,nh " khngt+t ,nh
P 49 h>9 tt c nhng ,i t&n c0 th3 gii :>c ,Dngnhng gii thut tt nh t7&ng thi gian a thc&
.T+t ,nh/ 0Deterministic1 khi gii thut ang #8 g6cFng chW c0 8)t vic uy nht c0 th3 :>c th?c hin kAtiA9. XYhatZvZ7 thZ a#g&7ith8 i* &ing6 thZ7Z i* &n#y &nZthing it c&u# & nZt[.
4hI J \A9 th t? ,Dng 9h:@ng 9h9 ch]n thu)c #9 P v c0) 9hc t
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T2nh khng t+t ,nh
()t cch 3 8_ 7)ng `uyn nng ca 8y tInh # ch& n0 c0
nng #?c #8 vic khng tt nh Xn&n-ZtZ78ini*8[.Khng tt nh: khi 8)t gii thut gb9 8)t *? #?a chQngia nhiu kh nng6 n0 c0 `uyn nng Cti5n 0anE 3 ,iAtchQn 8)t kh nng thIch ng.
Gii thut khng tt nh Xn&nZtZ78ini*tic a#g&7ith8[4hI JK %h& # 8)t 8ng *+ nguy5n. ()t gii thut khng
tt nh NT^d4X6 n[ *e9 th t? cc *+ thZ& th t? tng vut ch/ng 7a thZ& th t? ny.
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Th2 #3 "4 5t gii thut khng t+t ,nh
// An array B is used as temporary array.
procedureN789T0:;n1t n ?=iti"@ int@g@>= int0B1F successend;
f8 choice(1:n)c0 kh
nng c nh 8)t v t7I/ng t7&ng t8 t7 tM 1 Ann.
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Th2 #3 "4 5t gii thut khng t+t ,nh 0tt&1
T? 9hBn gii 8)t gii thut khng tt nh c0 th3 :>cth?c hin ,Dng 8)t *? *&ng *&ng h0a khng hc th?c hin cng 8)t #/c.
- Rn *a& u ti5n kAt th/c thnh cng th #8 kAt th/ctt c cc `u t7nh tInh t0an khc.
- NAu 8)t ,n *a& kAt th/c tht ,
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'ii thut khng t+t ,nh 0tt&1
4ht 7a6 8)t 8y tInh khng tt nh khng tc nh ngha nh: # 8)t chui ngennht ca nhng #?a chQnXshortest sequence of choices)8jn An *? kAt th/c thnh cng.
47&ng t7:ng h>9 khng t;n t
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'ii thut khng t+t ,nh 0tt&1
Ghi ch#
%c thng ,& successvfailure# t:@ng :@ng vi9ht ,i3u stopt7&ng 8)t gii thut tt nh.
") 9hc t9 tt c nhng ,i t&n 8 c0 th3 :>c gii,Dng gii thut khng tt nh t7&ng thi gian athc.
4hI J K Ri t&n c0 t;n t
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Bi t!n thJa 5Kn 5*h Lgi* 0*i>*uit=ati=MiabiLity ?>bL@51
%h& 8)t cng thc #&gic c0
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& O+n 4 NP-y
%0 8)t anh *ch nhng ,i t&n 8 = ,iAt # thu)c v#9 NP nh:ng khng 7q c0 th3 thu)c v #9 P hay khng.X'c l# ta "i*i ch+n" d, d#n" tr-n m.t m& h!n" t/t 0nhnh2n" ch2a ai c th3 t4m th/& m.t "i*i thu5t h6u hi7u ch8&
tr-n m& tnh th!n" th29n" 03 "i*i b/t m.t b#i ton n#oc;a ch+n"[.
Nhng ,i t&n NP ny #c t7&ng thi gian a thc th tt cnhng ,i t&nthu)c #9 NP cFng *s :>c gii t7&ng thi gian a thct75n 8)t 8y tt nh.E
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Nhng ,i t&n nh: vy :>c gQi # nhng ,i t&n
NP-y XN
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T2nh kh thu gi5 a th)* 0PLyn5iaL>@#u*ibiLity1
p9 NP-y # #9 c&n ca nhng ,i t&n kh0 nhtt7&ng #9 NP.
%ng cJ chInh 3 chng 8inh 8)t ,i t&n thu)c #& Rt c gii thut n& gii :>c ,i t&n 8i thu)c #&c ng 3 gii 8)t ,i t&n NP-y n& 0= ,iAt,Dng cch *auK
bi?n th3 m.t th3 hi7n b/t c;a b#i ton N
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T2nh kh thu gi5 a th)* 0tt&1
"3 chng 8inh 8)t ,i t&n thu)c #&
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T2nh kh thu gi5 a th)* 0tt&1
"3 chng 8inh 8)t ,i t&n 8i p # NP-y 6
ch/ng ta cn chng 8inhK 1. Ri t&n p thu)c #9 NP
2. ()t ,i t&n NP-y = ,iAt thu gi8 v p.
4hI JK %h& hai ,i t&n Ri t&n ng:i th:@ng gia u hnh X4TP[K ch& 8)t t9 cc
thnh 9h+ v kh&ng cch gia 8i cb9 thnh 9h+6 t88)t #) t7nh i `ua tt c 8Qi thnh 9h+ *a& ch& tng
kh&ng cch ca #) t7nh nhO h@n (. Ri t&n chu t7nh fa8i#t&n Xf%P[K %h& 8)t ; th6 t8
8)t chu t7nh @n 8 i `ua tt c 8Qi Wnh.
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T2nh kh thu gi5 a th)* 0tt&1
Gi * ta ,iAt f%P #Nc ng3 gii ,i t&n 4TP cFng c0 th3 :>c ng 3 gii ,i t&n f%P6thng `ua *? thu gi8 *auK
%h& 8)t th3 hin ca ,i t&n f%P X8)t ; th[6 h=y t
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T2nh kh thu gi5 a th)* 0tt&1
Ngha # f%P thu "i*m FG4TP6 nh: vy tInh cht NP-y ca f%P h8 $ tInh cht tInh cht NP-y ca 4TP.
T? thu gi8 f%P v 4TP # @n gin v hai ,i t&n c0nhng not t:@ng t? nhau.
T? thu gi8 thi gian a thc c0 th3 *s 7t 9hc t
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1!
& Q,nh LR Ck
Nh:ngK Ri t&n n& # ,i t&n NP-y u ti5n
T.. %&&k X1x1[ = ut :>c 8)t chng 8inh t7?c tiA9u ti5n 7Dng ,i t&n thOa 8=n 8$
%hng 8inh ca %&&k 7t 9hc t
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S& t =U bi t!n NP-y
fng nghn ,i t&n khc nhau :>c ,iAt # NP-y .Lanh *ch ny ,et u ,Dng ,i t&n th& 8=n 8
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2$
=?p lch c!n" Fi7c tr-n 0a b. %O lP ( multiprocessor
schedulin")K %h& 8)t kr hcth?c thi t75n hai ,) #$. Vn # c0 th3 *e9 A9 3th?c thi tt c nhng cng tc 0 *a& ch& thOa 8=n krh
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P NP V
Nhng ,i t&n n5u t75n v nhiu ,i t&n #i5n `uan c0
nhng ng Jng th?c tA `uan t7Qng.
T? kin khng c0 nhng gii thut t+t :>c t8 thy ch&,t kr ,i t&n n& t7&ng *+ nhng ,i t&n n5u t75n #
8)t ,Dng chng 8
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t =U kW thut X Ui ?h "Yi nhng bit!n NP-y
%& Lng Cgii thut 9 WCXa997&i8ati&n a#g&7ith8[ 3t8 #i gii 9 W t+i :u XnZa7-&9ti8a#[.
2. L?a v& hiu nng ca t7:ng h>9 t7ung ,nh 3 9ht
t7i3n 8)t gii thut 8 t8 7a #i gii t7&ng 8)t *+ t7:ngh>9 n& 06 8bc khng #8 vic :>c t7&ng 8Qi t7:ngh>9.
!. T Jng nhng gii thut c0 ) 9hc t
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Z@u>i=ti* " 5@ta h@u>i=ti*
fZu7i*tic# t7i thc v ,i t&n cJ th3 :>c * Jng 3
jn et `u t7nh t8 7a #i gii ca gii thut. Nh *?th58 v& cc hZu7i*tic 8 gii thut t7_ n5n hu hiu h@n.
(Zta hZu7i*tic# #&
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Qng g? *a "+n 4 NP-y
%0 nhiu ,i t&n NP-y t7&ng cc #=nh v?c gii tIch *+ Xnu8Z7ica# ana#y*i*[6 *e9 th t? v t8 kiA86 #$ zng k$ t? X*t7ing 97&cZ**ing[6
( hnh h0a hnh hQc XgZ&8Zt7y 8&Z#ing[ #$ ; th Xg7a9h 97&cZ**ing[.
T? 0ng g09 uan t7Qng nht ca #$ thuyAt v NP-y #K
n cun" c/p m.t c\ ch? 03 %c 0nh m.t b#i ton mBi tron"cc lAnh F]c tr-n l# d,$ ha& h$>
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BUn LY? bi t!n ?h[n th@ kh
Nh6n" b#i ton b/t h* qu&?t (^ndecidable problems):"By# nhng ,i t&n ch:a h c0 gii thut 3 gii.
4hI JK Ri t&n `uyAt nh Z8 8)t ch:@ng t7nh c0 Mngt75n 8)t 8y 4u7ing.
Nh6n" b#i ton h "i*i (intractable) K By # nhng ,it&n 8 khng t;n t