4.pdf

&RPSXWDWLRQDO&RPSOH[LW\
KDUG
HDV\
&RPSXWDWLRQDO&RPSOH[LW\
‡ ³LQWUDFWDEOH´
‡ XQOLNHO\WKDWSRO\QRPLDO
WLPHDOJRULWKPV H[LVW
13 KDUG
3RO\QRPLDOO\
VROYDEOH
‡ HIILFLHQWSRO\QRPLDOWLPH
DOJRULWKPV H[LVW
5XQQLQJWLPHLVERXQGHGE\DSRO\QRPLDOLQLQSXWVL]H
&Q
2Q WKHQXPEHURIVWHSVJURZVDV
2QP WKHQXPEHURIVWHSVJURZVDV &QP
2QORJQ WKHQXPEHURIVWHSVJURZVDV&QORJQ
&RPSXWDWLRQDO&RPSOH[LW\
3__&PD[
13 KDUG
3RO\QRPLDOO\
VROYDEOH
__&PD[
&RPSXWDWLRQDO&RPSOH[LW\
13 KDUG
"
3RO\QRPLDOO\
VROYDEOH
&RPSXWDWLRQDO&RPSOH[LW\
3
‡ HIILFLHQWSRO\QRPLDO
WLPHDOJRULWKPV H[LVW
13KDUG
‡ ³LQWUDFWDEOH´
‡ XQOLNHO\WKDWDSRO\QRPLDO
WLPHDOJRULWKPH[LVWV
/LYLQJZLWK13KDUG3UREOHPV
6FKHGXOLQJ
$OJRULWKPV
([DFW
$OJRULWKPV
$SSUR[LPDWLRQ
$OJRULWKPV
)LQGRSWLPDO
VROXWLRQV
'LVSDWFKLQJUXOHV
IRUµHDV\¶SUREOHPV
+HXULVWLF
$OJRULWKPV
)DVWSHUIRUPDQFHLV
YHULILHGDQDO\WLFDOO\
)DVWVORZ
SHUIRUPDQFHLVYHULILHGE\
FRPSXWDWLRQDOH[SHULPHQWV
%UDQFKDQGERXQG
IRUµKDUG¶SUREOHPV
)DVWOLNH637UXOHWR
VROYH__&M
0D\WDNHORQJRIWHQVXLWDEOH
IRUVPDOOSUREOHPVRQO\
3UREOHP_UM _Σ&M
_UM _Σ&M
13 KDUG
3RO\QRPLDOO\
VROYDEOH
__Σ&M
_UM3PWQ_Σ&M
_UM 3PWQ_Σ&M
6537
6FKUDJH
DQG _UM _Σ&M
DSSUR[LPDWLRQ
3KLOLSV6WHLQ:HLQ
$OJRULWKP$ PRGLILFDWLRQRIWKH6537DOJRULWKP
6ROYHWKHSUHHPSWLYHYHUVLRQRIWKHSUREOHPXVLQJ6537UXOH
6HTXHQFH WKH MREV QRQSUHHPSWLYHO\ LQ WKH RUGHU WKDW WKH\
FRPSOHWHLQWKHVROXWLRQRIWKHSUHHPSWLYHSUREOHP
_UM 3PWQ_Σ&M
U
M
S
)6$ M
-1 0 13
-2 3 6
-3 14 8
-4 18 3
-5 22 5
-6 25 3
-7 30 4
-8 33 1
)6237 $FWXDODFFXUDF\ RU
_UM 3PWQ_Σ&M
-
DQG _UM _Σ&M
-
-
-
-
-
-
-
-
-
-
-
-
- -
-
-
-
_UM _Σ&M
-
-
-
-
-
-
-
-
6$
U
U
7KHRUHP
For 1 | rj | ∑ C j ,
U
F (S A )
≤2
F (S OPT )
3URRI/HWXVUHQXPEHUWKHMREVLQWKHRUGHUWKH\DUHFRPSOHWHGLQ6$
7KHQWKHFRPSOHWLRQWLPHRIHDFKMREM LQVFKHGXOH6$ LV
j
C j ( S A ) = ru + ∑k =u pk
ZKHUHX LVWKHQHDUHVWMREWKDWSUHFHGHVMREM DQGVWDUWVDWUX
'HQRWHWKHFRPSOHWLRQWLPHRIMREM LQWKHSUHHPSWLYHVFKHGXOHE\&M63PWQ



∑
j
k =u
ru
< Cu (S Pmtn ) < C j (S Pmtn )
pk
≤
C j (S Pmtn )
n
∑ C (S
j =1
j
n
A
) ≤ 2∑ C j ( S Pmtn ).
j =1
7KHREVHUYDWLRQWKDWΣ&M63PWQLVDORZHUERXQGRQWKHRSWLPDOYDOXHRI
WKHWRWDOFRPSOHWLRQWLPHIRUWKHQRQSUHHPSWLYHVFKHGXOHΣ&M6237
SURYLGHVWKHUDWLRJXDUDQWHHRI