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978-1-7281-7649-9/20/$31.00 ©2020 IEEE
DOI 10.1109/HPCC-SmartCity-DSS50907.2020.00025
2020 IEEE 22nd International Conference on High Performance Computing and Communications | 978-1-7281-7649-9/20/$31.00 ©2020 IEEE | DOI: 10.1109/HPCC-SmartCity-DSS50907.2020.00025
Authorized licensed use limited to: University of Science & Technology of China. Downloaded on May 07,2021 at 02:48:28 UTC from IEEE Xplore. Restrictions apply.
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+H+mHiBQMbX
AMTmi,
:`QmM/@bii2 2M2`;B2b i
qp27mM+iBQMb Ψμ(r)M/ Ψν(r)/Bbi`B#mi2/ ++Q`/BM;
iQ i?2 +QHmKM #HQ+F BM/2tX
R, 7Q` 2+? JSA ibF BM G_@h..6h +H+mHiBQM /Q
k, AMBiBHBx2 Pvc(r)={Ψμ(r)Ψν(r)}BM `2H bT+2 ∼
O(NvNcNr)
j, *``v Qmi JSAnHHiQHH iQ rp27mM+iBQMb ΨiQ i`Mb@
72` /i /Bbi`B#miBQM b+?2K2 7`QK `Qr #HQ+F T`iBiBQM
iQ +QHmKM #HQ+F T`iBiBQM
9, i`Mb72` Pvc(r)BMiQ `2+BT`Q+H bT+2 Uzi_k*V ∼
O(NrHQ;NrNvNc)
8, TTHv i?2 >`i`22 TQi2MiBH BM `2+BT`Q+H bT+2 M/
i`Mb72` BMiQ `2H bT+2 v>Pvc ∼O(NrHQ;NrNvNc+
NcNvNr)
e, *``v Qmi JSAnHHiQHH iQ rp27mM+iBQMb ΨiQ
i`Mb72` /i /Bbi`B#miBQM b+?2K2 7`QK +QHmKM #HQ+F
T`iBiBQM iQ `Qr #HQ+F T`iBiBQM
d, *QKTmi2 i?2 >`i`22@2t+?M;2@+Q``2HiBQM BMi2;`Hb
V>t+ BM `2H bT+2 U:1JJV ∼O(NrN2
vN2
c)
3, bmKK`Bx2 V>t+ rBi?BM HH JSA ibFb #v
JSAnHH`2/m+2
N, 2M/ 7Q`
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RR, .B;QMHBx2 i?2 G_@h..6h >KBHiQMBM H
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{xij }
T`iBiBQM- 2+? +QHmKM Q7 rp27mM+iBQM `2 biQ`2/ iQ QM2
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T`iBiBQM Q7 JSA ibFbX h?Bb /Bbi`B#miBQM b+?2K2 7+BHBii2b
i?2 2pHmiBQM Q7 Ki`Bt@Ki`Bt KmHiBTHB+iBQM U:1JJVX AM
G_@h..6h i?2 rp27mM+iBQMb Ψ`2 KQbiHv /Bbi`B#mi2/ BM
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+QHmKM #HQ+F T`iBiBQM iQ `Qr #HQ+F T`iBiBQM Bb T2`7Q`K
pB JSAnHHiQHHX
AAAX JmHiB@:Sl ++2H2`iBQM
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bQHB/b rBi? THM2 rp2 #bBb b2i- Bi mbmHHv iF2b 3yW Q7 rHH
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bm+? b 6bi 6Qm`B2` h`Mb7Q`K U66hV- :2M2`H Ji`Bt
JmHiBTHv U:1JJV- Ki`Bt /B;QMHBxiBQM Uau1o.V M/
bQK2 JSA +QKKmMB+iBQMb bm+? b JSAnHH`2/m+2X h?2b2
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i?2b2 F2`M2Hb iQ :Slb rBi? 2Bi?2` :Sl@++2H2`i2/ Q`
*l. +mbiQK F2`M2HbX q2 HbQ +``v #2ii2` /i T`@
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Q7 i?2 ?2i2`Q;2M2Qmb `+?Bi2+im`2X
6B;X RX S`HH2H /i M/ ibF /Bbi`B#miBQM b+?2K2b Q7 G_@h..6hX UV
"M/ T`HH2HBxiBQM rBi? +QHmKM #HQ+F T`iBiBQM U7Q` 66hV M/ U#V
;`B/ T`HH2HBxiBQM rBi? `Qr #HQ+F T`iBiBQM U7Q` :1JJVX AHHmbi`iBQM
Q7 i?2 T`HH2H b+?2K2 rBi? rp27mM+iBQM MmK#2` Ncv 4 3 M/ 9
+QKTmiiBQM +Q`2bX
Authorized licensed use limited to: University of Science & Technology of China. Downloaded on May 07,2021 at 02:48:28 UTC from IEEE Xplore. Restrictions apply.
AM Q`/2` iQ +``v Qmi 2{+B2Mi ++2H2`iBQM QM KmHiB@:Sl
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*Slb QMHv T2`7Q`K bTQi Q7 +QKTmiiBQM bi2Tb- M/ KQbi
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2t+?M;2@+Q``2HiBQM BMi2;`Hb pB :2M2`H Ji`Bt JmHiBTHv
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JSA ibFbX .m2 iQ /i /2T2M/2M+2- JSAnHH`2/m+2 Kmbi
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Q7 +QKTmiiBQM M/ +QKKmMB+iBQM Bb /Bb`mTi2/X q?2M i?2
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T2`7Q`K JSAnHH`2/m+2 iQ ;i?2` i?2 r?QH2 V>t+ Ki`Bt-
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bKHH #HQ+Fb M/ T2`7Q`K :1JJ KMmHHv iQ i?2b2 bKHH
#HQ+FbX h?2 #bB+ ~Qr Q7 :1JJ M/ _2/m+2 Bb b?QrM BM
6B;m`2 9 M/ -i?2 TBT2HBM2 Q7 :1JJ M/ `2/m+2 7i2` Qm`
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i?2 `2bmHi- r2 +M BKK2/Bi2Hv `2/m+2 i?2 #HQ+F Ki`Bt iQ
2+? JSA ibF #v JSAn_2/m+2X 7i2`r`/ r2 rBHH ;2i i?2
r?QH2 V>t+ #mi /Bbi`B#mi2/ BM 2+? JSA ibFX
JSA `MF y
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i?2 G_@h..6h 2[miBQM Bb Km+? bKHH2` i?M .- i?2
2t+BiiBQM 2M2`;v Q7 G_@h..6h Bb bB;MB}+MiHv z2+i2/
#v i?2 2M2`;v H2p2H /Bz2`2M+2- BM i?Bb rv r2 +M `2Ht
i?2 ++m`+v BM i?2 +QMbi`m+iBQM T`Q+2bb Q7 V>t+ iQ
+2`iBM 2ti2MiX hQ 7m`i?2` QTiBKBx2 i?2 +Q/2 r?BH2 `2@
KBMBM; +QKTmiiBQMH ++m`+v- r2 i2bi /Bz2`2Mi H2p2Hb Q7
KBt2/ T`2+BbBQMX b `2bmHi- r2 }M/ M ++m`i2 M/ 7bi
T`2b+`BTiBQM i?i mb2b bBM;H2 T`2+BbBQM BM :1JJ M/ 66h
QT2`iBQMb #mi mb2b /Qm#H2 T`2+BbBQM BM BMBiBHBxBM; Pvc(r)BM
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#HQ+F T`iBiBQM Bb +QMp2`i2/ 7`QK /Qm#H2 T`2+BbBQM iQ bBM;H2
Authorized licensed use limited to: University of Science & Technology of China. Downloaded on May 07,2021 at 02:48:28 UTC from IEEE Xplore. Restrictions apply.
T`2+BbBQM #27Q`2 i?2 :1JJ M/ 66h- r?2M +``vBM; i?2
Qi?2` MmK2`B+H +H+mHiBQMb- r2 i`Mb72` i?2 QmiTmi Ki`Bt
iQ /Qm#H2 T`2+BbBQM iQ KBMiBM ++m`+vX
q2 +QKT`2 i?2 KBt2/@T`2+BbBQM BKTH2K2MiiBQM rBi?
i?2 /Qm#H2 T`2+BbBQM KQ/2H #v mbBM; ivTB+H +QM};m`iBQM
Q7 bBHB+QM +`vbiH bvbi2K +QKTQb2/ Q7 Ryk9 iQKb M/
rBi? Nvc = 128 ×128 = 16384- M/ Q#b2`p2 /2pBiBQM Q7
`QQi K2M b[m`2 yXkN2ofKQH2+mH2 BM i?2 2M2`;v T`2/B+iBQMX
aBM+2 i?2b2 /2pBiBQMb `2 Km+? H2bb i?M i?2 2``Q` +mb2/
#v HQ+H@/2MbBiv TT`QtBKiBQM- bQ i?2 KBt2/ T`2+BbBQM
BKTH2K2MiiBQM Bb Q7 biBb7+iQ`v ++m`+vX AM i2`Kb Q7
bT22/ M/ :Sl K2KQ`v `2[mB`2K2Mi- i?2 F2`M2H rBi?
KBt2/ T`2+BbBQM Bb ∼RXd iBK2b 7bi2` i?M M/ +QMbmK2b
8yW H2bb K2KQ`v i?M i?2 /Qm#H2 T`2+BbBQM p2`bBQMX 7i2`
i2biBM; HQi Q7 Qi?2` KBt2/ T`2+BbBQM THMb- r2 `2K`F
i?i Hi?Qm;? 7mHHv@~Qi BKTH2K2MiiBQM Bb KQ`2 TQr2`
2{+B2Mi QM i?2 LoA.A oRyy :Sl- Qm` i2bib b?Qr i?i-
/m2 iQ i?2 HBKBi2/ `2T`2b2MiiBQM `M;2 rBi? jk #BM`v #Bib-
i?2 +Q``2bTQM/BM; ii2KTi +MMQi T`2b2`p2 i?2 `2[mB`2/ +@
+m`+v Q7 i?2 2t+Bi2/ 2M2`;v M/ rp27mM+iBQMbX h?2`27Q`2-
i i?Bb KQK2Mi- r2 +MMQi iF2 /pMi;2 Q7 i?2 K2`Bib Q7
i?2 7mHHv@~Qi BKTH2K2MiiBQMX
.X J2KQ`v ++2bb QTiBKBxiBQM
AM i?2 #b2HBM2 :Sl BKTH2K2MiiBQM- Ki`Bt fxc M/
p2+iQ` Eigenvalue `2 biQ`2/ BM i?2 :Sl ;HQ#H K2KQ`v
7Q` i?2 T2MmHiBKi2 T`i Q7 i?2 +QKTmiiBQM iQ +H+mHi2
fxc+=Eigenvaluej−EigenvaluekX >Qr2p2`- :Sl ;HQ#H
K2KQ`v ?b ?B;? Hi2M+v M/ HQr #M/rB/i? +QKT`2/
iQ i?2 b?`2/ K2KQ`v BMbB/2 2+? :Sl bi`2KBM; KmH@
iBT`Q+2bbQ` UaJVX q2 `2K`F i?i fxc Bb +H+mHi2/ THmb
i?2 2H2K2Mi@rBb2 T`Q/m+i Q7 Eigenvaluej−EigenvaluekX
hQ BKT`Qp2 i?2 T2`7Q`KM+2- r2 mb2 i?2 HQr@Hi2M+v QM@
+?BT b?`2/ K2KQ`v iQ `2TH+2 i?2 :Sl ;HQ#H K2KQ`v
iQ biQ`2 fxc M/ EigenvalueX h?2M- r?2M +H+mHiBM; fxc-
i?2 H;Q`Bi?K ++2bb2b i?2 b?`2/ K2KQ`v i?i Bb Km+?
7bi2` i?M ++2bbBM; :Sl ;HQ#H K2KQ`vX
1X aBM;H2 T`2+BbBQM JSA
7i2` i?2 #Qp2 QTiBKBxiBQMb Q7 G_@h..6h- r2 7QmM/
i?i b i?2 MmK#2` Q7 JSA ibF ;`Qrb- i?2 rHH@+HQ+F iBK2
Q7 G_@h..6h Bb /QKBMi2/ #v k bi2Tb Q7 JSAnHHiQHH QT@
2`iBQMX h?Bb `2bmHi Bb [mBi2 BMimBiBp2 #2+mb2 JSAnHHiQHH
b2M/b /i 7`QK HH iQ HH T`Q+2bb2b- K2Mr?BH2- i?2 /i
Bb p2`v H`;2 b i?2 bBx2 Q7 BMTmi BM+`2b2bX hQ `2/m+2
i?2 +QKKmMB+iBQM iBK2 Q7 i?2 /i i`Mb7Q`K #2ir22M
b+?2K2b BM 6B;m`2 R- r2 mb2 i?2 bBM;H2 T`2+BbBQM 7Q`Ki 7Q`
b2M/BM; M/ `2+2BpBM; i?2 rp27mM+iBQMb- r?B+? `2/m+2b i?2
+QKKmMB+iBQM i?`Qm;?Tmi #v ?H7X q2 HbQ K2MiBQM i?i
i?2 bBM;H2 T`2+BbBQM 7Q`Ki Bb QMHv mb2/ BM i?2 JSAnHHiQHH
+QKKmMB+iBQM- bQ rp27mM+iBQMb rBHH #2 +QMp2`i2/ #+F
iQ i?2 /Qm#H2 T`2+BbBQM 7Q`Ki 7Q` +QKTmiiBQMX q2 }M/
i?i i?Bb QTiBKBxiBQM H2/b iQ M2;HB;B#H2 /2pBiBQM BM
i?2 ++m`+v Q7 i?2 `2bmHi BM i?2 G_@h..6h- BM Qm`
2tT2`BK2Mi- i?2 2``Q` Q7 i?2 iQiH 2M2`;v Bb b HBiiH2 b
10−72ofKQH2+mH2 7Q` bBHB+QM bvbi2K rBi? Ryk9 iQKb M/
Nvc = 128×128 = 16384- +QKT`2/ iQ i?2 /Qm#H2 T`2+BbBQM
BKTH2K2MiiBQMX
6B;m`2 e b?Qrb i?2 `2/m+iBQM Q7 i?2 +QKTmiiBQMH iBK2
bbQ+Bi2/ rBi? /Bz2`2Mi bi2Tb Q7 QTiBKBxiBQMX h?2 i2biBM;
bvbi2K Bb Ryk9 bBHB+QM iQKb bvbi2K b?QrM BM 6B;m`2 d-
r?B+? rBHH #2 /Bb+mbb2/ BM b2+iBQM oX h?2 Mśp2 *Sl p2`bBQM
Q7 G_@h..6h mb2b /mH AMi2H s2QM 18@keN8 Rk@+Q`2 bQ+F2ib
M/ BM Qm` i2bib r2 mb2 e *Sl +Q`2 #QmM/ iQ 2+? JSA ibFX
h?2 :Sl p2`bBQM mb2b /mH oRyy :Sl BM LoA.A .:s@R
b2`p2` (Rd)- M/ Bb `QmM/ eXd iBK2b 7bi2` i?M i?2 *Sl
p2`bBQM BM i2`Kb Q7 G_@h..6h +H+mHiBQMX q2 }M/ i?i
bi2T R UTQBMi@iQ@TQBMi `2TH+2Ki2MiV H2/b iQ KQbi Q7 i?2
T2`7Q`KM+2 BKT`Qp2K2Mi 7`QK *Slb iQ :Slb- M/ i?Bb
bi2T Bb `2bTQMbB#H2 7Q` KQbi Q7 i?2 BKTH2K2MiiBQM 2zQ`ib
b r2HHX
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bi2Tb Q7 QTiBKBxiBQMb 7Q` bvbi2K rBi? Ryk9 bBHB+QM iQKbX h?2 *Sl
p2`bBQM mb2b k9 *Sl +Q`2b- M/ i?2 :Sl p2`bBQM mb2b k :Slb
AoX LmK2`B+H _2bmHi M/ MHvbBb
AM i?Bb b2+iBQM- r2 `2TQ`i i?2 MmK2`B+H `2bmHib- BM+Hm/BM;
i?2 bT22/mT- bi`QM; M/ r2H b+HBM; T2`7Q`KM+2 Q7 i?2
G_h..6h +Q/2 rBi? b2p2`H bBx2b Q7 #mHF bBHB+QM bvbi2KbX
.Bz2`2Mi bBx2 Q7 i2biBM; bvbi2Kb `2 ;2M2`i2/ iQ 7Bi?@
7mHHv BM/B+i2 i?2 T2`7Q`KM+2 Q7 G_@h..6h rBi? :Sl
++2H2`i2/- BM+Hm/BM; bBHB+QM bvbi2Kb rBi? e9- k8e- 8Rk-
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