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An Efficient Method for the Coordinate Transformation Problem of Massively Three-Dimensional Networks

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HAL Id: inria-00072550

https://hal.inria.fr/inria-00072550

Submitted on 24 May 2006

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An Efficient Method for the Coordinate Transformation Problem of Massively Three-Dimensional Networks

Károly Németh, Olivier Coulaud, Gérald Monard, János G. Angyán

To cite this version:

Károly Németh, Olivier Coulaud, Gérald Monard, János G. Angyán. An Efficient Method for the Coordinate Transformation Problem of Massively Three-Dimensional Networks. [Research Report]

RR-4083, INRIA. 2000, pp.16. �inria-00072550�

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ISRN INRIA/RR--4083--FR+ENG

a p p o r t

d e r e c h e r c h e

THÈME 4

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

An efficient method for the coordinate transformation problem of massively

three-dimensional networks

Károly Németh — Olivier Coulaud — Gérald Monard — János G. Ángyán

N° 4083

Décembre 2000

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Unité de recherche INRIA Lorraine

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^ u‡ŒuC}ƒui1€‚P|†€.‚L}ƒ|6t_„:‡5‚ · €ˆq6u>&ãt~‰€ˆyƎ´‡ˆuCÀ\|su7„\€y{~P}ƒ}{‹PÂzt~ކy{t)|stÁ¢i˜P˜‚P}{|st^„6‡~‰uꇈu7}{uC€ˆu Š

~‰€ê~_€ˆy{t^uPÂE~‰„ Š €qsu7‹¸~Pˆu&‡Œ€ˆ‚Lˆu Š y{„-€ˆq6u)t~€ˆyƒŽ2&

*

¾pq6u7„?±u s|sy{}Š €ˆqsu)7‚Pˆui‡Œ…A‚P„ Š yƒ„6¥_…6ˆ‚P’“uC1»

€‚PiÂ

*

€‚?€ˆq6u‡ˆ…6~P7u´‡Œ…6~P„s„su Š  z‹ €qsu‡ˆu7}{uC€ˆu Š 7‚P}{|st^„6‡C¾ pqsy‡&…s‚‰’“ui1€ˆ‚L)~P€‡)‚P„ ih%¾ pqsu

ºLuC€ˆ‚Pi ih (+*.

"

±qsy{–q q6~L‡" :uCu7„8…s‚‰’“ui1€u Š ‚P|†€iÂy‡&‡Œ€ˆ‚Pu Š y{„ ~- 6| AuCC¾ ih ±y{}{}‘ :u¨t_‚ Š y0P6u Š

(13)

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 z‹8‡ˆ|s †€ˆ–~P€ˆy{„s¥ih (+*.

" ¾ pqsuC„8€ˆqsu„su7Ž\€^…s‚‰’“ui1€ˆ‚L&y‡7‚P„6‡Œ€ˆ|61€u Š ·‚Pt €qsu„6uŽz€_7‚P}{|st^„6‡)‚ ·

&µ~‰„ Š ~P€‡ê‚P„¸€qsu_~L1€|6~‰}Eih%¾¶pq6uuC‡ˆ|s}ƒ€êy‡ê~ ŠsŠ u Š €ˆ‚€ˆqsu s| Eu7~‰„ Š u7}{yƒt^y{„6~€u Џ·‚Pt ih%¾

pqz|6‡CÂPuCºPuC„y· „s‚L„†»Y‚LŒ€qs‚P¥L‚P„6~P}z…sˆ‚P’“uC€ˆ‚P–‡(~‰u|6‡ˆu Š ÂP€ˆqsuê„s‚P„s»Yu Š |6„ Š ~‰„\€W~P„ Š ˆu Š |s„ Š ~P„\€5‚Lt_…A‚‰»

„6u7„\€‡C~‰„- :u&‡ˆu7…:~‰–~€ˆu

Š

Âs‡ˆyƒ„67u¶€ˆqsut^‚

Š

y0P6u

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ihA»¿‡±yƒ}{}¼„s‚P€.q6~RºPu"‚Lt^…:‚L„su7„\€‡

·

‚Pt¹€ˆqsu&‡ˆ…6~LuC‡

|:‡Œu

Š

y{„¨…su7ºzy{‚P|6‡5…s‚‰’“uC€ˆy{‚P„6‡C¾%pqsu"…sˆ‚P’“uC€ˆy{‚P„€uC–qs„syÀ\|su"7~‰„ :u"‡ˆ|st^t^~Pˆy{Ç7u

Š

 z‹^€ˆq6u

·

‚L}ƒ}{‚±yƒ„6¥

u7ކ…sˆui‡ˆ‡ˆy{‚P„6‡R;

ih3(+*,3- .

"

ih3(+*.

"

0(+*.Bih3(+*.

E 9

¢7v

A

ih (+*,3- .) ih (+*. 1 ih (+*,3- .

"

1Tih (4*.

" E 9

¢I

A

(+*.U & * I -

* & 5* E 9 ¢C¤ A

±yƒ€ˆq

I * & 5* & * $ 9

¢@M

A

pq6u›t~€ˆyƒŽ I *

t~R‹I Au ‡Œy{„s¥P|6}{~PC€qz|6‡yƀ–‡y{„zºPuC‡ˆu?t)|:‡“€- :u8C~‰}|s}~€u Š  z‹ ‡ˆyƒ„s¥L|s}~‰¨º~P}ƒ|su

Š uC‚Lt^…:‚\‡Œyƒ€ˆy{‚P„

9x W¶œ

A

¾gZŸ‚±5uCºPu7iÂs‡ˆyƒ„67u"yƀ–‡.‡Œy{Ç7uy‡½Lu7…†€Ÿ~‰€~RP6Žzu Š ‡Œt~‰}{}¼º~‰}{|suLÂs…:uC ·‚Lˆt^y{„s¥_€ˆqsu

x Wêœ y‡¶uC~P‡ˆ‹P¾ih

( #.

uCÀ\|6~P}{‡¶±yƒ€ˆq ihç¥LyƒºLu7„  z‹¸€qsu^t^yƒ„sy{t^yƒÇCu7i¾R3?|s}ƀyƒ…6}ƒy7~‰€ˆy{‚P„6‡" z‹¸€qsu

(+*.

…6ˆ‚P’“uC1€‚PŸC~‰„¸t^‚L‡Œ€êu7³´y{u7„\€ˆ}{‹ AuC~‰ˆy{u Š ‚L|†€Ÿ z‹¸‡ŒuiÀ\|su7„\€ˆy~‰}t)|s}ƒ€ˆy{…s}{y{C~€yƒ‚L„6‡. z‹€ˆqsu…s‚‰’“uC€ˆ‚L

7‚Pt^…A‚P„suC„L€–‡7¾

xzy{t^yƒ}~‰}{‹PÂRˆ‚P€~‰€ˆy{‚P„6‡o~P„ Š €ˆ–~‰„6‡ˆ}~€ˆy{‚P„:‡E‚ · €ˆqsuW±qs‚P}{u‘t^‚P}{uC7|s}ƒuWt)|6‡Œ€$ Au‘…s‚‰’“uC€ˆu Š ‚L|†€ ·‚Ptg€ˆqsu

Š

y{‡ˆ…s}~PuCt^u7„\€‡Ÿ‚

·

€ˆq6u^Ã~‰ˆ€ˆui‡Œy~‰„¸7‚\‚L

Š

yƒ„6~‰€ˆui‡7¾.pqsy‡¶7~‰„¸ Au

Š

‚P„su)º\y~´7‚P„6‡Œ€ˆ|61€yƒ„6¥€ˆqsu_ºPui1€‚P–‡

‚ ·

t^‚L}ƒui|s}~‰¶€ˆ–~‰„:‡Œ}~€yƒ‚L„6‡~‰„

Š

y{„ P6„syƒ€ˆui‡Œy{t~‰}‘‚‰€–~€yƒ‚L„6‡7¾N¿„ ‚L|suކ…Au7yƒuC„6uL¼€ˆ–~‰„:‡Œ}~€yƒ‚L„6~‰}(~‰„

Š

‚‰€–~€yƒ‚L„6~‰}o‚Lt^…:‚L„su7„\€‡‚ · €qsuÃ~‰ˆ€ˆui‡Œy~‰„ Š y{‡ˆ…s}~P7u7t^u7„\€‡€|s„su Š ‚P|s€€ˆ‚^ :uºLu7‹´‡Œt~P}ƒ}Y¾

',1'!& '$ ''$ )

2! 1 , ! -*

76‚P~‰}{}¼‡ˆ…6~‰–‡Œu¶t~€ˆyƒŽ~‰}{¥PuC s–~‰y.‚P…Au7–~€yƒ‚L„6‡~_Ç7u7‚€ˆqsuC‡ˆqs‚P}Š ‚ · ~€‚Pt^y{¶|s„6yƀ–‡

9

~s¾|¼¾

A

q6~P‡

 Au7uC„/~‰…s…s}{y{u Š ¾fpq6u?‡Œ…AuC€ˆ–~‰}.‡ˆqsy·€´q:~P‡ Au7uC„ō–q6‚L‡ˆu7„N€ˆ‚ZY

~s¾|¼¾ƒ¾gpqsu ·‚P}{}ƒ‚±y{„s¥ €ˆui‡“€

‡ˆ‹†‡“€u7t‡q6~RºPuê :uCu7„-|6‡ˆu Š ¾(œêy{~Pt^‚P„ Ѝ·~P¥Pt^u7„\€–‡W‚ · |6 sy{"‡ˆq6~‰…AuP†±q6y{–qq6~RºPu¶ :uCu7„¥PuC„su7–~€u Š  z‹

€~P„6‡ˆ}{~‰€ˆy{„s¥¶€ˆqsu.uC}ƒuCt^u7„\€~Pˆ‹)7u7}{}s‚ ·¼Š y~‰t^‚L„ Š ¾‘Ã5|s sy.}{|6‡Œ€ˆu7–‡%‚ · ±~€u7(t^‚P}{uC7|s}ƒui‡7¾ Dyƒ‚Lt^‚P}{uC|6}{~P

7‚z‚P Š yƒ„:~€ˆui‡^q6~RºPu- Au7uC„N€–~‰½Lu7„ ·ˆ‚Lt pqsu¸Wˆ‚P€ˆu7y{„ œ¶~€~TD~P„s½

9

5œD

A

5{¢C¤6Y¾ Ã5~Pt) sy{„

9

WœOD

uC„\€ˆ‹I¢ÃD”&Â(¤‰vz¡?~€‚Pt‡

A

Â[D‚ºzyƒ„6u¨(~‰„67ˆui~€y{p$‹z…6‡Œy{„ N¿„sq6yƒ syƒ€ˆ‚L

9 ¢ DEN1‘™ UP™›~€ˆ‚Lt‡

A

‘Ä.–~€ˆu

ŸŽ†yŠ ~P‡ˆu

9

¢CÄ )Âv\¤P™‰vN~€ˆ‚Lt‡

A

~‰„ Š D5u7€~‰»~P1€–~‰t~P‡ˆu

9v DQ38Âv\˜L¡‰š ~€ˆ‚Lt‡

A ¾ x†‚Pt^u›‚ · €ˆq6y{‡

 6yƒ‚Lt_‚L}ƒui|s}{uC‡q6~RºLu ~‰}‡Œ‚N :uCu7„ ‡“€| Š y{u Š yƒ„ ‡Œ…sq6u7y{C~‰}¶±~‰€ˆu7u7„zºzy{ˆ‚L„st^u7„\€C¾ãpqsu ‚Pt^…s}{u€u ‡ˆu€

‚ ·

…syƒt^yƒ€ˆy{ºPu¨y{„\€ˆuCˆ„6~P}57‚\‚L

Š

yƒ„6~‰€ˆui‡q6~P‡ Au7u7„N~‰…s…s}{y{u

Š

y{„N~P}ƒ}7~‰}|6}{~‰€ˆy{‚P„6‡C¾F7s‚L±~€u7_}{|6‡“€u7–‡7Â

y{„Å~

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yƒ€ˆy{‚P„N€ˆ‚ €qsu-…sˆy{t^yƀyƒºLu¸‚z‚P

Š

y{„6~€uC‡CÂ

Š

y‡“€–~‰„67u-7‚z‚P

Š

yƒ„:~€ˆui‡)q:~RºPu :uCu7„Iyƒ„\€ˆ‚

Š

|67u

Š

¾Åp$‚

~P}ƒ}ê sy{‚Pt^‚P}{uC7|s}ƒui‡¨‡ˆ½PuC}ƒu7€~‰}¶‚z‚P

Š

y{„6~€uC‡q:~RºPu? Au7uC„f~

ŠsŠ

u Š Ÿ~L‡

Š

uP6„su

Š

~‰ A‚ºPuL¾cpqsu Ã5qs‚L}ƒui‡Œ½z‹

äâ

(14)

¢L¢

·~L1€‚P–‡^q6~RºPu :uCu7„/uCC~‰}|s}~€u Š ~‰€´uC~L–qNyƒ€ˆuC~‰€ˆy{‚P„Ň“€u7…Å‚ · €ˆqsu-€~P„6‡ ·‚Pt^~‰€ˆy{‚P„¼¾ pq6u¸…sˆy‡ˆt^‡

q:~RºPu" :uCu7„ ~s¾|¼¾‘±yŠ u 9

€“±yu"€qsu&}{u7„s¥P€ˆq-‚ · €ˆq6uu7}{u7t^u7„\€~Pˆ‹u7}{}¼‚ ·%Š y~‰t^‚L„ Š A

¾5œŸ|sy{„s¥^€ˆqsu

yƒ€ˆuC~‰€ˆy{ºPu 6~L–½\»G€~P„6‡ ·‚Lˆt~‰€ˆy{‚P„¼Â,P6–‡Œ€)‚P„zºLu7¥Pu7„:u_y{‡~P–qsy{u7ºLu Š ·‚P)~¸¥LyƒºLu7„ …sy{‡ˆt_»Š y{‡Œ€ˆyƒ 6|†€ˆy{‚P„¼Â

€qsu7„_€qsu 6~P–½\»Y€ˆ–~‰„6‡ ·‚Pt~€yƒ‚L„…sˆ‚†7u7u Š ‡(‡Œy{t^yƒ}~‰}ƒ‹)‚P„€ˆqsu„su7Žz€‘…sˆy‡ˆt Š y‡“€ˆy{ s|†€yƒ‚L„¼¾ ¯.·€ˆuCW~‰}{}s‡ŒyƒŽ

Š y{‡Œ€ˆyƒ 6|†€ˆy{‚P„6‡.‚ · …sˆy‡ˆt^‡~PˆuLP:„sy{‡ˆqsu Š Âs 6~L–½L»Y€ˆ–~‰„:‡ ·‚Lˆt~€yƒ‚L„´uC‡Œ€~‰ˆ€‡±yƒ€ˆq-€qsuLP6–‡“€.‚L„suP¾ 4¶}ƒ‚L 6~‰}

7‚P„zºPuCˆ¥Lu7„67u"y{‡¶~P–qsy{u7ºLu Š ÂA±qsuC„¸€ˆqsu_t~ކy{t)|st–q6~‰„6¥Pu&‚ · €ˆqsu_¥PuC‚Pt^u€ˆ‹y{‡¶‡ˆt^~P}ƒ}{u7Ÿ€ˆq6~P„ ˜s¾˜P˜6¢

~6¾|$¾

·

‚L.~‰}{}¼…sy{‡ˆt‡7¾

pqsu"~‰}{¥P‚Lˆyƒ€ˆq6t q6~L‡W Au7uC„y{t^…s}{u7t^u7„\€ˆu

Š

y{„X76‚Pˆ€ˆ–~‰„"M M¶~‰„

Š

~‰€Œ€–~P–qsu

Š

€ˆ‚€ˆqsuS4

¯

Äêx6x N¯ ” ‡ˆ|syƀ

‚ ·

…sˆ‚L¥P–~‰t‡R5ƒ¢M 6¾ W„su7¥Py{uC‡&~P„

Š

Ã~‰ˆ€ˆui‡Œy~‰„ ¥P–~

Š

yƒuC„L€–‡"q6~RºPu^ Au7uC„çu7º~‰}{|6~‰€ˆu

Š

 z‹ t_ui~‰„6‡&‚

·

€ˆqsu

œ¶• EN“œN“”4 ·‚P–u P6uC}Š 5{¢C™6Y¾ ¯ }{}E7~‰}|6}{~‰€ˆy{‚P„6‡(q:~RºPu Au7u7„7~‰yƒu Š ‚L|†€W‚L„´~&‡Œy{„s¥L}ƒu 3>N¿5x•¢i˜P˜P˜L˜

9 ¢C™L˜3>Z.Ç A …sˆ‚†7uC‡‡Œ‚L¼‚ · ~¶x4ON¼%‚±u7Ã5q6~‰}{}ƒuC„s¥Pu‘7‚Pt^…s|†€u7i¾pqsu¥P–~ Š yƒuC„L€€ˆ–~‰„6‡·‚Pt~€yƒ‚L„6‡oq6~RºLu

 Au7uC„)‚L„6‡ˆyŠ uCˆu Š ~P‡¼7‚P„zºPuCˆ¥Lu Š ÂC±qsu7„€qsu‘t~ކy{t)|st ‚LˆuC€ˆy{‚P„"‚ · d (+*.

f

q6~L‡o AuC‚Lt^u5‡ˆt^~P}ƒ}{u7¼€ˆq6~P„

~6¾|¼¾ ·‚L~P}ƒ}E…sy{‡ˆt Š y‡“€ˆy{ s|†€yƒ‚L„6‡C¾ N¿„~‰}{}o‡“€u7…6‡‚ · €ˆqsu¶yƀu7–~€yƒºLuê 6~L–½\»G€~P„6‡ ·‚Lˆt~‰€ˆy{‚P„_€ˆqsu

&ãt~‰€ˆyƎ¨y‡uC7~P}{7|s}~€ˆu Š ¾87s‚L¥Pu7‚Lt^u€ˆ‹‚P…s€ˆy{t_y{ÇC~‰€ˆy{‚P„¨€ˆqsu&‡Œ€ˆuCu7…AuC‡Œ€ Š uC‡uC„L€t^u€qs‚ Š q6~P‡ Au7uC„

|:‡Œu Š Â(yƒ„N‚P Š u7)€ˆ‚ ‡ˆ~RºLut^u7t^‚P‹P¾ œŸ|6ˆy{„s¥›€ˆqsu-‚z‚P Š y{„6~€u€ˆ–~‰„:‡ ·‚Lˆt~€yƒ‚L„6‡&~P}ƒ}t~€ˆyui‡&q6~RºLu

 Au7uC„-ˆui7~‰}|6}{~‰€ˆu Š ~€.ui~P–q¨yƒ€ˆuC~‰€ˆy{‚P„-‡“€u7…6‡C¾

'& ! * *+

7y{¥ 9 ¢ A ‡Œqs‚±.‡&€ˆqsu„z|st) Au7_‚ · „6‚P„sÇCu7‚?u7}{u7t^u7„\€–‡)y{„瀁qsu¸Ã5q6‚P}{uC‡ˆ½\‹ ·~P€ˆ‚L‡ 9<A ‚ ·ŸŠ yAuCˆuC„L€

Š y{~Pt_‚L„ Š ~‰„ Š ±~‰€ˆu7_}{|6‡Œ€ˆu7_‡Œ‹†‡Œ€ˆuCt^‡C¾?pqsu´}~‰¥Pui‡“€&t^‚L}ƒui|s}{uC‡CÂ%±qsy{–q8q:~RºPu´ Au7uC„8|6‡Œu Š y{„8€ˆqsu

€uC‡Œ€‡_‚L„L€–~‰y{„ ~‰ A‚P|s€¢i¡P˜P˜L˜¸~€ˆ‚Lt‡7¾ xzyƒ„:u€ˆqsuCˆu~‰u¨‡ŒyƒŽ Š yAuCˆuC„L€_…sy{‡ˆt Š y{‡Œ€ˆy{ s|†€ˆy{‚P„:‡ ·‚L_~P}ƒ}

t^‚L}ƒui|s}{uC‡CÂQ7yƒ¥

9 ¢ A

‡ˆqs‚±.‡~‰}{}‘‚LˆuC‡ˆ…A‚P„ Š y{„s¥

<

»‡C¾N€)7~P„› Au¨}{uC~Pˆ}{‹?‡ˆu7u7„ €q6~€€qsu„z|st) Au7

0 5 10 15 20 25 30 35 40

0 2000 4000 6000 8000 10000 12000

NZ / 100000

Number of atoms diamond

water cluster

7y{¥P|su.¢ ;¼”.|st :uC‚

·

„6‚P„sÇCu7‚u7}{u7t^u7„\€‡$yƒ„&€ˆqsu5}ƒ‚±u7o€ˆy~‰„6¥P}{u(‚

·

€ˆq6uÃ5qs‚L}ƒui‡Œ½z‹

·

~L1€‚P–‡$7~P}{7|s}~€ˆu

Š

·‚L Š y~‰t^‚P„ Ѝ·–~‰¥Pt^uC„L€–‡~‰„ Š ±~€ˆuC}{|6‡“€u7–‡~€ Š yEu7u7„\€…sˆy‡ˆt Š y‡“€ˆy{ s|†€yƒ‚L„6‡C¾

(15)

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‚ · „s‚L„sÇ7uCˆ‚ u7}{u7t^uC„L€–‡^‚ · €ˆqsu Ã5qs‚L}ƒui‡Œ½z‹ ·~L1€‚P–‡_‡7~P}ƒui‡_}ƒy{„suC~Pˆ}{‹ç±yƒ€ˆqҌ‹†‡Œ€ˆuCt ‡ˆyƒÇCuPÂW±q6yƒ}{u?‡Œ‚Lt^u

…6ˆy‡Œt Š y‡“€ˆy{ s|†€yƒ‚L„6‡ˆui‡Œ|s}ƒ€¨y{„f‡ˆ…6~‰–‡ŒuC´t~€ˆyui‡€ˆq:~‰„/€qsu ‚P€ˆqsuC‡C¾Ÿ€ˆq6u7¨t~‰€ˆy{7uC‡CÂ|6‡Œu Š y{„

€qsu›€ˆ–~‰„6‡ ·‚Pt~€ˆy{‚P„:‡¨~‰u t|6–qf‡ˆ…6~‰–‡ˆu7´€q6~‰„f€ˆqsu Ã5qs‚L}ƒui‡Œ½z‹ ·~P€ˆ‚P–‡C¾ $yƒ„6uC~‰-‡7~‰}{y{„s¥ ‚ · €ˆqsu

„z|st :uC$‚ · „6‚P„sÇCu7‚uC}ƒuCt^u7„\€‡$yƒ„€qsuÃ5qs‚L}ƒui‡Œ½z‹ ·~P1€‚P–‡oy‡$~uC‡ˆ|s}ƒ€$‚ · €ˆq6uWÀ\|6~P‡ˆyP‚L„su»Š y{t_uC„6‡ˆyƒ‚L„6~‰}{yƀ“‹

y{„\€ˆ‚ Š |6u Š  z‹€qsu Š y{ºzyŠ u7»~P„ Š »¿‚L„6À\|su7‡–qsu7t^u"ºzy{~€ˆq6u…sˆy‡ˆt Š y‡“€ˆy{ s|†€yƒ‚L„6‡7¾

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pq6u„z|st :uC(‚ · yƀu7–~€yƒ‚L„_‡Œ€ˆuC…6‡%yƒ„_€qsu¥P–~ Š y{u7„\€€ˆ–~‰„6‡·‚Pt~€yƒ‚L„ Š ‚zuC‡%„6‚‰€‘–q6~‰„6¥Put)|6–q^±yƒ€ˆq_€ˆqsu

‡ˆ‹†‡“€u7t‡ˆyƒÇCu ·‚L Š y{~Pt_‚L„ Š ¾87s‚L€ˆqsu‡ˆt^~P}ƒ}{uC‡Œ€ Š y{~Pt_‚L„ Š·–~‰¥Lt^u7„\€‡ 9~P :‚L|†€¢C˜P˜~€‚Pt‡ A yƒ€y‡Mz ·‚P

€qsuŸ}~‰¥Pui‡“€5‚P„sui‡ 9~P :‚L|†€ê¢R¡‰˜L˜P˜"~€‚Pt‡ A yƀy{‡ê¢C˜6¾ 76‚P5±~‰€ˆu7}{|6‡Œ€ˆu7–‡(€qsy‡W„z|st :uC5y{„6uC~L‡Œui‡ ·‚Pt

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A

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9

}~‰¥Pui‡“€}{|6‡“€u7iÂo¢i¡P˜P˜P˜)~€ˆ‚Lt‡

A

¾‘pqsy{‡„z|st :uCy{‡

‡Œ€ˆ‚P„6¥P}{‹y{„ \6|6u7„67u Š  z‹-€qsu_–q6‚Pyu_‚ · y{„\€ˆu7„6~P}7‚\‚L Š yƒ„6~‰€ˆui‡7¾LN€y{‡"~P}{‡ˆ‚¨±‚Pˆ€ˆq?t^uC„L€yƒ‚L„sy{„s¥¨€q6~€

y· €ˆqsuCˆu´~Pˆu~€‚Pt‡CÂ$±qsy–q ˆuCt^~Pyƒ„87‚Pt^…s}{u€ˆuC}ƒ‹ y{‡ˆ‚P}~€u Š yƒ„8~P„\‹ ‚ · €ˆqsu´…6ˆy‡Œt‡C¼€qsu„z|st) Au7&‚ ·

yƒ€ˆuC~‰€ˆy{‚P„ ‡“€u7…6‡"t~R‹ ‡Œ€ˆ‚P„6¥P}{‹?yƒ„:uC~P‡ˆuP¾ ¯ €‚\‚L}%€ˆ‚?~RºL‚PyŠ €ˆq6y{‡…6ˆ‚L s}ƒuCtÁy‡"€ˆqsuy{„\€ˆ‚ Š |61€yƒ‚L„›‚ ·

‡ˆ½PuC}ƒu7€~P}6‚z‚P Š y{„6~€uC‡C¾pqsuê„z|st) Au75‚ · yƀu7–~€yƒ‚L„´‡“€u7…6‡Wyƒ„€qsu.yƒ€ˆuC~‰€ˆy{ºPu. 6~L–½\»G€~P„6‡ ·‚Lˆt~‰€ˆy{‚P„)±~P‡

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Š y{~Pt_‚L„ Š ~‰„ Š ±~€u7&}{|6‡Œ€ˆuC)‡Œ‹†‡Œ€ˆuCt^‡C¾¨pqsu-Ã5WÄ〈y{t^uC‡&‡7~P}ƒu}{y{„suC~Pˆ}{‹?±yƒ€ˆq燈‹z‡Œ€ˆuCt#‡ˆyƒÇCuP¾Y7s‚P

0 10 20 30 40 50 60 70 80 90

0 2000 4000 6000 8000 10000 12000

CPU time (sec)

Number of atoms diamond

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7y{¥P|su)¡ ;Ã5WÄ €yƒt^ui‡

9

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±~€u7}{|6‡Œ€ˆuC‡C¾

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€ˆqsu ¥P–~

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