Genetic Algorithm Based Design of Combinational Logic Circuits

10 downloads 0 Views 442KB Size Report
Abstract. A new approach for the evolutionary design of combinational logic circuits using Genetic Algorithm and 2-1 ... multiplexers with Genetic programming.
Available online at www.sciencedirect.com

ScienceDirect Procedia Computer Science 46 (2015) 1246 – 1253

,QWHUQDWLRQDO&RQIHUHQFHRQ,QIRUPDWLRQDQG&RPPXQLFDWLRQ7HFKQRORJLHV ,&,&7 

*HQHWLF$OJRULWKPEDVHGGHVLJQRI&RPELQDWLRQDOORJLFFLUFXLWV XVLQJ8QLYHUVDO/RJLF0RGXOHV 9LMD\DNXPDUL&.D 0\WKLOL3E5HNKD.-DPHVE$QLO.XPDU&9F E

D 5DMLY*DQGKL,QVWLWXWHRI7HFKQRORJ\.RWWD\DP.HUDOD,QGLD 6FKRRORI(QJLQHHULQJ&RFKLQ8QLYHUVLW\RI6FLHQFHDQG7HFKQRORJ\.HUDOD,QGLD F &ROOHJHRI(QJJ.DUXQDJDSSDOO\.HUDOD,QGLD

$EVWUDFW $ QHZ DSSURDFK IRU WKH HYROXWLRQDU\ GHVLJQ RI FRPELQDWLRQDO ORJLF FLUFXLWV XVLQJ *HQHWLF $OJRULWKP DQG  PXOWLSOH[HUV LV SUHVHQWHG %LQDU\ PXOWLSOH[HU LV WKH RQO\ GHVLJQ XQLW XVHG 5HSHDWHG XVH RI WKH VDPH HOHPHQW UHGXFHV WKH PDQXIDFWXULQJ FRVW ZKLFKLVRISULPHLPSRUWDQFHLQ9/6,GHVLJQ$Q\%RROHDQIXQFWLRQFDQEHUHDOL]HGXVLQJPXOWLSOH[HUVZLWKWKLVPHWKRG 7KHSHUIRUPDQFHRIWKHFLUFXLWVHYROYHGZDVFRPSDUHGZLWKVWDQGDUGLPSOHPHQWDWLRQWHFKQLTXH3RZHUDUHDDQGGHOD\LQYROYHG ZHUH DQDO\]HG XVLQJ 6\QRSV\V GHVLJQ FRPSLOHU :LWK WKH SURSRVHG WHFKQLTXH WKH QXPEHU RI PRGXOHV QHHGHG LV UHGXFHG VLJQLILFDQWO\WKHUHE\UHGXFLQJWKHSRZHUDUHDFRVWDQGGHOD\



© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ‹7KH$XWKRUV3XEOLVKHGE\(OVHYLHU%9 (http://creativecommons.org/licenses/by-nc-nd/4.0/). 3HHUUHYLHZXQGHUUHVSRQVLELOLW\RIRUJDQL]LQJFRPPLWWHHRIWKH,QWHUQDWLRQDO&RQIHUHQFHRQ,QIRUPDWLRQDQG&RPPXQLFDWLRQ Peer-review under responsibility of organizing committee of the International Conference on Information and Communication 7HFKQRORJLHV ,&,&7  Technologies (ICICT 2014) .H\ZRUGV*HQHWLF$OJRULWKP&RPELQDWLRQDOORJLFFLUFXLW0XOWLSOH[HU6KDQQRQ¶VGHFRPSRVLWLRQWHFKQLTXH(YROXWLRQDU\GHVLJQ

,QWURGXFWLRQ 1RUPDOO\ HOHFWURQLF FLUFXLWV ZHUH GHVLJQHG E\ H[SHULHQFHG GHVLJQHUV KDYLQJ D JRRG NQRZOHGJH DERXW WKH GHVLJQLQJUXOHV+HUHKLVKDELWVWHFKQRORJ\LPDJLQDWLRQFUHDWLYHWKLQNLQJDQGURXWLQHZLOOUHIOHFWLQWKHGHVLJQHG 



&RUUHVSRQGLQJDXWKRU7HO (PDLODGGUHVVYLMD\DNXPDUL#ULWDFLQ

1877-0509 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of organizing committee of the International Conference on Information and Communication Technologies (ICICT 2014) doi:10.1016/j.procs.2015.01.041

C.K. Vijaya Kumari et al. / Procedia Computer Science 46 (2015) 1246 – 1253

1247

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³DFWLYHORZ´ RU ³DFWLYH KLJK´ GHQRWHG DV &ODVV $ DQG &ODVV % PXOWLSOH[HUV ,Q D &ODVV $ PXOWLSOH[HU LQSXW ODEHOHG DV µ¶ LV GLUHFWHGWRWKHRXWSXWIRUDKLJKYDOXHRIFRQWUROVLJQDOVDQGLQSXWZKLFKLVODEHOHGDVµ¶LVGLUHFWHGWRWKHRXWSXWIRU DORZYDOXHRIFRQWUROVLJQDO+HUHZHXVHWKHFODVV$PXOWLSOH[HUUHSUHVHQWDWLRQRIWKHFLUFXLWDVVKRZQLQ)LJ ,WVEHKDYLRXULVGHVFULEHGDV  ‫ ܨ‬ൌ ሾሺ… ഥ Ǥ ƒሻ ൅ ሺ…Ǥ „ሻሿ    5HODWHGZRUN &HFÕOLD 5HLV SURSRVHG WKH GHVLJQ RI FRPELQDWLRQDO ORJLF FLUFXLWV EDVHG RQ *HQHWLF $OJRULWKP XVLQJ PLQLPXP QXPEHU RI JDWHV 6RPH RI WKH FLUFXLWV LPSOHPHQWHG ZHUH  PXOWLSOH[HU  ELW SDULW\ FKHFNHU HWF 7KH PDMRU ERWWOHQHFNKHVXJJHVWHGZDVWKHSUREOHPRIVFDOHDQGWLPHIRUFRQYHUJHQFH$VWKHQXPEHURILQSXWVLQFUHDVHVD ODUJH VHDUFK VSDFH LV QHHGHG $+$JXLUUH PDGH DQ DWWHPSW WR GHVLJQ FRPELQDWLRQDO GLJLWDO FLUFXLWV XVLQJ  PXOWLSOH[HUVZLWK*HQHWLFSURJUDPPLQJ,QDXWKRUVSURSRVHGWKHGHVLJQRIFRPELQDWLRQDOORJLFFLUFXLWVZLWKWR PXOWLSOH[HUVXVLQJ*$ZLWKRQO\VDQGVDVLQSXWV7ZRGLIIHUHQWDOJRULWKPVKDYHEHHQSURSRVHGE\6KDKDQD7. HWDO XVLQJPXOWLSOH[HUVEXWLWZDVQRWEDVHGRQHYROXWLRQDU\WHFKQLTXHV7KH\KDYHWHVWHG%RROHDQIXQFWLRQV RQO\XSWRYDULDEOHV2+3DQG$OPDLQL$($GHVFULEHVWKHHYROXWLRQRIGLJLWDOFLUFXLWVXVLQJ%''WHFKQLTXH DQG5HHG0XOOHU8/0 ,Q WKLV SDSHU HYROXWLRQDU\ GHVLJQ RI FRPELQDWLRQDO ORJLF FLUFXLWV XVLQJ  PXOWLSOH[HUV ZLWK 6KDQQRQ¶V GHFRPSRVLWLRQ WHFKQLTXH DQG *$ DORQJ ZLWK FHUWDLQ PRGLILFDWLRQV LV SUHVHQWHG :LWK WKLV DSSURDFK FLUFXLWV KDYH EHHQHYROYHGZLWKOHVVHUQXPEHURIPRGXOHVDQGOHYHOVWKDQVWDQGDUGLPSOHPHQWDWLRQWKHUHE\UHGXFLQJWKHFRVWDQG FRPSOH[LW\RIWKHFLUFXLW

 )LJ/RJLFV\PERORIPXOWLSOH[HU

;

;

;

;

;

;

;

;

;

 )LJ&KURPRVRPDOUHSUHVHQWDWLRQRIWKHPXOWLSOH[HULQWKHILUVWOHYHO

7KH SDSHU LV VWUXFWXUHG DV IROORZV 6HFWLRQ  GLVFXVVHV WKH UHSUHVHQWDWLRQ RI FKURPRVRPHV IRU WKH FLUFXLW DQG VHFWLRQJLYHVWKHLPSOHPHQWDWLRQRIORJLFFLUFXLWVXVLQJWKHSURSRVHGPHWKRGVDQGVHFWLRQGHDOVZLWKWKHUHVXOWV

1248

C.K. Vijaya Kumari et al. / Procedia Computer Science 46 (2015) 1246 – 1253

DQGFRPSDULVRQZLWKVWDQGDUGLPSOHPHQWDWLRQWHFKQLTXHDQGILQDOO\FRQFOXVLRQ 5HSUHVHQWDWLRQRIFKURPRVRPHIRUWKHFLUFXLW ,QWKLVVHFWLRQHQFRGLQJRIDQLQGLYLGXDO$ VDPSOHFLUFXLW LVVKRZQLQ)LJ,QGLYLGXDO$LVFUHDWHGDWUDQGRP ZKLFKFRQWDLQVWKHLQIRUPDWLRQDERXWWKHSUHVHQFHRIDXQLWFRUUHVSRQGLQJLQSXWVFRQWUROVLJQDOVDQGRXWSXWV7KH FKURPRVRPHV IRU *$ LV FRGHG LQ D RQH GLPHQVLRQDO SDWWHUQ ZKHUH HDFK ELW RU D FRPELQDWLRQ RI ELWV GHQRWH D SDUWLFXODULQSXWRUFRQWUROVLJQDOWRWKHPXOWLSOH[HUV$QQYDULDEOHIXQFWLRQFDQEHUHDOL]HGLQQOHYHOVDQGQXQLWV LQVWDQGDUGLPSOHPHQWDWLRQHJ)RUDYDULDEOHIXQFWLRQWKHUHZLOOEHXQLWV7KHUHDUHIRXUXQLWVLQWKHILUVWOHYHO ERWWRPPRVWOHYHO XQLWVLQWKHVHFRQGOHYHODQGXQLWLQWKHWKLUG WRS OHYHO$WWHPSWKDVEHHQPDGHWRUHGXFH WKH QXPEHU RI OHYHOVXQLWV 7KH RSWLPDO FLUFXLW QHHG QRW KDYH DOO WKH VHYHQ XQLWV +HQFH WKH SUHVHQFH RI D XQLW LV LGHQWLILHGE\DQGDEVHQFHE\LQWKHFKURPRVRPH )LJ  UHSUHVHQWV WKH FKURPRVRPH XVHG WR UHSUHVHQW D  PX[ LQ WKH ILUVW OHYHO RI LPSOHPHQWDWLRQ RI D WKUHH YDULDEOH FLUFXLW %LW ; LV XVHG WR FKHFN WKH SUHVHQFH RI WKH PRGXOH DQG ELWV ;; FRPELQDWLRQV UHSUHVHQW WKH GLIIHUHQW LQSXW FRQGLWLRQV WR WKH XQLW DQG ; DQG ; FRPELQDWLRQV FKHFN WKH FRQWURO LQSXW WR WKH PXOWLSOH[HU &KURPRVRPHVDUHFRGHGLQDVLPLODUIDVKLRQIRUWKHRWKHUOHYHOVDOVR 6HOHFWLRQSURFHVVVDQGILWQHVVIXQFWLRQ 7KHUDQGRPO\FUHDWHGSRSXODWLRQ VHWRILQGLYLGXDOV LVPDGHWRXQGHUJRWKHSURFHVVRIVHOHFWLRQRILQGLYLGXDOV IRUWKHQH[WJHQHUDWLRQ*HQHWLFRSHUDWRUVVXFKDVFURVVRYHUDQGPXWDWLRQVDUHDSSOLHGRQWKHVHOHFWHGPHPEHUVWR IRUP WKH QHZ SRSXODWLRQ 5RXOHWWH ZKHHO VHOHFWLRQ WHFKQLTXH KDV EHHQ XVHG KHUH 7KH WRWDO QXPEHU RI FRUUHFW RXWSXWVLQUHVSRQVHWRWKHFRUUHVSRQGLQJLQSXWVJLYHVWKHPHDVXUHRIILWQHVVIXQFWLRQ%DVHGRQWKHSUR[LPLW\WRWKH GHVLUHGWUXWKWDEOHILWQHVVIRUHDFKLQGLYLGXDOLQWKHSRSXODWLRQLVFDOFXODWHGDV  ୒ିୗ୙୑ሺଡ଼୓ୖሺ୓ଵǡ୓ଶሻሻ ቁ ൈ ͳͲͲ   Ψ  ൌ ቀ ୒

 ZKHUH2LVWKHHYROYHGRXWSXW2LVWKHGHVLUHGRXWSXWDQG1LVWKHQXPEHURIURZVLQWKHWUXWKWDEOH,QIHZUXQV RI WKH *HQHWLF $OJRULWKP D  ILW FLUFXLW PDWFKLQJ H[DFWO\ ZLWK WKH XVHU GHILQHG WUXWK WDEOH PD\ EH HYROYHG $IWHUHYROYLQJILWFLUFXLWFKHFNIRUUHGXQGDQF\RIXQLWVLVPDGHDQGUHGXQGDQWXQLWVDUHHOLPLQDWHGVRWKDW WKHFLUFXLWJHQHUDWHGLVRSWLPDO 9DULRXVGHVLJQWHFKQLTXHV 'HVLJQXVLQJ6KDQQRQ¶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

C.K. Vijaya Kumari et al. / Procedia Computer Science 46 (2015) 1246 – 1253

1249

([DPSOH) DEF  Ȉ   7KHFLUFXLWHYROYHG IRUWKHIXQFWLRQLV VKRZQ LQ )LJ D ,WFDQEHVHHQ WKDWWKHIXQFWLRQ ZDVUHDOL]HGLQRQH PRGXOHLQVWHDGRIXQLWVZLWKVWDQGDUGLPSOHPHQWDWLRQWHFKQLTXH,Q WKHLQSXWVWRWKHILUVWOHYHOVZHUHRQO\¶V DQG¶VDQGWKHVDPHFLUFXLWQHHGHGXQLWV7KHVDYLQJLQQXPEHURIPRGXOHVLVLQFRPSDULVRQWRWKHVWDQGDUG PHWKRG)LWQHVVZDVDFKLHYHGLQOHVVWKDQJHQHUDWLRQV ([DPSOHELW2GG3DULW\FKHFNHUFLUFXLW) DEF  Ȉ   7KHRSWLPDOFLUFXLWHYROYHGIRUWKHELWRGGSDULW\FKHFNHUFLUFXLWLVVKRZQLQ)LJ E ,WLVREVHUYHGWKDWWKH FLUFXLWZDVUHDOL]HGZLWKXQLWVDQGOHYHOVDVFRPSDUHGWRXQLWVDQGOHYHOVLQVWDQGDUGLPSOHPHQWDWLRQ8VLQJ 6KDQQRQ¶VGHFRPSRVLWLRQPHWKRGDQG*$WKHIXQFWLRQZDVUHDOL]HGXVLQJXQLWVDQGOHYHOV7KHVDYLQJLQ QXPEHURIXQLWVLVDQGKHQFHWKHDUHDDQGFRVWFDQEHUHGXFHGDFFRUGLQJO\ ([DPSOH) DEFG Ȉ   7KHFLUFXLWZDVUHDOL]HGLQRQHPRGXOHDVVKRZQLQ)LJ F :KHUHDVWRUHDOL]HDYDULDEOHIXQFWLRQXQLWV DUHQHHGHGLQVWDQGDUGLPSOHPHQWDWLRQLQOHYHOV:LWK6KDQQRQ¶VGHFRPSRVLWLRQWHFKQLTXHVXVLQJ*$WKHVDPH FLUFXLWZDVUHDOL]HGXVLQJXQLWVZLWK¶VDQG¶VDVLQSXWVDQGIOH[LELOLW\LVSURYLGHGIRUWKHVHOHFWVLJQDOV       

)LJ D ) DEF Ȉ   E ) DEF Ȉ   F ) DEFG Ȉ  

                )LJ D ) DEFG  Ȉ   E ) DEFGH  Ȉ  

1250

C.K. Vijaya Kumari et al. / Procedia Computer Science 46 (2015) 1246 – 1253

([DPSOH)RXUELWRGGSDULW\FKHFNHU) DEFG Ȉ   7KHFLUFXLWIRUELWRGGSDULW\FKHFNHUZDVHYROYHGLQXQLWVDQGOHYHOVDVFRPSDUHGWRXQLWVDQGOHYHOV ZLWK VWDQGDUG LPSOHPHQWDWLRQ WHFKQLTXH WKHUHE\ VDYLQJ  XQLWV DV LQ )LJ  D 7KXV WKH GHOD\ SRZHU DUHD DQG FRVWFDQEHUHGXFHGVLJQLILFDQWO\ ([DPSOH) DEFGH Ȉ   7KHORJLFFLUFXLWHYROYHGIRUWKHDERYHIXQFWLRQDVVKRZQLQ)LJ E KDVRQO\XQLWVDQGOHYHOVDVFRPSDUHG WR  XQLWV DQG  OHYHOV LQ WUDGLWLRQDO PHWKRGV 7KXV WKHUH LV D VDYLQJ RI  LQ WKH QXPEHU RI 8/0V QHHGHG ZKLFKMXVWLILHVWKHYDOLGLW\RIWKHSURSRVHGPHWKRG 0HWKRG,, ,QPHWKRG,FRQWUROLQSXWVRIWKHPRGXOHVZHUHVHOHFWHGDWUDQGRPIURPWKHVHWRIYDULDEOHVRIWKHIXQFWLRQ+HUH DIXUWKHUPRGLILFDWLRQKDVEHHQPDGHLQVHOHFWLQJWKHFRQWUROLQSXWV,QVWHDGRISURYLGLQJYDULDEOHVDORQHDVFRQWURO VLJQDOVPRUHIOH[LELOLW\LVDGGHGE\JLYLQJIXQFWLRQVZKLFKDUHGHULYHGIURPWKHRXWSXWVRIWKHLPPHGLDWHSUHFHGLQJ OHYHO 7KXV WKH FRQWURO LQSXWV FDQ EH YDULDEOHV RI WKH IXQFWLRQ RU WKH RXWSXWV RI PRGXOHV LQ LPPHGLDWH SUHFHGLQJ OHYHOV7KHLQSXWVWRWKHPRGXOHVLQVHFRQGOD\HURQZDUGVFDQEHFRPELQDWLRQVRIYDULDEOHVWKHLUFRPSOHPHQWV DQGWKHRXWSXWVRISUHYLRXVOHYHO 0HWKRG,,LVDSSOLFDEOHZKHUHFRQWUROWRWKHQH[WOHYHOLVGHULYHGIURPSUHFHGLQJOHYHO6LQFHDOOWKHELWFLUFXLWV ZHUHHYROYHGLQOHYHOVZLWKPHWKRG,PHWKRG,,KDVQRUHOHYDQFHLQWKRVHFDVHV6RIRXUDQGILYHLQSXWFLUFXLWVDUH FRQVLGHUHGIRULQYHVWLJDWLRQ ([DPSOHELWRGGSDULW\FKHFNHU) DEFG Ȉ   7KHRSWLPDOFLUFXLWHYROYHGIRUWKHDERYHIXQFWLRQDVVKRZQLQ)LJ D KDVRQO\XQLWVDQGOHYHOVLQFRQWUDVWWR XQLWVDQGOHYHOVLQVWDQGDUGLPSOHPHQWDWLRQDQGXQLWVLQPHWKRG,7KXVLWLVREYLRXVWKDWWKHORJLFFLUFXLW HYROYHGLQWKLVPHWKRGKDVEHWWHUSHUIRUPDQFHWKDQWKHSUHYLRXVPHWKRGV ([DPSOHELWIXQFWLRQ) DEFGH Ȉ   7KHORJLFFLUFXLWHYROYHGDIWHUVHYHUDOUXQVRI*$LVVKRZQLQ)LJ E ,WFDQEHVHHQWKDWWKHFLUFXLWZDVUHDOLVHG ZLWKXQLWVDQGOHYHOV%XWZLWKWUDGLWLRQDOPHWKRGVWKHFLUFXLWQHHGVXQLWVDQGOHYHOV,QPHWKRG,WKHVDPH IXQFWLRQ ZDV UHDOL]HG XVLQJ  XQLWV DQG  OHYHOV 7KH  VDYLQJ LQ QXPEHU RI XQLWV LV  DV FRPSDUHG WR WKH VWDQGDUGLPSOHPHQWDWLRQWHFKQLTXH        

)LJ D ) DEFG  Ȉ   E ) DEFGH  Ȉ  

C.K. Vijaya Kumari et al. / Procedia Computer Science 46 (2015) 1246 – 1253

1251

             )LJ1XXPEHURIJHQHUDWLRQVIRUILWQHVV

)XQFWLRQVLPSOHPHQWHG x x x x

) DE Ȉ   ) DEF Ȉ   ) DEFG Ȉ   ) DEFGH Ȉ  

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

6WDQGDUG

9DULDEOHV

LPSOHPHQWDWLRQ



1RRI0X[HHV

































0HWKRG,

0HWKRG,,

1RRI0X[HV6DYLQJV

1RRI0X[HV6DYLQJV

 L YDULRXV DSSURDFKHV LQ WHUPV RI QXPEHU RI PRGXOHV IRRU WKH DERYH 7DEOH  VKRZV WKH FRPSDULVRQ RI UHVXOWV LQ IXQFWLRQVZLWKVWDQGDUGLPSOHPHQWDWLRQWHFKQLTTXH,WLVHYLGHQWWKDWWKHUHLVDVLJQLILFDQWUHGXFWLRQLQWKKHKDUGZDUH DVWKHQXPEHURIXQLWVLVOHVV7KHUHGXFWLRQLLQQXPEHURIPRGXOHVZLOOOHDGWRUHGXFHGSRZHUFRQVXP PSWLRQDVLV HYLGHQW IURP 7DEOH  3HUFHQWDJH UHGXFWLRQ LQ L DUHD LQYROYHG LQ WKH SURSRVHG PHWKRGV DV FRPSDUHG WR VWDQGDUG

1252

C.K. Vijaya Kumari et al. / Procedia Computer Science 46 (2015) 1246 – 1253

LPSOHPHQWDWLRQLVGHSLFWHGLQ7DEOH)URP7DEOHLWLVREYLRXVWKDWDVWKHQXPEHURIOHYHOVJHWVUHGXFHGWKH GHOD\LQYROYHGLVDOVRUHGXFHGFRQVLGHUDEO\ 7DEOH3RZHUFRQVXPSWLRQE\YDULRXVPHWKRGV )XQFWLRQ1RRI 9DULDEOHV

6WDQGDUG '\QDPLF/HDNDJH 3RZHU —Z 3RZHU QZ 



0HWKRG,

0HWKRG,,

LPSOHPHQWDWLRQ '\QDPLF/HDNDJH 3RZHU —Z 3RZHU QZ

'\QDPLF/HDNDJH 3RZHU —Z 3RZHU QZ 

































7DEOH1HW,QWHUFRQQHFWDUHDDQG&HOODUHDLQQXPEHURIXQLWV )XQFWLRQ1RRI

6WDQGDUG

9DULDEOHV

LPSOHPHQWDWLRQ



0HWKRG,

0HWKRG,,

7RWDO$UHD

7RWDO$UHD6DYLQJV

7RWDO$UHD6DYLQJV

































7DEOH'HOD\LQYROYHGLQYDULRXVPHWKRGV )XQFWLRQ1RRI

6WDQGDUG

9DULDEOHV

LPSOHPHQWDWLRQ

0HWKRG,

0HWKRG,,

 

1RRI/HYHOV'HOD\ QV 

1RRI/HYHOV'HOD\ QV

1RRI/HYHOV'HOD\ QV 





 























 )URP)LJLWFDQEHVHHQWKDWWKHGHOD\HYROYHGLQWKHFLUFXLWVIRUDOOWKHIXQFWLRQVLVGHILQLWHO\OHVVWKDQWKDWRI WUDGLWLRQDO PHWKRG %XW WKH GHFUHDVH LQ GHOD\ LV PRUH SUHGRPLQDQW LQ SURSRVHG PHWKRGV DV WKH QXPEHU RI ELWV LQFUHDVHV             )LJ&RPSDULVRQRIGHOD\LQYDULRXVDSSURDFKHV

C.K. Vijaya Kumari et al. / Procedia Computer Science 46 (2015) 1246 – 1253

1253

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Õ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